Topological insulator

910:(i.e., the incremental change in voltage due to an incremental change in temperature). Topological insulators are often composed of heavy atoms, which tends to lower thermal conductivity and are therefore beneficial for thermoelectrics. A recent study also showed that good electrical characteristics (i.e., electrical conductivity and Seebeck coefficient) can arise in topological insulators due to band inversion-driven warping of the bulk band structure. Often, the electrical conductivity and Seebeck coefficient are conflicting properties of thermoelectrics and difficult to optimize simultaneously. Band warping, induced by band inversion in a topological insulator, can mediate the two properties by reducing the effective mass of electrons/holes and increasing the valley degeneracy (i.e., the number of electronic bands that are contributing to charge transport). As a result, topological insulators are generally interesting candidates for thermoelectric applications. 575:) Hamiltonian that is topologically nontrivial. This system replicates the effective Hamiltonians from all universal classes of 1- to 3-D topological insulators. Interestingly, topological properties of Floquet topological insulators could be controlled via an external periodic drive rather than an external magnetic field. An atomic lattice empowered by distance selective Rydberg interaction could simulate different classes of FTI over a couple of hundred sites and steps in 1, 2 or 3 dimensions. The long-range interaction allows designing topologically ordered periodic boundary conditions, further enriching the realizable topological phases. 77: 942:(MBE). MBE has so far been the most common experimental technique. The growth of thin film topological insulators is governed by weak van der Waals interactions. The weak interaction allows to exfoliate the thin film from bulk crystal with a clean and perfect surface. The van der Waals interactions in epitaxy also known as van der Waals epitaxy (VDWE), is a phenomenon governed by weak van der Waal's interactions between layered materials of different or same elements in which the materials are stacked on top of each other. This approach allows the growth of layered topological insulators on other substrates for 1812:. These crystal structures can consist of a large number of elements. Band structures and energy gaps are very sensitive to the valence configuration; because of the increased likelihood of intersite exchange and disorder, they are also very sensitive to specific crystalline configurations. A nontrivial band structure that exhibits band ordering analogous to that of the known 2D and 3D TI materials was predicted in a variety of 18-electron half-Heusler compounds using first-principles calculations. These materials have not yet shown any sign of intrinsic topological insulator behavior in actual experiments. 1117:). The resulted single crystals have a well-defined crystallographic orientation; their composition, thickness, size, and the surface density on the desired substrate can be controlled. The thickness control is particularly important for 3D TIs in which the trivial (bulky) electronic channels usually dominate the transport properties and mask the response of the topological (surface) modes. By reducing the thickness, one lowers the contribution of trivial bulk channels into the total conduction, thus forcing the topological modes to carry the electric current. 115: 7303: 935: 990:

influence the growth rate and the ratio of species of source materials present at the substrate interface. Furthermore, in MBE, samples can be grown layer by layer which results in flat surfaces with smooth interface for engineered heterostructures. Moreover, MBE synthesis technique benefits from the ease of moving a topological insulator sample from the growth chamber to a characterization chamber such as angle-resolved photoemission spectroscopy (ARPES) or

7731: 7755: 25: 7767: 7743: 6828: 1767:. Different materials will have different wave propagation properties, and thus different vector bundles. If we consider all insulators (materials with a band gap), this creates a space of vector bundles. It is the topology of this space (modulo trivial bands) from which the "topology" in topological insulators arises. 1367:

on different substrates and the resulting lattice mismatch. Generally, regardless of the substrate used, the resulting films have a textured surface that is characterized by pyramidal single-crystal domains with quintuple-layer steps. The size and relative proportion of these pyramidal domains vary

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at the interface, the substrate and thin film are expected to have similar lattice constants. MBE has an advantage over other methods due to the fact that the synthesis is performed in high vacuum hence resulting in less contamination. Additionally, lattice defect is reduced due to the ability to

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with factors that include film thickness, lattice mismatch with the substrate and interfacial chemistry-dependent film nucleation. The synthesis of thin films have the stoichiometry problem due to the high vapor pressures of the elements. Thus, binary tetradymites are extrinsically doped as n-type (

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symmetries are usually significant in quantum mechanics, they have no effect on the topology here. Instead, the three symmetries typically considered are time-reversal symmetry, particle-hole symmetry, and chiral symmetry (also called sublattice symmetry). Mathematically, these are represented as,

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Topological insulators are challenging to synthesize, and limited in topological phases accessible with solid-state materials. This has motivated the search for topological phases on the systems that simulate the same principles underlying topological insulators. Discrete time quantum walks (DTQW)

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of the space indicates how many different "islands" of insulators exist amongst the metallic states. Insulators in the connected component containing the vacuum state are identified as "trivial", and all other insulators as "topological". The connected component in which an insulator lies can be

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topological invariant was constructed and the importance of the time reversal symmetry was clarified in the work by Kane and Mele. Subsequently, Bernevig, Taylor L. Hughes and Zhang made a theoretical prediction that 2D topological insulator with one-dimensional (1D) helical edge states would be

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The first step of topological insulators identification takes place right after synthesis, meaning without breaking the vacuum and moving the sample to an atmosphere. That could be done by using angle-resolved photoemission spectroscopy (ARPES) or scanning tunneling microscopy (STM) techniques.

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The physical vapor deposition (PVD) technique does not suffer from the disadvantages of the exfoliation method and, at the same time, it is much simpler and cheaper than the fully controlled growth by molecular-beam epitaxy. The PVD method enables a reproducible synthesis of single crystals of

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Tu, Ngoc Han, Tanabe, Yoichi; Satake, Yosuke, Huynh, Khuong Kim; Le, Phuoc Huu, Matsushita, Stephane Yu; Tanigaki, Katsumi (2017). "Large-Area and Transferred High-Quality Three-Dimensional Topological Insulator Bi2–x Sb x Te3–y Se y Ultrathin Film by Catalyst-Free Physical Vapor Deposition".

1267:. However, the use of sapphire as substrate has not been so encouraging due to a large mismatch of about 15%. The selection of appropriate substrate can improve the overall properties of TI. The use of buffer layer can reduce the lattice match hence improving the electrical properties of TI. 1807:

The field of topological insulators still needs to be developed. The best bismuth chalcogenide topological insulators have about 10 meV bandgap variation due to the charge. Further development should focus on the examination of both: the presence of high-symmetry electronic bands and simply

176:, local (symmetry-preserving) perturbations cannot damage this surface state. This is unique to topological insulators: while ordinary insulators can also support conductive surface states, only the surface states of topological insulators have this robustness property. 587:

if superconductivity is induced on the surface of 3D topological insulators via proximity effects. (Note that Majorana zero-mode can also appear without topological insulators.) The non-trivialness of topological insulators is encoded in the existence of a gas of

596:: the gapless surface states of topological insulators are symmetry-protected (i.e., not topological), while the gapless surface states in quantum Hall effect are topological (i.e., robust against any local perturbations that can break all the symmetries). The 6446:

Bansal, Namrata; Kim, Yong Seung; Edrey, Eliav; Brahlek, Matthew; Horibe, Yoichi; Iida, Keiko; Tanimura, Makoto; Li, Guo-Hong; Feng, Tian; Lee, Hang-Dong; Gustafsson, Torgny; Andrei, Eva; Oh, Seongshik (2011-10-31). "Epitaxial growth of topological insulator

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S. The choice of chalcogenides is related to the van der Waals relaxation of the lattice matching strength which restricts the number of materials and substrates. Bismuth chalcogenides have been studied extensively for TIs and their applications in

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The first models of 3D topological insulators were proposed by B. A. Volkov and O. A. Pankratov in 1985, and subsequently by Pankratov, S. V. Pakhomov, and Volkov in 1987. Gapless 2D Dirac states were shown to exist at the band inversion contact in

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Further measurements includes structural and chemical probes such as X-ray diffraction and energy-dispersive spectroscopy but depending on the sample quality, the lack of sensitivity could remain. Transport measurements cannot uniquely pinpoint the

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Hsieh, D.; D. Hsieh; Y. Xia; L. Wray; D. Qian; A. Pal; J. H. Dil; F. Meier; J. Osterwalder; C. L. Kane; G. Bihlmayer; Y. S. Hor; R. J. Cava; M. Z. Hasan (2009). "Observation of Unconventional Quantum Spin Textures in Topological Insulators".

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Xu, Y; Miotkowski, I.; Liu, C.; Tian, J.; Nam, H.; Alidoust, N.; Hu, J.; Shih, C.-K; Hasan, M.Z.; Chen, Y.-P. (2014). "Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator".

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are now believed to exhibit topological surface states. In some of these materials, the Fermi level actually falls in either the conduction or valence bands due to naturally-occurring defects, and must be pushed into the bulk gap by

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Although the topological classification and the importance of time-reversal symmetry was pointed in the 2000s, all the necessary ingredients and physics of topological insulators were already understood in the works from the 1980s.

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An (informal) phase diagram with topological insulators, trivial insulators, and conductors. There is no path from the topological insulators to the trivial insulators that does not cross the conducting phase. The diagram depicts a

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Chang, Cui-Zu; Zhang, Jinsong; Feng, Xiao; Shen, Jie; Zhang, Zuocheng; Guo, Minghua; Li, Kang; Ou, Yunbo; Wei, Pang (2013-04-12). "Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator".

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Lin, Hsin; L. Andrew Wray; Yuqi Xia; Suyang Xu; Shuang Jia; Robert J. Cava; Arun Bansil; M. Zahid Hasan (July 2010). "Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena".

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Hasan, M. Zahid; Xu, Su-Yang; Neupane, M (2015). "Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators". In Ortmann, F.; Roche, S.; Valenzuela, S. O. (eds.).

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realized in quantum wells (very thin layers) of mercury telluride sandwiched between cadmium telluride. The transport due to 1D helical edge states was indeed observed in the experiments by Molenkamp's group in 2007.

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Mellnik, A. R; Lee, J. S; Richardella, A; Grab, J. L; Mintun, P. J; Fischer, M. H; Vaezi, A; Manchon, A; Kim, E. -A; Samarth, N; Ralph, D. C (2014). "Spin-transfer torque generated by a topological insulator".

592:. Dirac particles which behave like massless relativistic fermions have been observed in 3D topological insulators. Note that the gapless surface states of topological insulators differ from those in the 513:

S) with slightly Sn - doping, exhibits an intrinsic semiconductor behavior with Fermi energy and Dirac point lie in the bulk gap and the surface states were probed by the charge transport experiments.

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Chadov, Stanislav; Xiao-Liang Qi; Jürgen Kübler; Gerhard H. Fecher; Claudia Felser; Shou-Cheng Zhang (July 2010). "Tunable multifunctional topological insulators in ternary Heusler compounds".

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Jerng, Sahng-Kyoon; Joo, Kisu; Kim, Youngwook; Yoon, Sang-Moon; Lee, Jae Hong; Kim, Miyoung; Kim, Jun Sung; Yoon, Euijoon; Chun, Seung-Hyun (2013). "Ordered growth of topological insulator

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Noh, H.-J.; H. Koh; S.-J. Oh; J.-H. Park; H.-D. Kim; J. D. Rameau; T. Valla; T. E. Kidd; P. D. Johnson; Y. Hu; Q. Li (2008). "Spin-orbit interaction effect in the electronic structure of

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transformed into an ordinary insulator without passing through an intermediate conducting state. In other words, topological insulators and trivial insulators are separate regions in the

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Zhang, X.M.; Liu, E.K.; Liu, Z.Y.; Liu, G.D.; Wu, G.H.; Wang, W.H. (2013-04-01). "Prediction of topological insulating behavior in inverse Heusler compounds from first principles".

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Hasan, M. Zahid; Xu, Su-Yang; Neupane, Madhab (2015), "Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators",

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Fully bulk-insulating or intrinsic 3D topological insulator states exist in Bi-based materials as demonstrated in surface transport measurements. In a new Bi based chalcogenide (Bi

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Zhang, Guanhua; Qin, Huajun; Teng, Jing; Guo, Jiandong; Guo, Qinlin; Dai, Xi; Fang, Zhong; Wu, Kehui (2009-08-03). "Quintuple-layer epitaxy of thin films of topological insulator

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with the Hamiltonian; and a unitary operator which anti-commutes with the Hamiltonian. All combinations of the three together with each spatial dimension result in the so-called

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transformed into a trivial one without untwisting the bands, which closes the band gap and creates a conducting state. Thus, due to the continuity of the underlying field, the

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Chiatti, Olivio; Riha, Christian; Lawrenz, Dominic; Busch, Marco; Dusari, Srujana; Sánchez-Barriga, Jaime; Mogilatenko, Anna; Yashina, Lada V.; Valencia, Sergio (2016-06-07).

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Hsieh, D.; Y. Xia; D. Qian; L. Wray; F. Meier; J. H. Dil; J. Osterwalder; L. Patthey; A. V. Fedorov; H. Lin; A. Bansil; D. Grauer; Y. S. Hor; R. J. Cava; M. Z. Hasan (2009).

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labelled by the type of discrete symmetry (time-reversal symmetry, particle-hole symmetry, and chiral symmetry) has a corresponding group of topological invariants (either

808: 267: 906:(p-type thermoelectrics). High thermoelectric power conversion efficiency is realized in materials with low thermal conductivity, high electrical conductivity, and high 157:

of the material. But in a topological insulator, these bands are, in an informal sense, "twisted", relative to a trivial insulator. The topological insulator cannot be

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The surface states of topological insulators can have exotic properties. For example, in time-reversal symmetric 3D topological insulators, surface states have their

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Cui, Hongmei; Liu, Hong; Wang, Jiyang; Li, Xia; Han, Feng; Boughton, R.I. (2004-11-15). "Sonochemical synthesis of bismuth selenide nanobelts at room temperature".

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Alegria, L. D.; Schroer, M. D.; Chatterjee, A.; Poirier, G. R.; Pretko, M.; Patel, S. K.; Petta, J. R. (2012-08-06). "Structural and Electrical Characterization of

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It was proposed in 2008 and 2009 that topological insulators are best understood not as surface conductors per se, but as bulk 3D magnetoelectrics with a quantized

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Roy, Rahul (2009-05-21). "Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect".

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effect. This can be revealed by placing topological insulators in magnetic field. The effect can be described in language similar to that of the hypothetical

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König, Markus; Wiedmann, Steffen; Brüne, Christoph; Roth, Andreas; Buhmann, Hartmut; Molenkamp, Laurens W.; Qi, Xiao-Liang; Zhang, Shou-Cheng (2007-11-02).

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Essin, Andrew M.; Moore, Joel E.; Vanderbilt, David (2009-04-10). "Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators".

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topological invariants cannot be measured using traditional transport methods, such as spin Hall conductance, and the transport is not quantized by the

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locked at a right-angle to their momentum (spin-momentum locking). At a given energy the only other available electronic states have different spin, so

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Due to the weak van der Waals bonding, which relaxes the lattice-matching condition, TI can be grown on a wide variety of substrates such as Si(111),

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Bismuth chalcogenides have been successfully grown on different substrates. In particular, Si has been a good substrate for the successful growth of

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Witting, Ian T.; Chasapis, Thomas C.; Ricci, Francesco; Peters, Matthew; Heinz, Nicholas A.; Hautier, Geoffroy; Snyder, G. Jeffrey (June 2019).

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Shuichi Murakami (2007). "Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase".

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The properties of topological insulators and their surface states are highly dependent on both the dimension of the material and its underlying

38: 6603:

Richardella, A.; Zhang, D. M.; Lee, J. S.; Koser, A.; Rench, D. W.; Yeats, A. L.; Buckley, B. B.; Awschalom, D. D.; Samarth, N. (2010-12-27).

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Despite their origin in quantum mechanical systems, analogues of topological insulators can also be found in classical media. There exist

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Hsieh, D.; Xia, Y.; Wray, L.; Qian, D.; Pal, A.; Dil, J. H.; Osterwalder, J.; Meier, F.; Bihlmayer, G.; Kane, C. L.; et al. (2009).

1431:). Due to the weak van der Waals bonding, graphene is one of the preferred substrates for TI growth despite the large lattice mismatch. 5337:

Potter, Andrew C.; Lee, Patrick A. (23 March 2012). "Topological superconductivity and Majorana fermions in metallic surface states".

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Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng (2008-11-24). "Topological field theory of time-reversal invariant insulators".

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Later sets of theoretical models for the 2D topological insulator (also known as the quantum spin Hall insulators) were proposed by

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Behnia, Kamran; Balicas, Luis; Kopelevich, Yakov (2007-09-21). "Signatures of Electron Fractionalization in Ultraquantum Bismuth".

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Khanikaev, Alexander B.; Hossein Mousavi, S.; Tse, Wang-Kong; Kargarian, Mehdi; MacDonald, Allan H.; Shvets, Gennady (March 2013).

1851: 1796: 1748: 840: 206:. Some combinations of dimension and symmetries forbid topological insulators completely. All topological insulators have at least 203: 571:

have been proposed for making Floquet topological insulators (FTI). This periodically driven system simulates an effective (

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Heremans, Joseph P.; Cava, Robert J.; Samarth, Nitin (2017-09-05). "Tetradymites as thermoelectrics and topological insulators".

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allows a full characterization of the wave propagation properties of a material by assigning a matrix to each wave vector in the

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Wang, Debao; Yu, Dabin; Mo, Maosong; Liu, Xianming; Qian, Yitai (2003-06-01). "Preparation and characterization of wire-like

3834: 1220:. The van der Waals interaction in TIs exhibit important features due to low surface energy. For instance, the surface of 215: 962:

method for the growth of a crystalline material on a crystalline substrate to form an ordered layer. MBE is performed in

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He, Cheng; Ni, Xu; Ge, Hao; Sun, Xiao-Chen; Chen, Yan-Bin; Lu, Ming-Hui; Liu, Xiao-Ping; Chen, Yan-Feng (December 2016).

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Buot, F. A. (1973-09-01). "Weyl Transform and the Magnetic Susceptibility of a Relativistic Dirac Electron Gas".

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falls within the bulk band gap which is traversed by topologically-protected spin-textured Dirac surface states.

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MBE is an appropriate technique for the growth of high quality single-crystal films. In order to avoid a huge

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Chiu, C.; J. Teo; A. Schnyder; S. Ryu (2016). "Classification of topological quantum matter with symmetries".

49: 7771: 7716: 7327: 2319: 991: 859: 199: 5215:"Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction" 7262: 1826: 495: 384:, and in particular "strong topological insulators" exist that cannot be reduced to multiple copies of the 154: 6683:

Kong, D.; Dang, W.; Cha, J.J.; Li, H.; Meister, S.; Peng, H. K.; Cui, Y (2010). "SFew-layer nanoplates of

6391:"Review of 3D topological insulator thin-film growth by molecular beam epitaxy and potential applications" 1778:

This space can be restricted under the presence of symmetries, changing the resulting topology. Although

269:, allow classification of insulators as trivial or topological, and can be computed by various methods. 7507: 7416: 1836: 1713: 813: 751: 716: 686: 657: 628: 599: 380:

In 2007, it was predicted that 3D topological insulators might be found in binary compounds involving

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The most promising applications of topological insulators are spintronic devices and dissipationless

173: 119: 2607:"Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe" 982: 583:

Spin-momentum locking in the topological insulator allows symmetry-protected surface states to host

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heterostructures. Existence of interface Dirac states in HgTe/CdTe was experimentally verified by

187:, connected only by conducting phases. In this way, topological insulators provide an example of a 146: 5274:"Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator" 862:. In addition, topological insulator materials have also found practical applications in advanced 791: 250: 76: 7798: 7472: 6788:"Josephson current mediated by ballistic topological states in Bi2Te2.3Se0.7 single nanocrystals" 5080:"Toward simulation of topological phenomena with one-, two-, and three-dimensional quantum walks" 1998: 986: 139: 179:

This leads to a more formal definition of a topological insulator: an insulator which cannot be

7117: 929: 559: 211: 135: 5671:"Intrinsically core-shell plasmonic dielectric nanostructures with ultrahigh refractive index" 5460:

Read, N.; Sachdev, Subir (1991). "Large-N expansion for frustrated quantum antiferromagnets".

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Liang Fu; C. L. Kane; E. J. Mele (2007-03-07). "Topological insulators in three dimensions".

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from the absence of a magnetic field. In this way, topological insulators are an example of

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Wen, Xiao-Gang (1991). "Mean Field Theory of Spin Liquid States with Finite Energy Gaps".

4142:"Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in 8: 7446: 7426: 7411: 7360: 6881: 2861: 2796: 2731: 1841: 1036: 907: 784:) for each spatial dimensionality, each of the ten Altland—Zirnbauer symmetry classes of 593: 544: 273: 158: 7032: 6986: 6803: 6748: 6651: 6573: 6491: 6406: 6326: 6198: 6124: 6081: 5974: 5949: 5904: 5751: 5686: 5623: 5569: 5516: 5473: 5422: 5360: 5299: 5240: 5170: 5105: 5048: 4983: 4918: 4853: 4759: 4688: 4639: 4574: 4515: 4454: 4327: 4273: 4199: 4102: 4040: 3969: 3873: 3771: 3698: 3636: 3563: 3502: 3457: 3406: 3341: 3285: 3240: 3180: 3127: 3066: 2952: 2887: 2822: 2757: 2684: 2622: 2538: 2473: 2410: 2345: 2280: 2214: 2146: 2076: 2021: 1962: 1893: 1075:

various layered quasi-two-dimensional materials including topological insulators (i.e.,

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Fu, Liang; Kane, C. L. (2007-07-02). "Topological insulators with inversion symmetry".

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Thus far, the field of topological insulators has been focused on bismuth and antimony

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Fu, Liang; C. L. Kane (2007-07-02). "Topological insulators with inversion symmetry".

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Hasan, M. Zahid; Moore, Joel E. (2011). "Three-Dimensional Topological Insulators".

3301: 3204: 3188: 3143: 2580: 2497: 2457: 2442: 2369: 2304: 2230: 1978: 491: 7671: 7563: 7543: 7538: 7533: 7528: 7385: 7365: 7322: 7287: 7257: 7162: 7152: 7127: 7089: 7054: 7036: 6990: 6924: 6861: 6807: 6786:

Stolyarov, V.S.; Yakovlev, D.S.; Kozlov, S.N.; Skryabina, O.V.; Lvov, D.S. (2020).

6752: 6655: 6577: 6495: 6410: 6330: 6266: 6202: 6132: 6128: 6085: 5978: 5908: 5837: 5804: 5763: 5755: 5706: 5690: 5627: 5573: 5520: 5477: 5426: 5364: 5323: 5307: 5303: 5244: 5174: 5109: 5052: 4987: 4922: 4857: 4767: 4763: 4692: 4643: 4578: 4547: 4523: 4519: 4458: 4403: 4395: 4331: 4289: 4281: 4277: 4207: 4203: 4106: 4044: 3989: 3973: 3877: 3822: 3775: 3730: 3702: 3640: 3567: 3526: 3506: 3461: 3430: 3410: 3345: 3289: 3244: 3184: 3131: 3090: 3070: 3017: 2984: 2956: 2911: 2891: 2846: 2826: 2781: 2761: 2716: 2688: 2626: 2542: 2477: 2414: 2349: 2284: 2218: 2150: 2088: 2080: 2045: 2025: 1966: 1925: 1897: 1856: 1809: 1302: 1027: 1021: 851: 536:

who showed that the Faraday rotation was quantized by the fine structure constant.

486: 482: 466: 3510: 3074: 2895: 2830: 2765: 2029: 7696: 7651: 7317: 7234: 5982: 5841: 5577: 5273: 5079: 4729: 4016: 3610: 2927:"Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells" 1031: 999: 517: 439: 340: 328: 188: 7141:"Topological insulators promise computing advances, insights into matter itself" 5481: 5144: 5113: 4582: 4359: 461:

Shortly thereafter symmetry-protected surface states were also observed in pure

7759: 7706: 7588: 7477: 6994: 6832: 6334: 5368: 5178: 4956:

Cayssol, Jérôme; Dóra, Balázs; Simon, Ferenc; Moessner, Roderich (2013-01-28).

4462: 3746:"Observation of Unconventional Quantum Spin Textures in Topological Insulators" 3644: 3479:

Kane, C. L.; Mele, E. J. (2005-11-23). "Quantum Spin Hall Effect in Graphene".

3380: 3293: 3135: 3021: 2222: 2154: 2084: 1779: 1757: 975: 943: 867: 572: 451: 435: 332: 305: 7058: 6812: 6787: 6499: 5249: 4612:

Wu, Liang; Salehi, M.; Koirala, N.; Moon, J.; Oh, S.; Armitage, N. P. (2016).

3826: 3672: 2481: 454:. This prediction is of particular interest due to the observation of charge 7787: 7631: 7613: 7598: 7578: 7482: 7451: 7282: 7019: 6936: 6669: 6589: 6507: 6424: 6342: 6278: 6214: 6140: 6097: 5920: 5816: 5702: 5639: 5524: 5376: 5186: 5121: 4999: 4934: 4775: 4733: 4706: 4590: 4531: 4470: 4118: 3985: 3891: 3787: 3714: 3579: 3357: 3227: 3196: 2968: 2700: 2638: 2554: 2489: 2426: 2361: 2296: 2162: 2102: 1939:

Hasan, M.Z.; Moore, J.E. (2011). "Three-Dimensional Topological Insulators".

1909: 1764: 785: 494:

or gating. The surface states of a 3D topological insulator is a new type of

309: 192: 184: 162: 48:

Please replace inadequate primary references with secondary sources. See the

7157: 5631: 5430: 5143:

Kitagawa, Takuya; Rudner, Mark S.; Berg, Erez; Demler, Eugene (2010-09-24).

4957: 4892: 4648: 4613: 3779: 3673:"A tunable topological insulator in the spin helical Dirac transport regime" 3571: 3465: 2960: 2692: 970:, the elements are heated in different electron beam evaporators until they 7568: 7390: 7292: 7195: 7176: 7103: 6764: 6415: 6390: 6286: 6222: 5990: 5928: 5808: 5777: 5734:

Yue, Zengji; Xue, Gaolei; Liu, Juan; Wang, Yongtian; Gu, Min (2017-05-18).

5720: 5694: 5647: 5489: 5438: 5315: 4991: 4926: 4869: 4783: 4714: 4657: 4598: 4539: 4417: 4215: 4126: 4056: 4003: 3899: 3882: 3857: 3795: 3722: 3587: 3518: 3422: 3379:

Hsieh, David; Dong Qian; Andrew L. Wray; Yuqi Xia; Yusan Hor; Robert Cava;

3082: 2976: 2903: 2838: 2773: 2708: 2512: 2434: 2384: 2037: 1917: 1126: 777: 540: 442:

points and the bulk features massive Dirac fermions. Additionally, bulk Bi

169:, which is topologically trivial) is forced to support a conducting state. 5669:

Yue, Zengji; Cai, Boyuan; Wang, Lan; Wang, Xiaolin; Gu, Min (2016-03-01).

5532: 4561:

Wilczek, Frank (1987-05-04). "Two applications of axion electrodynamics".

142:, meaning that electrons can only move along the surface of the material. 7688: 7406: 7375: 7355: 7302: 6866: 6849: 6247:

Geim, A. K.; Grigorieva, I. V. (2013). "Van der Waals heterostructures".

3493: 3276: 3118: 3057: 3012: 2943: 2878: 2813: 2748: 2012: 934: 713: 554:, can be manipulated by topological insulators. The effect is related to 280:

is strongly suppressed and conduction on the surface is highly metallic.

172:

Since this results from a global property of the topological insulator's

123: 6270: 5759: 4861: 4399: 3706: 3414: 2925:

Bernevig, B. Andrei; Hughes, Taylor L.; Zhang, Shou-Cheng (2006-12-15).

2093: 1901: 7603: 7441: 7277: 6850:"Topological Insulator Film Growth by Molecular Beam Epitaxy: A Review" 6206: 5022: 3856:

Chen, Xi; Ma, Xu-Cun; He, Ke; Jia, Jin-Feng; Xue, Qi-Kun (2011-03-01).

847: 683:

topological invariants was demonstrated which provide a measure of the

6882:"10 symmetry classes and the periodic table of topological insulators" 6756: 6660: 6604: 6581: 5912: 5056: 4335: 3977: 3383:(2008). "A Topological Dirac insulator in a quantum spin Hall phase". 2546: 2456:

Tokura, Yoshinori; Yasuda, Kenji; Tsukazaki, Atsushi (February 2019).

2288: 7661: 7487: 7272: 4110: 4048: 2418: 419: 407:

The first 3D topological insulator to be realized experimentally was

292: 7094: 7077: 6961:

Hasan, M. Zahid; Kane, Charles L. (2010). "Topological Insulators".

4697: 4672: 3378: 2382: 1775:

identified with a number, referred to as a "topological invariant".

918:

Topological insulators can be grown using different methods such as

5965: 5614: 5560: 5231: 5096: 4630: 4390: 3960: 2529: 2513:"Acoustic topological insulator and robust one-way sound transport" 2059:

Zhu, Zhiyong; Cheng, Yingchun; Schwingenschlögl, Udo (2012-06-01).

498:(2DEG) where the electron's spin is locked to its linear momentum. 462: 396:

2D Topological insulators were first realized in system containing

150: 110:

topological invariant, since there are two "islands" of insulators.

6977: 6919: 6739: 6642: 6564: 6482: 6261: 6189: 5895: 5881:

Nanostructures Grown by Metal–Organic Chemical Vapor Deposition".

5413: 5351: 5290: 5161: 5039: 4974: 4909: 4844: 4750: 4506: 4445: 4318: 4302: 4264: 4093: 4077: 4031: 3762: 3689: 3627: 3554: 3397: 3332: 3171: 2675: 2401: 2336: 2271: 2205: 2137: 1953: 7711: 7678: 7656: 7636: 959: 550:

In 2014, it was shown that magnetic components, like the ones in

524:

of particle physics. The effect was reported by researchers at

381: 24: 6785: 5736:"Nanometric holograms based on a topological insulator material" 4360:

Kushwaha, S. K.; Pletikosić, I.; Liang, T.; et al. (2015).

2862:"$ {Z}_{2}$ Topological Order and the Quantum Spin Hall Effect" 34:

reads like a scientific review article and potentially contains

7646: 7641: 7247: 5859: 5023:"Periodic table for topological insulators and superconductors" 5021:

Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail (2009).

4374:

S bulk crystal topological insulator with excellent properties"

2605:

Pankratov, O. A.; Pakhomov, S. V.; Volkov, B. A. (1987-01-01).

2255:"Periodic table for topological insulators and superconductors" 963: 166: 165:

of a topological insulator with a trivial insulator (including

145:

A topological insulator is an insulator for the same reason a "

1880:

Moore, Joel E. (2010). "The birth of topological insulators".

7621: 7242: 6848:

Ginley, Theresa P.; Wang, Yong; Law, Stephanie (2016-11-23).

6831:

Text was copied from this source, which is available under a

6827: 780:

discovered in 1991.) More generally (in what is known as the

521: 3923:"2D layered transport properties from topological insulator 3671:

Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; et al. (2009).

3042: 928:(PVD), solvothermal synthesis, sonochemical technique and 878:

Some of the most well-known topological insulators are also

122:

for a 3D time-reversal symmetric topological insulator. The

16:

State of matter with insulating bulk but conductive boundary

5545: 4228: 3858:"Molecular Beam Epitaxial Growth of Topological Insulators" 2581:"Two-dimensional massless electrons in an inverted contact" 1243:

is usually terminated by Te due to its low surface energy.

207: 5790: 5397: 7252: 4828: 4139: 2659:"Quantum Spin Hall Insulator State in HgTe Quantum Wells" 2320:"Symmetry-Protected Topological Phases of Quantum Matter" 6602: 5142: 4955: 4250:

observed by angle-resolved photoemission spectroscopy".

2058: 6362:"Topological Insulators: Fundamentals and Perspectives" 5020: 4727: 3920: 3539: 2604: 1120: 1069: 426:, and many other measurements, it was observed that Bi 218:. So-called "topological invariants", taking values in 6833:

Creative Commons Attribution 4.0 International License

4683:(7428). Springer Science and Business Media LLC: 165. 2656: 6960: 6445: 5833:

Are Topological Insulators Promising Thermoelectrics?

3608: 2795:

Bernevig, B. Andrei; Zhang, Shou-Cheng (2006-03-14).

2455: 1996:

Topological Order and the Quantum Spin Hall Effect".

1716: 816: 794: 754: 719: 689: 660: 631: 602: 349: 253: 224: 87: 6389:

He, Liang; Kou, Xufeng; Wang, Kang L. (2013-01-31).

5830:

Toriyama, Michael; Snyder, G. Jeffrey (2023-11-06),

5793:"The Thermoelectric Properties of Bismuth Telluride" 4491: 6312: 4611: 2924: 7009: 6468:film on Si(111) with atomically sharp interface". 5598: 5077: 4569:(18). American Physical Society (APS): 1799–1802. 1731: 831: 802: 769: 734: 704: 675: 646: 617: 364: 261: 239: 210:from particle number conservation, and often have 102: 6175:thin films on dielectric amorphous SiO2 by MBE". 5145:"Exploring topological phases with quantum walks" 565: 547:, which is a bulk insulator at low temperatures. 485:. Many semiconductors within the large family of 7785: 7185:"The Strange Topology That Is Reshaping Physics" 3743: 3670: 3217: 3156: 2119:Qi, Xiao-Liang; Zhang, Shou-Cheng (2011-10-14). 1808:synthesized materials. One of the candidates is 7145:Proceedings of the National Academy of Sciences 6528: 6153: 4439:(19). American Physical Society (APS): 195424. 4296: 3821:, John Wiley & Sons, Ltd, pp. 55–100, 2578: 1991: 7047: 6904: 6246: 5829: 5668: 4736:(2010-03-12). "Topological Kondo Insulators". 3816: 2600: 2598: 2579:Volkov, B. A.; Pankratov, O. A. (1985-08-25). 654:invariants. An experimental method to measure 578: 7211: 6847: 6682: 5733: 4806:"Weird materials could make faster computers" 4430: 4355: 4353: 2794: 7225: 6110: 6011:: CS1 maint: multiple names: authors list ( 5271: 4670: 3103: 2121:"Topological insulators and superconductors" 324:group in 2D topological insulators in 2007. 202:, and can be classified using the so-called 6025: 5459: 5078:Panahiyan, S.; Fritzsche, S. (2021-01-05). 3855: 2595: 2574: 2572: 938:Schematic of the components of a MBE system 391: 149:" (ordinary) insulator is: there exists an 134:is a material whose interior behaves as an 7301: 7218: 7204: 4350: 3666: 3664: 3662: 3609:Hasan, M. Zahid; Kane, Charles L. (2010). 3317: 2652: 2650: 2648: 1938: 1763:Mathematically, this assignment creates a 7166: 7156: 7093: 7010:Kane, Charles L.; Moore, Joel E. (2011). 6976: 6918: 6865: 6811: 6738: 6725:with highly tunable chemical potential". 6659: 6641: 6563: 6481: 6414: 6388: 6260: 6188: 5964: 5894: 5767: 5710: 5613: 5559: 5412: 5350: 5336: 5289: 5248: 5230: 5160: 5095: 5038: 4973: 4908: 4843: 4749: 4696: 4647: 4629: 4505: 4444: 4407: 4389: 4317: 4263: 4092: 4030: 3993: 3959: 3881: 3761: 3688: 3626: 3553: 3492: 3396: 3331: 3320:Annual Review of Condensed Matter Physics 3275: 3170: 3117: 3056: 3011: 2942: 2877: 2812: 2747: 2674: 2528: 2510: 2400: 2335: 2324:Annual Review of Condensed Matter Physics 2270: 2204: 2186: 2136: 2092: 2011: 1952: 1941:Annual Review of Condensed Matter Physics 1719: 1435:Lattice mismatch of different substrates 819: 796: 757: 722: 692: 663: 634: 605: 479:angle-resolved photoemission spectroscopy 424:angle-resolved photoemission spectroscopy 352: 255: 227: 90: 62:Learn how and when to remove this message 7110: 7075: 4897:Journal of the Physical Society of Japan 3478: 3350:10.1146/annurev-conmatphys-062910-140432 2859: 2729: 2569: 2354:10.1146/annurev-conmatphys-031214-014740 2187:Hasan, M. Z.; Kane, C. L. (2010-11-08). 1971:10.1146/annurev-conmatphys-062910-140432 1852:Periodic table of topological invariants 1797:periodic table of topological insulators 1749:Periodic table of topological invariants 933: 841:periodic table of topological invariants 712:topological order. (Note that the term 422:with a small electronic band gap. Using 204:periodic table of topological insulators 195:that defines ordinary states of matter. 113: 75: 7078:"Topological insulators: Star material" 5212: 4560: 3659: 2860:Kane, C. L.; Mele, E. J. (2005-09-28). 2730:Kane, C. L.; Mele, E. J. (2005-11-23). 2645: 2317: 2118: 920:metal-organic chemical vapor deposition 7786: 5330: 5213:Khazali, Mohammadsadegh (2022-03-03). 3261: 2732:"Quantum Spin Hall Effect in Graphene" 2252: 1802: 295:topological insulators, among others. 7199: 7138: 7125: 6843: 6841: 6384: 6382: 6356: 6354: 6352: 6308: 6306: 6304: 6242: 6240: 5208: 5206: 5204: 3851: 3849: 3847: 3845: 3313: 3311: 2248: 2246: 2244: 2242: 2240: 2182: 2180: 2114: 2112: 1879: 1739:topology by definition of the state. 7742: 4890: 3443: 2189:"Colloquium: Topological insulators" 1121:Bismuth-based topological insulators 1070:PVD growth of topological insulators 954:MBE growth of topological insulators 216:symmetry-protected topological order 18: 7766: 5502: 2997: 1992:Kane, C. L.; Mele, E. J. (2005). "Z 958:Molecular beam epitaxy (MBE) is an 744:has also been used to describe the 13: 6954: 6838: 6379: 6349: 6301: 6237: 5201: 3842: 3308: 3255: 3218:Kane, C. L.; Moore, J. E. (2011). 2237: 2177: 2109: 873: 438:(SS) crossing between any pair of 418:. Bismuth in its pure state, is a 14: 7810: 7113:"Focus on Topological Insulators" 4893:"Topological Insulator Materials" 3944:single crystals and micro flakes" 2458:"Magnetic topological insulators" 2385:"Photonic topological insulators" 1985: 1932: 1873: 1791:; an anti-unitary operator which 1742: 1704: 1288:can be grown on top of various Bi 458:in 2D graphene and pure bismuth. 400:quantum wells sandwiched between 7765: 7753: 7741: 7730: 7729: 6826: 4958:"Floquet topological insulators" 1832:Topological quantum field theory 1732:{\displaystyle \mathbb {Z} _{2}} 839:or trivial) as described by the 832:{\displaystyle \mathbb {Z} _{2}} 770:{\displaystyle \mathbb {Z} _{2}} 735:{\displaystyle \mathbb {Z} _{2}} 705:{\displaystyle \mathbb {Z} _{2}} 676:{\displaystyle \mathbb {Z} _{2}} 647:{\displaystyle \mathbb {Z} _{2}} 618:{\displaystyle \mathbb {Z} _{2}} 365:{\displaystyle \mathbb {Z} _{2}} 240:{\displaystyle \mathbb {Z} _{2}} 138:while its surface behaves as an 103:{\displaystyle \mathbb {Z} _{2}} 23: 6929:10.1016/j.commatsci.2012.12.013 6907:Computational Materials Science 6898: 6874: 6779: 6676: 6596: 6522: 6439: 6147: 6104: 6019: 5943: 5853: 5823: 5784: 5727: 5662: 5592: 5539: 5496: 5453: 5391: 5265: 5136: 5071: 5014: 4949: 4884: 4822: 4798: 4721: 4664: 4605: 4554: 4485: 4424: 4222: 4133: 4071: 4010: 3914: 3810: 3737: 3602: 3533: 3472: 3437: 3372: 3211: 3150: 3097: 3036: 2991: 2918: 2853: 2788: 2723: 2504: 2449: 898:(n-type thermoelectrics) and Sb 193:Landau symmetry-breaking theory 6133:10.1016/j.jcrysgro.2004.08.015 5308:10.1103/PhysRevLett.100.096407 4768:10.1103/physrevlett.104.106408 4671:Samuel Reich, Eugenie (2012). 4524:10.1103/physrevlett.102.146805 4208:10.1103/PhysRevLett.103.146401 2376: 2311: 2052: 1862:Photonic topological insulator 566:Floquet topological insulators 543:insulators were identified in 456:quantum Hall fractionalization 450:has been predicted to have 3D 1: 7328:Spontaneous symmetry breaking 6090:10.1016/S0022-0248(03)01019-4 5797:Advanced Electronic Materials 3511:10.1103/PhysRevLett.95.226801 3075:10.1103/PhysRevLett.98.106803 2896:10.1103/PhysRevLett.95.146802 2831:10.1103/PhysRevLett.96.106802 2766:10.1103/PhysRevLett.95.226801 2253:Kitaev, Alexei (2009-05-14). 2030:10.1103/PhysRevLett.95.146802 1867: 992:scanning tunneling microscopy 860:quantum anomalous Hall effect 298: 7126:Moore, Joel E. (July 2011). 5983:10.1021/acs.nanolett.6b05260 5842:10.26434/chemrxiv-2023-3nvl3 5578:10.1103/RevModPhys.88.035005 2631:10.1016/0038-1098(87)90934-3 1827:Topological quantum computer 1770:Specifically, the number of 913: 803:{\displaystyle \mathbb {Z} } 496:two-dimensional electron gas 262:{\displaystyle \mathbb {Z} } 155:valence and conduction bands 7: 6605:"Coherent heteroepitaxy of 5482:10.1103/physrevlett.66.1773 5272:Fu, L.; C. L. Kane (2008). 5114:10.1103/physreva.103.012201 4891:Ando, Yoichi (2013-10-15). 4583:10.1103/physrevlett.58.1799 1815: 579:Properties and applications 556:metal–insulator transitions 552:spin-torque computer memory 10: 7815: 7508:Spin gapless semiconductor 7417:Nearly free electron model 7111:Murakami, Shuichi (2010). 7053:. Wiley. pp. 55–100. 7041:10.1088/2058-7058/24/02/36 6995:10.1103/RevModPhys.82.3045 6335:10.1038/natrevmats.2017.49 5369:10.1103/physrevb.85.094516 5179:10.1103/physreva.82.033429 5027:AIP Conference Proceedings 4463:10.1103/physrevb.78.195424 4282:10.1209/0295-5075/81/57006 3645:10.1103/RevModPhys.82.3045 3294:10.1103/PhysRevB.76.045302 3249:10.1088/2058-7058/24/02/36 3136:10.1103/PhysRevB.76.045302 3022:10.1103/PhysRevB.79.195322 2797:"Quantum Spin Hall Effect" 2611:Solid State Communications 2318:Senthil, T. (2015-03-01). 2259:AIP Conference Proceedings 2223:10.1103/RevModPhys.82.3045 2155:10.1103/RevModPhys.83.1057 2085:10.1103/PhysRevB.85.235401 1837:Topological quantum number 1746: 7725: 7687: 7612: 7556: 7516: 7465: 7457:Density functional theory 7432:electronic band structure 7399: 7348: 7341: 7310: 7299: 7233: 7059:10.1002/9783527681594.ch4 6964:Reviews of Modern Physics 6813:10.1038/s43246-020-0037-y 6500:10.1016/j.tsf.2011.07.033 6395:Physica Status Solidi RRL 6113:Journal of Crystal Growth 6070:Journal of Crystal Growth 5250:10.22331/q-2022-03-03-664 4962:Physica Status Solidi RRL 3827:10.1002/9783527681594.ch4 3615:Reviews of Modern Physics 3189:10.1088/1367-2630/9/9/356 2482:10.1038/s42254-018-0011-5 2193:Reviews of Modern Physics 2125:Reviews of Modern Physics 926:physical vapor deposition 7794:Condensed matter physics 7627:Bogoliubov quasiparticle 7371:Quantum spin Hall effect 7263:Bose–Einstein condensate 7227:Condensed matter physics 7128:"Topological Insulators" 7012:"Topological Insulators" 6792:Communications Materials 6315:Nature Reviews Materials 5525:10.1103/physrevb.44.2664 4728:Dzero, Maxim; Sun, Kai; 3611:"Topological Insulators" 3220:"Topological Insulators" 1847:Quantum spin Hall effect 1787:which commutes with the 1300:buffers. Table 1 shows 1218:thermoelectric materials 1129:based materials such as 880:thermoelectric materials 526:Johns Hopkins University 392:Experimental realization 7158:10.1073/pnas.1611504113 6630:Applied Physics Letters 6552:Applied Physics Letters 5632:10.1126/science.1234414 5431:10.1126/science.1167733 4738:Physical Review Letters 4649:10.1126/science.aaf5541 4563:Physical Review Letters 4494:Physical Review Letters 4188:Physical Review Letters 3780:10.1126/science.1167733 3572:10.1126/science.1146509 3481:Physical Review Letters 3466:10.1103/PhysRevA.8.1570 3045:Physical Review Letters 2961:10.1126/science.1133734 2866:Physical Review Letters 2801:Physical Review Letters 2736:Physical Review Letters 2693:10.1126/science.1148047 1999:Physical Review Letters 386:quantum spin Hall state 7118:New Journal of Physics 7051:Topological Insulators 6416:10.1002/pssr.201307003 5809:10.1002/aelm.201800904 5695:10.1126/sciadv.1501536 4992:10.1002/pssr.201206451 4927:10.7566/jpsj.82.102001 3883:10.1002/adma.201003855 3819:Topological Insulators 3159:New Journal of Physics 2462:Nature Reviews Physics 1810:half-Heusler compounds 1733: 939: 930:molecular beam epitaxy 890:and its alloys with Bi 833: 804: 771: 736: 706: 677: 648: 619: 590:helical Dirac fermions 434:alloy exhibits an odd 366: 322:Laurens W. Molenkamp's 263: 241: 212:time-reversal symmetry 127: 111: 104: 7503:Topological insulator 7437:Anderson localization 7076:Brumfiel, G. (2010). 5740:Nature Communications 4378:Nature Communications 1785:anti-unitary operator 1734: 937: 834: 805: 772: 737: 707: 678: 649: 620: 539:In 2012, topological 367: 335:in 2005, and also by 264: 242: 191:not described by the 132:topological insulator 117: 105: 79: 7381:Aharonov–Bohm effect 7268:Fermionic condensate 6867:10.3390/cryst6110154 1772:connected components 1714: 814: 792: 752: 717: 687: 658: 629: 600: 347: 251: 222: 140:electrical conductor 136:electrical insulator 85: 7772:Physics WikiProject 7447:tight binding model 7427:Fermi liquid theory 7412:Free electron model 7361:Quantum Hall effect 7342:Electrons in solids 7189:Scientific American 7033:2011PhyW...24b..32K 6987:2010RvMP...82.3045H 6804:2020CoMat...1...38S 6749:2010NanoL..10.2245K 6652:2010ApPhL..97z2104R 6574:2009ApPhL..95e3114Z 6492:2011TSF...520..224B 6407:2013PSSRR...7...50H 6327:2017NatRM...217049H 6271:10.1038/nature12385 6199:2013Nanos...510618J 6125:2004JCrGr.271..456C 6082:2003JCrGr.253..445W 5975:2017NanoL..17.2354T 5905:2012NanoL..12.4711A 5760:10.1038/ncomms15354 5752:2017NatCo...815354Y 5687:2016SciA....2E1536Y 5624:2013Sci...340..167C 5570:2016RvMP...88c5005C 5517:1991PhRvB..44.2664W 5474:1991PhRvL..66.1773R 5423:2009Sci...323..919H 5361:2012PhRvB..85i4516P 5300:2008PhRvL.100i6407F 5241:2022Quant...6..664K 5171:2010PhRvA..82c3429K 5106:2021PhRvA.103a2201P 5049:2009AIPC.1134...22K 4984:2013PSSRR...7..101C 4919:2013JPSJ...82j2001A 4862:10.1038/nature13534 4854:2014Natur.511..449M 4760:2010PhRvL.104j6408D 4689:2012Natur.492..165S 4640:2016Sci...354.1124W 4575:1987PhRvL..58.1799W 4516:2009PhRvL.102n6805E 4455:2008PhRvB..78s5424Q 4400:10.1038/ncomms11456 4328:2014NatPh..10..956X 4274:2008EL.....8157006N 4200:2009PhRvL.103n6401H 4103:2010NatMa...9..546L 4041:2010NatMa...9..541C 3970:2016NatSR...627483C 3874:2011AdM....23.1162C 3772:2009Sci...323..919H 3707:10.1038/nature08234 3699:2009Natur.460.1101H 3637:2010RvMP...82.3045H 3564:2007Sci...317.1729B 3503:2005PhRvL..95v6801K 3458:1973PhRvA...8.1570B 3415:10.1038/nature06843 3407:2008Natur.452..970H 3342:2011ARCMP...2...55H 3286:2007PhRvB..76d5302F 3241:2011PhyW...24b..32K 3181:2007NJPh....9..356M 3128:2007PhRvB..76d5302F 3067:2007PhRvL..98j6803F 2953:2006Sci...314.1757B 2937:(5806): 1757–1761. 2888:2005PhRvL..95n6802K 2823:2006PhRvL..96j6802B 2758:2005PhRvL..95v6801K 2685:2007Sci...318..766K 2623:1987SSCom..61...93P 2539:2016NatPh..12.1124H 2474:2019NatRP...1..126T 2411:2013NatMa..12..233K 2346:2015ARCMP...6..299S 2281:2009AIPC.1134...22K 2215:2010RvMP...82.3045H 2147:2011RvMP...83.1057Q 2077:2012PhRvB..85w5401Z 2022:2005PhRvL..95n6802K 1963:2011ARCMP...2...55H 1902:10.1038/nature08916 1894:2010Natur.464..194M 1842:Quantum Hall effect 1803:Future developments 1436: 948:integrated circuits 908:Seebeck coefficient 856:quantum Hall effect 786:random Hamiltonians 594:quantum Hall effect 545:samarium hexaboride 278:"U"-turn scattering 7333:Critical phenomena 7139:Ornes, S. (2016). 6207:10.1039/C3NR03032F 3948:Scientific Reports 3862:Advanced Materials 1729: 1434: 940: 829: 800: 767: 732: 702: 673: 644: 615: 585:Majorana particles 560:Bose–Hubbard model 530:Rutgers University 475:antimony telluride 362: 337:B. Andrei Bernevig 259: 237: 128: 112: 100: 7781: 7780: 7667:Exciton-polariton 7552: 7551: 7524:Thermoelectricity 6757:10.1021/nl101260j 6661:10.1063/1.3532845 6582:10.1063/1.3200237 6255:(7459): 419–425. 5913:10.1021/nl302108r 5608:(6129): 167–170. 5554:(35005): 035005. 5407:(5916): 919–922. 5339:Physical Review B 5149:Physical Review A 5084:Physical Review A 5057:10.1063/1.3149495 5033:(1). AIP: 22–30. 4838:(7510): 449–451. 4433:Physical Review B 4336:10.1038/nphys3140 3978:10.1038/srep27483 3836:978-3-527-68159-4 3756:(5916): 919–922. 3548:(5845): 1729–31. 3446:Physical Review A 3264:Physical Review B 3106:Physical Review B 3000:Physical Review B 2669:(5851): 766–770. 2547:10.1038/nphys3867 2523:(12): 1124–1129. 2289:10.1063/1.3149495 2065:Physical Review B 1888:(7286): 194–198. 1822:Topological order 1783:respectively: an 1702: 1701: 968:ultra-high vacuum 864:magnetoelectronic 852:quantum computers 746:topological order 742:topological order 487:Heusler materials 471:bismuth telluride 402:cadmium telluride 72: 71: 64: 7806: 7769: 7768: 7757: 7745: 7744: 7733: 7732: 7672:Phonon polariton 7564:Amorphous magnet 7544:Electrostriction 7539:Flexoelectricity 7534:Ferroelectricity 7529:Piezoelectricity 7386:Josephson effect 7366:Spin Hall effect 7346: 7345: 7323:Phase transition 7305: 7288:Luttinger liquid 7235:States of matter 7220: 7213: 7206: 7197: 7196: 7192: 7180: 7170: 7160: 7135: 7122: 7107: 7097: 7072: 7044: 7016: 7006: 6980: 6949: 6948: 6922: 6902: 6896: 6895: 6893: 6892: 6878: 6872: 6871: 6869: 6845: 6836: 6830: 6825: 6815: 6783: 6777: 6776: 6742: 6724: 6723: 6722: 6714: 6713: 6703: 6702: 6701: 6693: 6692: 6680: 6674: 6673: 6663: 6645: 6625: 6624: 6623: 6615: 6614: 6600: 6594: 6593: 6567: 6549: 6548: 6547: 6539: 6538: 6526: 6520: 6519: 6485: 6470:Thin Solid Films 6467: 6466: 6465: 6457: 6456: 6443: 6437: 6436: 6418: 6386: 6377: 6376: 6374: 6373: 6358: 6347: 6346: 6310: 6299: 6298: 6264: 6244: 6235: 6234: 6192: 6183:(21): 10618–22. 6174: 6173: 6172: 6164: 6163: 6151: 6145: 6144: 6119:(3–4): 456–461. 6108: 6102: 6101: 6076:(1–4): 445–451. 6067: 6066: 6065: 6057: 6056: 6046: 6045: 6044: 6036: 6035: 6023: 6017: 6016: 6010: 6002: 5968: 5947: 5941: 5940: 5898: 5880: 5879: 5878: 5870: 5869: 5857: 5851: 5850: 5849: 5848: 5827: 5821: 5820: 5788: 5782: 5781: 5771: 5731: 5725: 5724: 5714: 5675:Science Advances 5666: 5660: 5659: 5617: 5596: 5590: 5589: 5563: 5543: 5537: 5536: 5511:(6): 2664–2672. 5500: 5494: 5493: 5457: 5451: 5450: 5416: 5395: 5389: 5388: 5354: 5334: 5328: 5327: 5293: 5269: 5263: 5262: 5252: 5234: 5210: 5199: 5198: 5164: 5140: 5134: 5133: 5099: 5075: 5069: 5068: 5042: 5018: 5012: 5011: 4977: 4968:(1–2): 101–108. 4953: 4947: 4946: 4912: 4888: 4882: 4881: 4847: 4826: 4820: 4819: 4817: 4816: 4802: 4796: 4795: 4753: 4730:Galitski, Victor 4725: 4719: 4718: 4700: 4668: 4662: 4661: 4651: 4633: 4624:(6316): 1124–7. 4609: 4603: 4602: 4558: 4552: 4551: 4509: 4489: 4483: 4482: 4448: 4428: 4422: 4421: 4411: 4393: 4357: 4348: 4347: 4321: 4300: 4294: 4293: 4267: 4249: 4248: 4247: 4239: 4238: 4226: 4220: 4219: 4183: 4182: 4181: 4173: 4172: 4162: 4161: 4160: 4152: 4151: 4137: 4131: 4130: 4111:10.1038/nmat2771 4096: 4075: 4069: 4068: 4049:10.1038/nmat2770 4034: 4019:Nature Materials 4014: 4008: 4007: 3997: 3963: 3943: 3942: 3941: 3933: 3932: 3918: 3912: 3911: 3885: 3853: 3840: 3839: 3814: 3808: 3807: 3765: 3741: 3735: 3734: 3692: 3683:(7259): 1101–5. 3668: 3657: 3656: 3630: 3606: 3600: 3599: 3557: 3537: 3531: 3530: 3496: 3494:cond-mat/0411737 3476: 3470: 3469: 3441: 3435: 3434: 3400: 3376: 3370: 3369: 3335: 3315: 3306: 3305: 3279: 3277:cond-mat/0611341 3259: 3253: 3252: 3224: 3215: 3209: 3208: 3174: 3154: 3148: 3147: 3121: 3119:cond-mat/0611341 3101: 3095: 3094: 3060: 3058:cond-mat/0607699 3040: 3034: 3033: 3015: 3013:cond-mat/0607531 2995: 2989: 2988: 2946: 2944:cond-mat/0611399 2922: 2916: 2915: 2881: 2879:cond-mat/0506581 2857: 2851: 2850: 2816: 2814:cond-mat/0504147 2792: 2786: 2785: 2751: 2749:cond-mat/0411737 2727: 2721: 2720: 2678: 2654: 2643: 2642: 2602: 2593: 2592: 2576: 2567: 2566: 2532: 2508: 2502: 2501: 2453: 2447: 2446: 2419:10.1038/nmat3520 2404: 2389:Nature Materials 2380: 2374: 2373: 2339: 2315: 2309: 2308: 2274: 2250: 2235: 2234: 2208: 2199:(4): 3045–3067. 2184: 2175: 2174: 2140: 2131:(4): 1057–1110. 2116: 2107: 2106: 2096: 2056: 2050: 2049: 2015: 2013:cond-mat/0506581 1989: 1983: 1982: 1956: 1936: 1930: 1929: 1877: 1857:Bismuth selenide 1738: 1736: 1735: 1730: 1728: 1727: 1722: 1689: 1688: 1687: 1665: 1664: 1663: 1655: 1654: 1618: 1617: 1616: 1552: 1551: 1550: 1508: 1507: 1506: 1498: 1497: 1485: 1484: 1483: 1475: 1474: 1462: 1461: 1460: 1452: 1451: 1437: 1433: 1430: 1429: 1428: 1420: 1419: 1409: 1408: 1407: 1399: 1398: 1388: 1387: 1386: 1378: 1377: 1366: 1364: 1363: 1355: 1354: 1343: 1342: 1341: 1333: 1332: 1322: 1320: 1319: 1311: 1310: 1287: 1286: 1285: 1277: 1276: 1266: 1265: 1264: 1256: 1255: 1242: 1240: 1239: 1231: 1230: 1191: 1190: 1189: 1181: 1180: 1170: 1169: 1168: 1160: 1159: 1149: 1148: 1147: 1139: 1138: 1116: 1115: 1114: 1106: 1105: 1095: 1094: 1093: 1085: 1084: 1065: 1063: 1062: 1054: 1053: 1045: 1044: 1019: 1017: 1016: 1008: 1007: 983:lattice mismatch 838: 836: 835: 830: 828: 827: 822: 809: 807: 806: 801: 799: 776: 774: 773: 768: 766: 765: 760: 741: 739: 738: 733: 731: 730: 725: 711: 709: 708: 703: 701: 700: 695: 682: 680: 679: 674: 672: 671: 666: 653: 651: 650: 645: 643: 642: 637: 624: 622: 621: 616: 614: 613: 608: 534:THz spectroscopy 483:bismuth selenide 467:bismuth selenide 371: 369: 368: 363: 361: 360: 355: 268: 266: 265: 260: 258: 246: 244: 243: 238: 236: 235: 230: 109: 107: 106: 101: 99: 98: 93: 67: 60: 56: 27: 19: 7814: 7813: 7809: 7808: 7807: 7805: 7804: 7803: 7784: 7783: 7782: 7777: 7721: 7702:Granular matter 7697:Amorphous solid 7683: 7608: 7594:Antiferromagnet 7584:Superparamagnet 7557:Magnetic phases 7548: 7512: 7461: 7422:Bloch's theorem 7395: 7337: 7318:Order parameter 7311:Phase phenomena 7306: 7297: 7229: 7224: 7183: 7151:(37): 10223–4. 7095:10.1038/466310a 7088:(7304): 310–1. 7084:(Nature News). 7069: 7014: 6957: 6955:Further reading 6952: 6903: 6899: 6890: 6888: 6886:topocondmat.org 6880: 6879: 6875: 6846: 6839: 6784: 6780: 6721: 6718: 6717: 6716: 6712: 6709: 6708: 6707: 6705: 6700: 6697: 6696: 6695: 6691: 6688: 6687: 6686: 6684: 6681: 6677: 6626:on GaAs (111)B" 6622: 6619: 6618: 6617: 6613: 6610: 6609: 6608: 6606: 6601: 6597: 6546: 6543: 6542: 6541: 6537: 6534: 6533: 6532: 6530: 6527: 6523: 6464: 6461: 6460: 6459: 6455: 6452: 6451: 6450: 6448: 6444: 6440: 6387: 6380: 6371: 6369: 6360: 6359: 6350: 6311: 6302: 6245: 6238: 6171: 6168: 6167: 6166: 6162: 6159: 6158: 6157: 6155: 6152: 6148: 6109: 6105: 6068:nanocrystals". 6064: 6061: 6060: 6059: 6055: 6052: 6051: 6050: 6048: 6047:and flake-like 6043: 6040: 6039: 6038: 6034: 6031: 6030: 6029: 6027: 6024: 6020: 6004: 6003: 5948: 5944: 5877: 5874: 5873: 5872: 5868: 5865: 5864: 5863: 5861: 5858: 5854: 5846: 5844: 5828: 5824: 5789: 5785: 5746:: ncomms15354. 5732: 5728: 5681:(3): e1501536. 5667: 5663: 5597: 5593: 5544: 5540: 5501: 5497: 5462:Phys. Rev. Lett 5458: 5454: 5396: 5392: 5335: 5331: 5278:Phys. Rev. Lett 5270: 5266: 5211: 5202: 5141: 5137: 5076: 5072: 5019: 5015: 4954: 4950: 4889: 4885: 4827: 4823: 4814: 4812: 4804: 4803: 4799: 4726: 4722: 4698:10.1038/492165a 4669: 4665: 4610: 4606: 4559: 4555: 4490: 4486: 4429: 4425: 4373: 4369: 4365: 4358: 4351: 4312:(12): 956–963. 4301: 4297: 4246: 4243: 4242: 4241: 4237: 4234: 4233: 4232: 4230: 4227: 4223: 4180: 4177: 4176: 4175: 4171: 4168: 4167: 4166: 4164: 4159: 4156: 4155: 4154: 4150: 4147: 4146: 4145: 4143: 4138: 4134: 4076: 4072: 4015: 4011: 3940: 3937: 3936: 3935: 3931: 3928: 3927: 3926: 3924: 3919: 3915: 3854: 3843: 3837: 3815: 3811: 3742: 3738: 3669: 3660: 3607: 3603: 3538: 3534: 3477: 3473: 3442: 3438: 3377: 3373: 3316: 3309: 3260: 3256: 3222: 3216: 3212: 3155: 3151: 3102: 3098: 3041: 3037: 2996: 2992: 2923: 2919: 2858: 2854: 2793: 2789: 2728: 2724: 2655: 2646: 2603: 2596: 2577: 2570: 2509: 2505: 2454: 2450: 2381: 2377: 2316: 2312: 2251: 2238: 2185: 2178: 2117: 2110: 2057: 2053: 1995: 1990: 1986: 1937: 1933: 1878: 1874: 1870: 1818: 1805: 1754:Bloch's theorem 1751: 1745: 1723: 1718: 1717: 1715: 1712: 1711: 1707: 1686: 1683: 1682: 1681: 1679: 1662: 1659: 1658: 1657: 1653: 1650: 1649: 1648: 1646: 1615: 1612: 1611: 1610: 1608: 1549: 1546: 1545: 1544: 1542: 1505: 1502: 1501: 1500: 1496: 1493: 1492: 1491: 1489: 1482: 1479: 1478: 1477: 1473: 1470: 1469: 1468: 1466: 1459: 1456: 1455: 1454: 1450: 1447: 1446: 1445: 1443: 1427: 1424: 1423: 1422: 1418: 1415: 1414: 1413: 1411: 1406: 1403: 1402: 1401: 1397: 1394: 1393: 1392: 1390: 1385: 1382: 1381: 1380: 1376: 1373: 1372: 1371: 1369: 1362: 1359: 1358: 1357: 1353: 1350: 1349: 1348: 1345: 1340: 1337: 1336: 1335: 1331: 1328: 1327: 1326: 1324: 1318: 1315: 1314: 1313: 1309: 1306: 1305: 1304: 1301: 1299: 1295: 1291: 1284: 1281: 1280: 1279: 1275: 1272: 1271: 1270: 1268: 1263: 1260: 1259: 1258: 1254: 1251: 1250: 1249: 1247: 1238: 1235: 1234: 1233: 1229: 1226: 1225: 1224: 1221: 1214: 1210: 1206: 1201: 1197: 1188: 1185: 1184: 1183: 1179: 1176: 1175: 1174: 1172: 1167: 1164: 1163: 1162: 1158: 1155: 1154: 1153: 1151: 1146: 1143: 1142: 1141: 1137: 1134: 1133: 1132: 1130: 1123: 1113: 1110: 1109: 1108: 1104: 1101: 1100: 1099: 1097: 1092: 1089: 1088: 1087: 1083: 1080: 1079: 1078: 1076: 1072: 1061: 1058: 1057: 1056: 1052: 1049: 1048: 1047: 1043: 1040: 1039: 1038: 1035: 1015: 1012: 1011: 1010: 1006: 1003: 1002: 1001: 998: 994:(STM) studies. 976:single crystals 944:heterostructure 916: 905: 901: 897: 893: 889: 885: 876: 874:Thermoelectrics 823: 818: 817: 815: 812: 811: 795: 793: 790: 789: 761: 756: 755: 753: 750: 749: 726: 721: 720: 718: 715: 714: 696: 691: 690: 688: 685: 684: 667: 662: 661: 659: 656: 655: 638: 633: 632: 630: 627: 626: 609: 604: 603: 601: 598: 597: 581: 568: 518:magnetoelectric 512: 508: 504: 452:Dirac particles 449: 445: 433: 429: 416: 412: 394: 356: 351: 350: 348: 345: 344: 341:Shoucheng Zhang 329:Charles L. Kane 301: 254: 252: 249: 248: 231: 226: 225: 223: 220: 219: 189:state of matter 94: 89: 88: 86: 83: 82: 68: 57: 54:(February 2024) 47: 43:primary sources 28: 17: 12: 11: 5: 7812: 7802: 7801: 7799:Semiconductors 7796: 7779: 7778: 7776: 7775: 7763: 7760:Physics Portal 7751: 7739: 7726: 7723: 7722: 7720: 7719: 7714: 7709: 7707:Liquid crystal 7704: 7699: 7693: 7691: 7685: 7684: 7682: 7681: 7676: 7675: 7674: 7669: 7659: 7654: 7649: 7644: 7639: 7634: 7629: 7624: 7618: 7616: 7614:Quasiparticles 7610: 7609: 7607: 7606: 7601: 7596: 7591: 7586: 7581: 7576: 7574:Superdiamagnet 7571: 7566: 7560: 7558: 7554: 7553: 7550: 7549: 7547: 7546: 7541: 7536: 7531: 7526: 7520: 7518: 7514: 7513: 7511: 7510: 7505: 7500: 7498:Superconductor 7495: 7490: 7485: 7480: 7478:Mott insulator 7475: 7469: 7467: 7463: 7462: 7460: 7459: 7454: 7449: 7444: 7439: 7434: 7429: 7424: 7419: 7414: 7409: 7403: 7401: 7397: 7396: 7394: 7393: 7388: 7383: 7378: 7373: 7368: 7363: 7358: 7352: 7350: 7343: 7339: 7338: 7336: 7335: 7330: 7325: 7320: 7314: 7312: 7308: 7307: 7300: 7298: 7296: 7295: 7290: 7285: 7280: 7275: 7270: 7265: 7260: 7255: 7250: 7245: 7239: 7237: 7231: 7230: 7223: 7222: 7215: 7208: 7200: 7194: 7193: 7181: 7136: 7123: 7108: 7073: 7067: 7045: 7007: 6971:(4): 3045–67. 6956: 6953: 6951: 6950: 6897: 6873: 6837: 6778: 6733:(6): 2245–50. 6719: 6710: 6698: 6689: 6675: 6636:(26): 262104. 6620: 6611: 6595: 6544: 6535: 6521: 6462: 6453: 6438: 6401:(1–2): 50–63. 6378: 6348: 6300: 6236: 6169: 6160: 6146: 6103: 6062: 6053: 6041: 6032: 6018: 5959:(4): 2354–60. 5942: 5875: 5866: 5852: 5822: 5783: 5726: 5661: 5591: 5548:Rev. Mod. Phys 5538: 5495: 5468:(13): 1773–6. 5452: 5390: 5329: 5264: 5200: 5135: 5070: 5013: 4948: 4903:(10): 102001. 4883: 4821: 4797: 4744:(10): 106408. 4734:Coleman, Piers 4720: 4663: 4604: 4553: 4500:(14): 146805. 4484: 4423: 4371: 4367: 4363: 4349: 4306:Nature Physics 4295: 4244: 4235: 4221: 4194:(14): 146401. 4178: 4169: 4157: 4148: 4132: 4070: 4009: 3938: 3929: 3913: 3841: 3835: 3809: 3736: 3658: 3621:(4): 3045–67. 3601: 3532: 3487:(22): 226801. 3471: 3452:(3): 1570–81. 3436: 3381:M. Zahid Hasan 3371: 3307: 3254: 3210: 3149: 3096: 3051:(10): 106803. 3035: 2990: 2917: 2872:(14): 146802. 2852: 2807:(10): 106802. 2787: 2742:(22): 226801. 2722: 2644: 2594: 2568: 2517:Nature Physics 2503: 2468:(2): 126–143. 2448: 2395:(3): 233–239. 2375: 2330:(1): 299–324. 2310: 2236: 2176: 2108: 2071:(23): 235401. 2051: 2006:(14): 146802. 1993: 1984: 1931: 1871: 1869: 1866: 1865: 1864: 1859: 1854: 1849: 1844: 1839: 1834: 1829: 1824: 1817: 1814: 1804: 1801: 1758:Brillouin zone 1747:Main article: 1744: 1743:Classification 1741: 1726: 1721: 1706: 1705:Identification 1703: 1700: 1699: 1696: 1693: 1690: 1684: 1676: 1675: 1672: 1669: 1666: 1660: 1651: 1643: 1642: 1639: 1636: 1633: 1629: 1628: 1625: 1622: 1619: 1613: 1605: 1604: 1601: 1598: 1595: 1591: 1590: 1587: 1584: 1581: 1577: 1576: 1573: 1570: 1567: 1563: 1562: 1559: 1556: 1553: 1547: 1539: 1538: 1535: 1532: 1529: 1525: 1524: 1521: 1518: 1515: 1511: 1510: 1503: 1494: 1487: 1480: 1471: 1464: 1457: 1448: 1441: 1425: 1416: 1404: 1395: 1383: 1374: 1360: 1351: 1338: 1329: 1316: 1307: 1297: 1293: 1289: 1282: 1273: 1261: 1252: 1236: 1227: 1212: 1208: 1204: 1199: 1195: 1186: 1177: 1165: 1156: 1144: 1135: 1122: 1119: 1111: 1102: 1090: 1081: 1071: 1068: 1059: 1050: 1041: 1013: 1004: 915: 912: 903: 899: 895: 891: 887: 883: 875: 872: 868:optoelectronic 826: 821: 798: 764: 759: 748:with emergent 729: 724: 699: 694: 670: 665: 641: 636: 612: 607: 580: 577: 567: 564: 522:axion particle 510: 506: 502: 447: 443: 431: 427: 414: 410: 393: 390: 359: 354: 333:Eugene J. Mele 300: 297: 257: 234: 229: 174:band structure 120:band structure 97: 92: 70: 69: 31: 29: 22: 15: 9: 6: 4: 3: 2: 7811: 7800: 7797: 7795: 7792: 7791: 7789: 7774: 7773: 7764: 7762: 7761: 7756: 7752: 7750: 7749: 7740: 7738: 7737: 7728: 7727: 7724: 7718: 7715: 7713: 7710: 7708: 7705: 7703: 7700: 7698: 7695: 7694: 7692: 7690: 7686: 7680: 7677: 7673: 7670: 7668: 7665: 7664: 7663: 7660: 7658: 7655: 7653: 7650: 7648: 7645: 7643: 7640: 7638: 7635: 7633: 7630: 7628: 7625: 7623: 7620: 7619: 7617: 7615: 7611: 7605: 7602: 7600: 7597: 7595: 7592: 7590: 7587: 7585: 7582: 7580: 7577: 7575: 7572: 7570: 7567: 7565: 7562: 7561: 7559: 7555: 7545: 7542: 7540: 7537: 7535: 7532: 7530: 7527: 7525: 7522: 7521: 7519: 7515: 7509: 7506: 7504: 7501: 7499: 7496: 7494: 7491: 7489: 7486: 7484: 7483:Semiconductor 7481: 7479: 7476: 7474: 7471: 7470: 7468: 7464: 7458: 7455: 7453: 7452:Hubbard model 7450: 7448: 7445: 7443: 7440: 7438: 7435: 7433: 7430: 7428: 7425: 7423: 7420: 7418: 7415: 7413: 7410: 7408: 7405: 7404: 7402: 7398: 7392: 7389: 7387: 7384: 7382: 7379: 7377: 7374: 7372: 7369: 7367: 7364: 7362: 7359: 7357: 7354: 7353: 7351: 7347: 7344: 7340: 7334: 7331: 7329: 7326: 7324: 7321: 7319: 7316: 7315: 7313: 7309: 7304: 7294: 7291: 7289: 7286: 7284: 7281: 7279: 7276: 7274: 7271: 7269: 7266: 7264: 7261: 7259: 7256: 7254: 7251: 7249: 7246: 7244: 7241: 7240: 7238: 7236: 7232: 7228: 7221: 7216: 7214: 7209: 7207: 7202: 7201: 7198: 7190: 7186: 7182: 7178: 7174: 7169: 7164: 7159: 7154: 7150: 7146: 7142: 7137: 7133: 7132:IEEE Spectrum 7129: 7124: 7120: 7119: 7114: 7109: 7105: 7101: 7096: 7091: 7087: 7083: 7079: 7074: 7070: 7068:9783527681594 7064: 7060: 7056: 7052: 7046: 7042: 7038: 7034: 7030: 7026: 7022: 7021: 7020:Physics World 7013: 7008: 7004: 7000: 6996: 6992: 6988: 6984: 6979: 6974: 6970: 6966: 6965: 6959: 6958: 6946: 6942: 6938: 6934: 6930: 6926: 6921: 6916: 6912: 6908: 6901: 6887: 6883: 6877: 6868: 6863: 6859: 6855: 6851: 6844: 6842: 6834: 6829: 6823: 6819: 6814: 6809: 6805: 6801: 6797: 6793: 6789: 6782: 6774: 6770: 6766: 6762: 6758: 6754: 6750: 6746: 6741: 6736: 6732: 6728: 6679: 6671: 6667: 6662: 6657: 6653: 6649: 6644: 6639: 6635: 6631: 6627: 6599: 6591: 6587: 6583: 6579: 6575: 6571: 6566: 6561: 6558:(5): 053114. 6557: 6553: 6525: 6517: 6513: 6509: 6505: 6501: 6497: 6493: 6489: 6484: 6479: 6475: 6471: 6442: 6434: 6430: 6426: 6422: 6417: 6412: 6408: 6404: 6400: 6396: 6392: 6385: 6383: 6367: 6363: 6357: 6355: 6353: 6344: 6340: 6336: 6332: 6328: 6324: 6321:(10): 17049. 6320: 6316: 6309: 6307: 6305: 6296: 6292: 6288: 6284: 6280: 6276: 6272: 6268: 6263: 6258: 6254: 6250: 6243: 6241: 6232: 6228: 6224: 6220: 6216: 6212: 6208: 6204: 6200: 6196: 6191: 6186: 6182: 6178: 6150: 6142: 6138: 6134: 6130: 6126: 6122: 6118: 6114: 6107: 6099: 6095: 6091: 6087: 6083: 6079: 6075: 6071: 6022: 6014: 6008: 6000: 5996: 5992: 5988: 5984: 5980: 5976: 5972: 5967: 5962: 5958: 5954: 5946: 5938: 5934: 5930: 5926: 5922: 5918: 5914: 5910: 5906: 5902: 5897: 5892: 5889:(9): 4711–4. 5888: 5884: 5856: 5843: 5839: 5835: 5834: 5826: 5818: 5814: 5810: 5806: 5802: 5798: 5794: 5787: 5779: 5775: 5770: 5765: 5761: 5757: 5753: 5749: 5745: 5741: 5737: 5730: 5722: 5718: 5713: 5708: 5704: 5700: 5696: 5692: 5688: 5684: 5680: 5676: 5672: 5665: 5657: 5653: 5649: 5645: 5641: 5637: 5633: 5629: 5625: 5621: 5616: 5611: 5607: 5603: 5595: 5587: 5583: 5579: 5575: 5571: 5567: 5562: 5557: 5553: 5549: 5542: 5534: 5530: 5526: 5522: 5518: 5514: 5510: 5506: 5499: 5491: 5487: 5483: 5479: 5475: 5471: 5467: 5463: 5456: 5448: 5444: 5440: 5436: 5432: 5428: 5424: 5420: 5415: 5410: 5406: 5402: 5394: 5386: 5382: 5378: 5374: 5370: 5366: 5362: 5358: 5353: 5348: 5345:(9): 094516. 5344: 5340: 5333: 5325: 5321: 5317: 5313: 5309: 5305: 5301: 5297: 5292: 5287: 5284:(9): 096407. 5283: 5279: 5275: 5268: 5260: 5256: 5251: 5246: 5242: 5238: 5233: 5228: 5224: 5220: 5216: 5209: 5207: 5205: 5196: 5192: 5188: 5184: 5180: 5176: 5172: 5168: 5163: 5158: 5155:(3): 033429. 5154: 5150: 5146: 5139: 5131: 5127: 5123: 5119: 5115: 5111: 5107: 5103: 5098: 5093: 5090:(1): 012201. 5089: 5085: 5081: 5074: 5066: 5062: 5058: 5054: 5050: 5046: 5041: 5036: 5032: 5028: 5024: 5017: 5009: 5005: 5001: 4997: 4993: 4989: 4985: 4981: 4976: 4971: 4967: 4963: 4959: 4952: 4944: 4940: 4936: 4932: 4928: 4924: 4920: 4916: 4911: 4906: 4902: 4898: 4894: 4887: 4879: 4875: 4871: 4867: 4863: 4859: 4855: 4851: 4846: 4841: 4837: 4833: 4825: 4811: 4807: 4801: 4793: 4789: 4785: 4781: 4777: 4773: 4769: 4765: 4761: 4757: 4752: 4747: 4743: 4739: 4735: 4731: 4724: 4716: 4712: 4708: 4704: 4699: 4694: 4690: 4686: 4682: 4678: 4674: 4667: 4659: 4655: 4650: 4645: 4641: 4637: 4632: 4627: 4623: 4619: 4615: 4608: 4600: 4596: 4592: 4588: 4584: 4580: 4576: 4572: 4568: 4564: 4557: 4549: 4545: 4541: 4537: 4533: 4529: 4525: 4521: 4517: 4513: 4508: 4503: 4499: 4495: 4488: 4480: 4476: 4472: 4468: 4464: 4460: 4456: 4452: 4447: 4442: 4438: 4434: 4427: 4419: 4415: 4410: 4405: 4401: 4397: 4392: 4387: 4383: 4379: 4375: 4356: 4354: 4345: 4341: 4337: 4333: 4329: 4325: 4320: 4315: 4311: 4307: 4299: 4291: 4287: 4283: 4279: 4275: 4271: 4266: 4261: 4257: 4253: 4225: 4217: 4213: 4209: 4205: 4201: 4197: 4193: 4189: 4185: 4136: 4128: 4124: 4120: 4116: 4112: 4108: 4104: 4100: 4095: 4090: 4086: 4082: 4074: 4066: 4062: 4058: 4054: 4050: 4046: 4042: 4038: 4033: 4028: 4024: 4020: 4013: 4005: 4001: 3996: 3991: 3987: 3983: 3979: 3975: 3971: 3967: 3962: 3957: 3953: 3949: 3945: 3917: 3909: 3905: 3901: 3897: 3893: 3889: 3884: 3879: 3875: 3871: 3868:(9): 1162–5. 3867: 3863: 3859: 3852: 3850: 3848: 3846: 3838: 3832: 3828: 3824: 3820: 3813: 3805: 3801: 3797: 3793: 3789: 3785: 3781: 3777: 3773: 3769: 3764: 3759: 3755: 3751: 3747: 3740: 3732: 3728: 3724: 3720: 3716: 3712: 3708: 3704: 3700: 3696: 3691: 3686: 3682: 3678: 3674: 3667: 3665: 3663: 3654: 3650: 3646: 3642: 3638: 3634: 3629: 3624: 3620: 3616: 3612: 3605: 3597: 3593: 3589: 3585: 3581: 3577: 3573: 3569: 3565: 3561: 3556: 3551: 3547: 3543: 3536: 3528: 3524: 3520: 3516: 3512: 3508: 3504: 3500: 3495: 3490: 3486: 3482: 3475: 3467: 3463: 3459: 3455: 3451: 3447: 3440: 3432: 3428: 3424: 3420: 3416: 3412: 3408: 3404: 3399: 3394: 3390: 3386: 3382: 3375: 3367: 3363: 3359: 3355: 3351: 3347: 3343: 3339: 3334: 3329: 3325: 3321: 3314: 3312: 3303: 3299: 3295: 3291: 3287: 3283: 3278: 3273: 3270:(4): 045302. 3269: 3265: 3258: 3250: 3246: 3242: 3238: 3234: 3230: 3229: 3228:Physics World 3221: 3214: 3206: 3202: 3198: 3194: 3190: 3186: 3182: 3178: 3173: 3168: 3164: 3160: 3153: 3145: 3141: 3137: 3133: 3129: 3125: 3120: 3115: 3112:(4): 045302. 3111: 3107: 3100: 3092: 3088: 3084: 3080: 3076: 3072: 3068: 3064: 3059: 3054: 3050: 3046: 3039: 3031: 3027: 3023: 3019: 3014: 3009: 3005: 3001: 2994: 2986: 2982: 2978: 2974: 2970: 2966: 2962: 2958: 2954: 2950: 2945: 2940: 2936: 2932: 2928: 2921: 2913: 2909: 2905: 2901: 2897: 2893: 2889: 2885: 2880: 2875: 2871: 2867: 2863: 2856: 2848: 2844: 2840: 2836: 2832: 2828: 2824: 2820: 2815: 2810: 2806: 2802: 2798: 2791: 2783: 2779: 2775: 2771: 2767: 2763: 2759: 2755: 2750: 2745: 2741: 2737: 2733: 2726: 2718: 2714: 2710: 2706: 2702: 2698: 2694: 2690: 2686: 2682: 2677: 2672: 2668: 2664: 2660: 2653: 2651: 2649: 2640: 2636: 2632: 2628: 2624: 2620: 2616: 2612: 2608: 2601: 2599: 2591:(4): 178–181. 2590: 2586: 2582: 2575: 2573: 2564: 2560: 2556: 2552: 2548: 2544: 2540: 2536: 2531: 2526: 2522: 2518: 2514: 2507: 2499: 2495: 2491: 2487: 2483: 2479: 2475: 2471: 2467: 2463: 2459: 2452: 2444: 2440: 2436: 2432: 2428: 2424: 2420: 2416: 2412: 2408: 2403: 2398: 2394: 2390: 2386: 2379: 2371: 2367: 2363: 2359: 2355: 2351: 2347: 2343: 2338: 2333: 2329: 2325: 2321: 2314: 2306: 2302: 2298: 2294: 2290: 2286: 2282: 2278: 2273: 2268: 2264: 2260: 2256: 2249: 2247: 2245: 2243: 2241: 2232: 2228: 2224: 2220: 2216: 2212: 2207: 2202: 2198: 2194: 2190: 2183: 2181: 2172: 2168: 2164: 2160: 2156: 2152: 2148: 2144: 2139: 2134: 2130: 2126: 2122: 2115: 2113: 2104: 2100: 2095: 2090: 2086: 2082: 2078: 2074: 2070: 2066: 2062: 2055: 2047: 2043: 2039: 2035: 2031: 2027: 2023: 2019: 2014: 2009: 2005: 2001: 2000: 1988: 1980: 1976: 1972: 1968: 1964: 1960: 1955: 1950: 1946: 1942: 1935: 1927: 1923: 1919: 1915: 1911: 1907: 1903: 1899: 1895: 1891: 1887: 1883: 1876: 1872: 1863: 1860: 1858: 1855: 1853: 1850: 1848: 1845: 1843: 1840: 1838: 1835: 1833: 1830: 1828: 1825: 1823: 1820: 1819: 1813: 1811: 1800: 1798: 1794: 1793:anti-commutes 1790: 1786: 1781: 1776: 1773: 1768: 1766: 1765:vector bundle 1761: 1759: 1755: 1750: 1740: 1724: 1697: 1694: 1691: 1678: 1677: 1673: 1670: 1667: 1645: 1644: 1640: 1637: 1634: 1631: 1630: 1626: 1623: 1620: 1607: 1606: 1602: 1599: 1596: 1593: 1592: 1588: 1585: 1582: 1579: 1578: 1574: 1571: 1568: 1565: 1564: 1560: 1557: 1554: 1541: 1540: 1536: 1533: 1530: 1527: 1526: 1522: 1519: 1516: 1513: 1512: 1488: 1465: 1442: 1439: 1438: 1432: 1410:) or p-type ( 1365: 1321: 1244: 1241: 1219: 1202: 1128: 1118: 1067: 1064: 1033: 1029: 1025: 1023: 1018: 995: 993: 988: 984: 979: 977: 973: 969: 965: 961: 956: 955: 951: 949: 945: 936: 932: 931: 927: 923: 921: 911: 909: 881: 871: 869: 865: 861: 857: 854:based on the 853: 849: 844: 842: 824: 787: 783: 779: 762: 747: 743: 727: 697: 668: 639: 610: 595: 591: 586: 576: 574: 563: 561: 557: 553: 548: 546: 542: 537: 535: 531: 527: 523: 519: 514: 499: 497: 493: 488: 484: 481:(ARPES). and 480: 476: 472: 468: 464: 459: 457: 453: 441: 437: 436:surface state 425: 421: 417: 405: 403: 399: 389: 387: 383: 378: 374: 357: 343:in 2006. The 342: 338: 334: 330: 325: 323: 319: 315: 311: 307: 296: 294: 290: 286: 281: 279: 275: 270: 232: 217: 213: 209: 208:U(1) symmetry 205: 201: 196: 194: 190: 186: 185:phase diagram 182: 181:adiabatically 177: 175: 170: 168: 164: 160: 156: 152: 148: 143: 141: 137: 133: 125: 121: 118:An idealized 116: 95: 78: 74: 66: 63: 55: 52:for details. 51: 46: 44: 40: 37: 32:This article 30: 26: 21: 20: 7770: 7758: 7746: 7734: 7652:Pines' demon 7502: 7391:Kondo effect 7293:Time crystal 7188: 7148: 7144: 7131: 7116: 7085: 7081: 7050: 7027:(2): 32–36. 7024: 7018: 6968: 6962: 6910: 6906: 6900: 6889:. Retrieved 6885: 6876: 6857: 6853: 6795: 6791: 6781: 6730: 6727:Nano Letters 6726: 6678: 6633: 6629: 6598: 6555: 6551: 6524: 6476:(1): 224–9. 6473: 6469: 6441: 6398: 6394: 6370:. Retrieved 6368:. 2015-06-29 6365: 6318: 6314: 6252: 6248: 6180: 6176: 6149: 6116: 6112: 6106: 6073: 6069: 6021: 6007:cite journal 5956: 5953:Nano Letters 5952: 5945: 5886: 5883:Nano Letters 5882: 5855: 5845:, retrieved 5832: 5825: 5800: 5796: 5786: 5743: 5739: 5729: 5678: 5674: 5664: 5605: 5601: 5594: 5551: 5547: 5541: 5508: 5505:Phys. Rev. B 5504: 5498: 5465: 5461: 5455: 5404: 5400: 5393: 5342: 5338: 5332: 5281: 5277: 5267: 5222: 5218: 5152: 5148: 5138: 5087: 5083: 5073: 5030: 5026: 5016: 4965: 4961: 4951: 4900: 4896: 4886: 4835: 4831: 4824: 4813:. Retrieved 4810:Science News 4809: 4800: 4741: 4737: 4723: 4680: 4676: 4666: 4621: 4617: 4607: 4566: 4562: 4556: 4497: 4493: 4487: 4436: 4432: 4426: 4381: 4377: 4362:"Sn-doped Bi 4309: 4305: 4298: 4258:(5): 57006. 4255: 4251: 4224: 4191: 4187: 4135: 4087:(7): 546–9. 4084: 4080: 4073: 4025:(7): 541–5. 4022: 4018: 4012: 3954:(1): 27483. 3951: 3947: 3916: 3865: 3861: 3818: 3812: 3753: 3749: 3739: 3680: 3676: 3618: 3614: 3604: 3545: 3541: 3535: 3484: 3480: 3474: 3449: 3445: 3439: 3391:(9): 970–4. 3388: 3384: 3374: 3326:(1): 55–78. 3323: 3319: 3267: 3263: 3257: 3235:(2): 32–36. 3232: 3226: 3213: 3162: 3158: 3152: 3109: 3105: 3099: 3048: 3044: 3038: 3003: 2999: 2993: 2934: 2930: 2920: 2869: 2865: 2855: 2804: 2800: 2790: 2739: 2735: 2725: 2666: 2662: 2617:(2): 93–96. 2614: 2610: 2588: 2585:JETP Letters 2584: 2520: 2516: 2506: 2465: 2461: 2451: 2392: 2388: 2378: 2327: 2323: 2313: 2265:(1): 22–30. 2262: 2258: 2196: 2192: 2128: 2124: 2094:10754/315777 2068: 2064: 2054: 2003: 1997: 1987: 1944: 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