{"topic":"topological-matter","sort":"top","limit":25,"offset":0,"count":25,"papers":[{"id":"arxiv:1002.3895","kind":"article","title":"Colloquium : Topological insulators","authors":["M. Zahid Hasan","C. L. Kane"],"author_count":2,"year":2010,"published":"2010-11-08","venue":"Reviews of Modern Physics","cited_by":19951,"doi":"10.1103/revmodphys.82.3045","arxiv_id":"1002.3895","nct_id":null,"source_url":"https://doi.org/10.1103/revmodphys.82.3045","archive_url":"https://space-kitty.com/papers/arxiv:1002.3895","updated":"2010-11-09","pmid":null,"pmcid":null,"openalex_id":"W2102074887","pdf_url":"https://arxiv.org/pdf/1002.3895","abstract":"Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A 3D topological insulator supports novel spin polarized 2D Dirac fermions on its surface. In this Colloquium article we will review the theoretical foundation for these electronic states and describe recent experiments in which their signatures have been observed. We will describe transport experiments on HgCdTe quantum wells that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. We will then discuss experiments on Bi_{1-x}Sb_x, Bi_2 Se_3, Bi_2 Te_3 and Sb_2 Te_3 that establish these materials as 3D topological insulators and directly probe the topology of their surface states. We will then describe exotic states that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions, and may provide a new venue for realizing proposals for topological quantum computation. We will close by discussing prospects for observing these exotic states, a well as other potential device applications of topological insulators.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1008.2026","kind":"article","title":"Topological insulators and superconductors","authors":["Xiao-Liang Qi","Shoucheng Zhang"],"author_count":2,"year":2011,"published":"2011-10-14","venue":"Reviews of Modern Physics","cited_by":14414,"doi":"10.1103/revmodphys.83.1057","arxiv_id":"1008.2026","nct_id":null,"source_url":"https://doi.org/10.1103/revmodphys.83.1057","archive_url":"https://space-kitty.com/papers/arxiv:1008.2026","updated":"2010-08-12","pmid":null,"pmcid":null,"openalex_id":"W2020332193","pdf_url":"https://arxiv.org/pdf/1008.2026","abstract":"Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi$_2$Te$_3$ and Bi$_2$Se$_3$ crystals. We review theoretical models, materials properties and experimental results on two-dimensional and three-dimensional topological insulators, and discuss both the topological band theory and the topological field theory. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. We review the theory of topological superconductors in close analogy to the theory of topological insulators.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"doi:10.1038/nature11082","kind":"article","title":"Topological domains in mammalian genomes identified by analysis of chromatin interactions","authors":["Jesse R. Dixon","Siddarth Selvaraj","Feng Yue","Audrey Kim","Yan Li","Yin Shen","Ming Hu","Jun S. Liu","Bing Ren"],"author_count":9,"year":2012,"published":"2012-04-10","venue":"Nature","cited_by":6829,"doi":"10.1038/nature11082","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.1038/nature11082","archive_url":"https://space-kitty.com/papers/doi:10.1038/nature11082","updated":null,"pmid":"22495300","pmcid":null,"openalex_id":"W2070021921","pdf_url":null,"abstract":null,"abstract_license":null,"license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Genomics and Chromatin Dynamics"],"details":null,"provenance":"openalex","attribution":"Metadata and citation counts: OpenAlex (CC0)."},{"id":"doi:10.1021/nn400280c","kind":"review","title":"Progress, Challenges, and Opportunities in Two-Dimensional Materials Beyond Graphene","authors":["Sheneve Butler","Shawna Hollen","Linyou Cao","Yi Cui","Jay Gupta","Humberto R. Gutiérrez","Tony F. Heinz","Seung Sae Hong","Jiaxing Huang","Ariel F. Ismach","Ezekiel Johnston‐Halperin","Masaru K. Kuno","Vladimir V. Plashnitsa","Richard D. Robinson","Rodney S. Ruoff","Sayeef Salahuddin","Jie Shan","Li Shi","Michael G. Spencer","Mauricio Terrones","Wolfgang Windl","Joshua E. Goldberger"],"author_count":22,"year":2013,"published":"2013-03-06","venue":"ACS Nano","cited_by":4888,"doi":"10.1021/nn400280c","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.1021/nn400280c","archive_url":"https://space-kitty.com/papers/doi:10.1021/nn400280c","updated":null,"pmid":"23464873","pmcid":null,"openalex_id":"W2024966938","pdf_url":null,"abstract":null,"abstract_license":null,"license":null,"is_open_access":false,"retracted":false,"peer_reviewed":null,"categories":["2D Materials and Applications"],"details":null,"provenance":"openalex","attribution":"Metadata and citation counts: OpenAlex (CC0)."},{"id":"arxiv:1007.0016","kind":"article","title":"Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates","authors":["Xiangang Wan","Ari M. Turner","Ashvin Vishwanath","Sergey Yu. Savrasov"],"author_count":4,"year":2011,"published":"2011-05-02","venue":"Physical Review B","cited_by":4724,"doi":"10.1103/physrevb.83.205101","arxiv_id":"1007.0016","nct_id":null,"source_url":"https://doi.org/10.1103/physrevb.83.205101","archive_url":"https://space-kitty.com/papers/arxiv:1007.0016","updated":"2010-06-30","pmid":null,"pmcid":null,"openalex_id":"W1538825449","pdf_url":"https://arxiv.org/pdf/1007.0016","abstract":"In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, (such as Y$_{2}$Ir$_{2}$O$_{7}$) using density functional theory, LDA+U method, and effective low energy models. A remarkably rich phase diagram emerges on tuning the correlation strength U. The Ir magnetic moment are always found to be non-collinearly ordered. However, the ground state changes from a magnetic metal at weak U, to a Mott insulator at large U. Most interestingly, the intermediate U regime is found to be a Dirac semi-metal, with vanishing density of states at the Fermi energy. It also exhibits topological properties - manifested by special surface states in the form of Fermi arcs, that connect the bulk Dirac points. This Dirac phase, a three dimensional analog of graphene, is proposed as the ground state of Y$_{2}$Ir$_{2}$O$_{7}$ and related compounds. A narrow window of magnetic `axion' insulator, with axion parameter $θ=π$, may also be present at intermediate U. An applied magnetic field induces ferromagnetic order and a metallic ground state.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1605.08829","kind":"article","title":"Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator","authors":["Cui‐Zu Chang","Jinsong Zhang","Xiao Feng","Jie Shen","Zuocheng Zhang","Minghua Guo","Kang Li","Yunbo Ou","P. Wei","Li-Li Wang","Zhong-Qing Ji","Yang Feng","Shuai‐Hua Ji","Xi Chen","Jinfeng Jia","Xi Dai","Zhong Fang","Shoucheng Zhang","Ke He","Yayu Wang","Li Lü","Xu-Cun Ma","Qi-Kun Xue"],"author_count":23,"year":2013,"published":"2013-03-15","venue":"Science","cited_by":3891,"doi":"10.1126/science.1234414","arxiv_id":"1605.08829","nct_id":null,"source_url":"https://doi.org/10.1126/science.1234414","archive_url":"https://space-kitty.com/papers/arxiv:1605.08829","updated":"2016-05-28","pmid":"23493424","pmcid":null,"openalex_id":"W1970188810","pdf_url":"https://arxiv.org/pdf/1605.08829","abstract":"The quantized version of the anomalous Hall effect has been predicted to occur in magnetic topological insulators, but the experimental realization has been challenging. Here, we report the observation of the quantum anomalous Hall (QAH) effect in thin films of Cr-doped (Bi,Sb)2Te3, a magnetic topological insulator. At zero magnetic field, the gate-tuned anomalous Hall resistance reaches the predicted quantized value of h/e^2,accompanied by a considerable drop of the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes whereas the Hall resistance remains at the quantized value. The realization of the QAH effect may lead to the development of low-power-consumption electronics.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1408.6730","kind":"article","title":"Topological photonics","authors":["Ling Lü","John D. Joannopoulos","Marin Soljacic A"],"author_count":3,"year":2014,"published":"2014-10-24","venue":"Nature Photonics","cited_by":3655,"doi":"10.1038/nphoton.2014.248","arxiv_id":"1408.6730","nct_id":null,"source_url":"https://doi.org/10.1038/nphoton.2014.248","archive_url":"https://space-kitty.com/papers/arxiv:1408.6730","updated":"2014-10-31","pmid":null,"pmcid":null,"openalex_id":"W2795835319","pdf_url":"https://arxiv.org/pdf/1408.6730","abstract":"Topology is revolutionizing photonics, bringing with it new theoretical discoveries and a wealth of potential applications. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without dissipation even in the presence of impurities. Similarly, new optical mirrors of different wave-vector space topologies have been constructed to support new states of light propagating at their interfaces. These novel waveguides allow light to flow around large imperfections without back-reflection. The present review explains the underlying principles and highlights the major findings in photonic crystals, coupled resonators, metamaterials and quasicrystals.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1212.3146","kind":"article","title":"Photonic Floquet topological insulators","authors":["Mikael C. Rechtsman","Julia M. Zeuner","Yonatan Plotnik","Yaakov Lumer","Daniel K. Podolsky","Felix Dreisow","Stefan Nolte","Mordechai Segev","Alexander Szameit"],"author_count":9,"year":2013,"published":"2013-04-01","venue":"Nature","cited_by":3330,"doi":"10.1038/nature12066","arxiv_id":"1212.3146","nct_id":null,"source_url":"https://doi.org/10.1038/nature12066","archive_url":"https://space-kitty.com/papers/arxiv:1212.3146","updated":"2012-12-13","pmid":"23579677","pmcid":null,"openalex_id":"W1978426240","pdf_url":"https://arxiv.org/pdf/1212.3146","abstract":"The topological insulator is a fundamentally new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, not within the bulk, and that conduction is topologically protected. Topological protection, the total lack of scattering of electron waves by disorder, is perhaps the most fascinating and technologically important aspect of this material: it provides robustness that is otherwise known only for superconductors. However, unlike superconductivity and the quantum Hall effect, which necessitate low temperatures or magnetic fields, the immunity to disorder of topological insulators occurs at room temperature and without any external magnetic field. For this reason, topological protection is predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Recently, a large theoretical effort has been directed towards bringing the concept into the domain of photonics: achieving topological protection of light at optical frequencies. Besides the interesting new physics involved, photonic topological insulators hold the promise for applications in optical isolation and robust photon transport. Here, we theoretically propose and experimentally demonstrate the first photonic topological insulator: a photonic lattice exhibiting topologically protected transport on the lattice edges, without the need for any external field. The system is composed of an array of helical waveguides, evanescently coupled to one another, and arranged in a graphene-like honeycomb lattice. The chirality of the waveguides results in scatter-free, one-way edge states that are topologically protected from scattering.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"doi:10.1038/nature08916","kind":"article","title":"The birth of topological insulators","authors":["Joel E. Moore"],"author_count":1,"year":2010,"published":"2010-03-01","venue":"Nature","cited_by":3232,"doi":"10.1038/nature08916","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.1038/nature08916","archive_url":"https://space-kitty.com/papers/doi:10.1038/nature08916","updated":null,"pmid":"20220837","pmcid":null,"openalex_id":"W2070931774","pdf_url":null,"abstract":null,"abstract_license":null,"license":null,"is_open_access":false,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex","attribution":"Metadata and citation counts: OpenAlex (CC0)."},{"id":"arxiv:1703.07789","kind":"article","title":"WannierTools: An open-source software package for novel topological materials","authors":["Quansheng Wu","ShengNan Zhang","Haifeng Song","Matthias Troyer","Alexey A. Soluyanov"],"author_count":5,"year":2017,"published":"2017-10-18","venue":"Computer Physics Communications","cited_by":2737,"doi":"10.1016/j.cpc.2017.09.033","arxiv_id":"1703.07789","nct_id":null,"source_url":"https://doi.org/10.1016/j.cpc.2017.09.033","archive_url":"https://space-kitty.com/papers/arxiv:1703.07789","updated":"2017-09-26","pmid":null,"pmcid":null,"openalex_id":"W2598009386","pdf_url":"https://arxiv.org/pdf/1703.07789","abstract":"We present an open-source software package WannierTools, a tool for investigation of novel topological materials. This code works in the tight-binding framework, which can be generated by another software package Wannier90. It can help to classify the topological phase of given materials by calculating the Wilson loop and can get the surface state spectrum which is detected by angle-resolved photoemission (ARPES) and in scanning tunneling microscopy (STM) experiments. It also identifies positions of Weyl/Dirac points and nodal line structures, calculates the Berry phase around a closed momentum loop and Berry curvature in a part of the Brillouin zone.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1105.5138","kind":"article","title":"Weyl Semimetal in a Topological Insulator Multilayer","authors":["A. A. Burkov","Leon Balents"],"author_count":2,"year":2011,"published":"2011-05-25","venue":"Phys. Rev. Lett. 107, 127205 (2011)","cited_by":2291,"doi":"10.1103/physrevlett.107.127205","arxiv_id":"1105.5138","nct_id":null,"source_url":"https://arxiv.org/abs/1105.5138","archive_url":"https://space-kitty.com/papers/arxiv:1105.5138","updated":"2011-09-16","pmid":"22026796","pmcid":null,"openalex_id":"W2046004949","pdf_url":"https://arxiv.org/pdf/1105.5138","abstract":"We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its bandstructure. This particular type of Weyl semimetal has a finite anomalous Hall conductivity, chiral edge states, and occurs as an intermediate phase between an ordinary insulator and a 3D quantum anomalous Hall insulator with a quantized Hall conductivity, equal to $e^2/h$ per TI layer. We find that the Weyl semimetal has a nonzero DC conductivity at zero temperature and is thus an unusual metallic phase, characterized by a finite anomalous Hall conductivity and topologically-protected edge states.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["cond-mat.mes-hall"],"details":null,"provenance":"arxiv+openalex","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1507.01603","kind":"article","title":"Type-II Weyl semimetals","authors":["Alexey A. Soluyanov","Dominik Gresch","Zhijun Wang","Quansheng Wu","Matthias Troyer","Xi Dai","Bogdan Andrei Bernevig"],"author_count":7,"year":2015,"published":"2015-11-01","venue":"Nature","cited_by":2526,"doi":"10.1038/nature15768","arxiv_id":"1507.01603","nct_id":null,"source_url":"https://doi.org/10.1038/nature15768","archive_url":"https://space-kitty.com/papers/arxiv:1507.01603","updated":"2015-11-28","pmid":"26607545","pmcid":null,"openalex_id":"W2175118067","pdf_url":"https://arxiv.org/pdf/1507.01603","abstract":"Fermions in nature come in several types: Dirac, Majorana and Weyl are theoretically thought to form a complete list. Even though Majorana and Weyl fermions have for decades remained experimentally elusive, condensed matter has recently emerged as fertile ground for their discovery as low energy excitations of realistic materials. Here we show the existence of yet another particle - a new type of Weyl fermion - that emerges at the boundary between electron and hole pockets in a new type of Weyl semimetal phase of matter. This fermion was missed by Weyl in 1929 due to its breaking of the stringent Lorentz symmetry of high-energy physics. Lorentz invariance however is not present in condensed matter physics, and we predict that an established material, WTe$_2$, is an example of this novel type of topological semimetal hosting the new particle as a low energy excitation around a type-2 Weyl node. This node, although still a protected crossing, has an open, finite-density of states Fermi surface, likely resulting in a plethora physical properties very different from those of standard point-like Fermi surface Weyl points.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1310.0391","kind":"article","title":"Discovery of a Three-Dimensional Topological Dirac Semimetal, Na 3 Bi","authors":["Zhongkai Liu","B. Zhou","Yi Zhang","Zhijun Wang","Hongming Weng","D. Prabhakaran","Sung‐Kwan Mo","Zhi‐Xun Shen","Zhenxing Fang","Xi Dai","Z. Hussain","Yulin Chen"],"author_count":12,"year":2014,"published":"2014-01-16","venue":"Science","cited_by":2334,"doi":"10.1126/science.1245085","arxiv_id":"1310.0391","nct_id":null,"source_url":"https://doi.org/10.1126/science.1245085","archive_url":"https://space-kitty.com/papers/arxiv:1310.0391","updated":"2013-10-01","pmid":"24436183","pmcid":null,"openalex_id":"W2237953221","pdf_url":"https://arxiv.org/pdf/1310.0391","abstract":"Three-dimensional (3D) topological Dirac semimetals (TDSs) represent a novel state of quantum matter that can be viewed as '3D graphene'. In contrast to two-dimensional (2D) Dirac fermions in graphene or on the surface of 3D topological insulators, TDSs possess 3D Dirac fermions in the bulk. The TDS is also an important boundary state mediating numerous novel quantum states, such as topological insulators, Weyl semi-metals, Axion insulators and topological superconductors. By investigating the electronic structure of Na3Bi with angle resolved photoemission spectroscopy, we discovered 3D Dirac fermions with linear dispersions along all momentum directions for the first time. Furthermore, we demonstrated that the 3D Dirac fermions in Na3Bi were protected by the bulk crystal symmetry. Our results establish that Na3Bi is the first model system of 3D TDSs, which can also serve as an ideal platform for the systematic study of quantum phase transitions between rich novel topological quantum states.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:0912.2157","kind":"article","title":"Topological insulators and superconductors: tenfold way and dimensional hierarchy","authors":["Shinsei Ryu","Andreas P. Schnyder","Akira Furusaki","Andreas W. W. Ludwig"],"author_count":4,"year":2010,"published":"2010-06-17","venue":"New Journal of Physics","cited_by":2325,"doi":"10.1088/1367-2630/12/6/065010","arxiv_id":"0912.2157","nct_id":null,"source_url":"https://doi.org/10.1088/1367-2630/12/6/065010","archive_url":"https://space-kitty.com/papers/arxiv:0912.2157","updated":"2010-06-15","pmid":null,"pmcid":null,"openalex_id":"W1501955150","pdf_url":"https://iopscience.iop.org/article/10.1088/1367-2630/12/6/065010/pdf","abstract":"It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on the case, by a Z or a Z_2 topological invariant. This is an exhaustive classification. Here we construct representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians. Using these representatives we demonstrate how topological insulators (superconductors) in different dimensions and different classes can be related via dimensional reduction by compactifying one or more spatial dimensions (in Kaluza-Klein-like fashion). For Z-topological insulators (superconductors) this proceeds by descending by one dimension at a time into a different class. The Z_2-topological insulators (superconductors), on the other hand, are shown to be lower-dimensional descendants of parent Z-topological insulators in the same class, from which they inherit their topological properties. The 8-fold periodicity in dimension d that exists for topological insulators (superconductors) with Hamiltonians satisfying at least one reality condition (arising from time-reversal or charge-conjugation/particle-hole symmetries) is a reflection of the 8-fold periodicity of the spinor representations of the orthogonal groups SO(N) (a form of Bott periodicity). We derive a relation between the topological invariant that characterizes topological insulators/superconductors with chiral symmetry and the Chern-Simons invariant: it relates the invariant to the electric polarization (d=1), or to the magnetoelectric polarizability (d=3). Finally, we discuss topological field theories describing the space time theory of linear responses, and study how the presence of inversion symmetry modifies the classification.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1002.0946","kind":"article","title":"Quantized Anomalous Hall Effect in Magnetic Topological Insulators","authors":["Rui Yu","Wei Zhang","Haijun Zhang","Shoucheng Zhang","Xi Dai","Zhong Fang"],"author_count":6,"year":2010,"published":"2010-06-03","venue":"Science","cited_by":2273,"doi":"10.1126/science.1187485","arxiv_id":"1002.0946","nct_id":null,"source_url":"https://doi.org/10.1126/science.1187485","archive_url":"https://space-kitty.com/papers/arxiv:1002.0946","updated":"2010-02-04","pmid":"20522741","pmcid":null,"openalex_id":"W2082294379","pdf_url":"https://arxiv.org/pdf/1002.0946","abstract":"The Hall effect, the anomalous Hall effect and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The quantum versions of the Hall effect and the spin Hall effect have been discovered in recent years. However, the quantized anomalous Hall (QAH) effect has not yet been realized experimentally. In a QAH insulator, spontaneous magnetic moments and spin-orbit coupling combine to give rise to a topologically non-trivial electronic structure, leading to the quantized Hall effect without any external magnetic field. In this work, based on state-of-art first principles calculations, we predict that the tetradymite semiconductors Bi$_2$Te$_3$, Bi$_2$Se$_3$, and Sb$_2$Te$_3$ form magnetically ordered insulators when doped with transition metal elements (Cr or Fe), in sharp contrast to conventional dilute magnetic semiconductor where free carriers are necessary to mediate the magnetic coupling. Magnetic order in two-dimensional thin films gives rise to a topological electronic structure characterized by a finite Chern number, with quantized Hall conductance $e^{2}/h$. Experimental realization of the long sought-after QAH insulator state could enable robust dissipationless charge transport at room temperature.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1406.7874","kind":"article","title":"Experimental realization of the topological Haldane model with ultracold fermions","authors":["Gregor Jotzu","Michael Messer","Rémi Desbuquois","Martin Lebrat","Thomas Uehlinger","Daniel Greif","Tilman Esslinger"],"author_count":7,"year":2014,"published":"2014-11-11","venue":"Nature","cited_by":2217,"doi":"10.1038/nature13915","arxiv_id":"1406.7874","nct_id":null,"source_url":"https://doi.org/10.1038/nature13915","archive_url":"https://space-kitty.com/papers/arxiv:1406.7874","updated":"2018-01-23","pmid":"25391960","pmcid":null,"openalex_id":"W2020595981","pdf_url":"https://arxiv.org/pdf/1406.7874","abstract":"The Haldane model on the honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band-structure, rather than being caused by an external magnetic field. Although an implementation in a material was considered unlikely, it has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors. Here we report on the experimental realisation of the Haldane model and the characterisation of its topological band-structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The model is based on breaking time-reversal symmetry as well as inversion symmetry. The former is achieved through the introduction of complex next-nearest-neighbour tunnelling terms, which we induce through circular modulation of the lattice position. For the latter, we create an energy offset between neighbouring sites. Breaking either of these symmetries opens a gap in the band-structure, which is probed using momentum-resolved interband transitions. We explore the resulting Berry-curvatures of the lowest band by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between both broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally and quantitatively compare it to calculations using Floquet theory without free parameters. We verify that our approach, which allows for dynamically tuning topological properties, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realise spin-dependent topological Hamiltonians.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1010.1802","kind":"article","title":"Topological Crystalline Insulators","authors":["Liang Fu"],"author_count":1,"year":2011,"published":"2011-03-08","venue":"Physical Review Letters","cited_by":2096,"doi":"10.1103/physrevlett.106.106802","arxiv_id":"1010.1802","nct_id":null,"source_url":"https://doi.org/10.1103/physrevlett.106.106802","archive_url":"https://space-kitty.com/papers/arxiv:1010.1802","updated":"2011-03-12","pmid":"21469822","pmcid":null,"openalex_id":"W2078822726","pdf_url":"https://arxiv.org/pdf/1010.1802","abstract":"The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point group symmetry of crystals. We find a class of three-dimensional \"topological crystalline insulators\" which have metallic surface states on certain high symmetry crystal surfaces. These topological crystalline insulators can be viewed as the counterpart of topological insulators in materials without spin-orbit coupling. Their surface states have quadratic band degeneracy instead of linear Dirac dispersion. Their band structures are characterized by new Z2 invariants. We hope this work will enlarge the family of topological phases in band insulators and stimulate the search for them in real materials.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1406.2749","kind":"article","title":"Quantum spin Hall effect in two-dimensional transition metal dichalcogenides","authors":["Xiaofeng Qian","Junwei Liu","Liang Fu","Ju Li"],"author_count":4,"year":2014,"published":"2014-11-21","venue":"Science","cited_by":2056,"doi":"10.1126/science.1256815","arxiv_id":"1406.2749","nct_id":null,"source_url":"https://doi.org/10.1126/science.1256815","archive_url":"https://space-kitty.com/papers/arxiv:1406.2749","updated":"2014-06-11","pmid":"25504715","pmcid":null,"openalex_id":"W2089608912","pdf_url":"https://arxiv.org/pdf/1406.2749","abstract":"We report a new class of large-gap quantum spin Hall insulators in two-dimensional transition metal dichalcogenides, namely, MX$_2$ with M=(Mo, W) and X=(S, Se, and Te), whose topological electronic properties are highly tunable by external electric field. We propose a novel topological field effect transistor made of these atomic layer materials and their van der Waals heterostructures. Our device exhibits parametrically enhanced charge-spin conductance through topologically protected transport channels, and can be rapidly switched off by electric field through topological phase transition instead of carrier depletion. Our work provides a practical material platform and device architecture for topological quantum electronics.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1611.07987","kind":"article","title":"Quantized electric multipole insulators","authors":["Wladimir A. Benalcazar","Bogdan Andrei Bernevig","Taylor L. Hughes"],"author_count":3,"year":2017,"published":"2017-07-07","venue":"Science","cited_by":2029,"doi":"10.1126/science.aah6442","arxiv_id":"1611.07987","nct_id":null,"source_url":"https://doi.org/10.1126/science.aah6442","archive_url":"https://space-kitty.com/papers/arxiv:1611.07987","updated":"2017-02-22","pmid":"28684520","pmcid":null,"openalex_id":"W2557414703","pdf_url":"https://arxiv.org/pdf/1611.07987","abstract":"In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they manifest topologically protected corner states carrying fractional charge, i.e., fractionalization at the boundary of the boundary. To characterize these new insulating phases of matter, we introduce a new paradigm whereby `nested' Wilson loops give rise to a large number of new topological invariants that have been previously overlooked. We propose three realistic experimental implementations of this new topological behavior that can be immediately tested.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1204.5700","kind":"article","title":"Photonic topological insulators","authors":["Alexander B. Khanikaev","S. Hossein Mousavi","Wang-Kong Tse","Mehdi Kargarian","Allan H. MacDonald","Gennady B. Shvets"],"author_count":6,"year":2012,"published":"2012-12-14","venue":"Nature Materials","cited_by":1971,"doi":"10.1038/nmat3520","arxiv_id":"1204.5700","nct_id":null,"source_url":"https://doi.org/10.1038/nmat3520","archive_url":"https://space-kitty.com/papers/arxiv:1204.5700","updated":"2012-04-25","pmid":"23241532","pmcid":null,"openalex_id":"W2053033894","pdf_url":"https://arxiv.org/pdf/1204.5700","abstract":"Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal invariant topological insulators. Because of limitations imposed by nature, topologically non-trivial electronic order seems to be uncommon except in small-band-gap semiconductors with strong spin-orbit interactions. In this Article we show that artificial electromagnetic structures, known as metamaterials, provide an attractive platform for designing photonic analogues of topological insulators. We demonstrate that a judicious choice of the metamaterial parameters can create photonic phases that support a pair of helical edge states, and that these edge states enable one-way photonic transport that is robust against disorder.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:0907.2239","kind":"article","title":"Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures","authors":["Jay Deep Sau","Roman M. Lutchyn","Sumanta Tewari","S. Das Sarma"],"author_count":4,"year":2010,"published":"2010-01-27","venue":"Physical Review Letters","cited_by":1940,"doi":"10.1103/physrevlett.104.040502","arxiv_id":"0907.2239","nct_id":null,"source_url":"https://doi.org/10.1103/physrevlett.104.040502","archive_url":"https://space-kitty.com/papers/arxiv:0907.2239","updated":"2010-01-12","pmid":"20366693","pmcid":null,"openalex_id":"W1965741196","pdf_url":"https://arxiv.org/pdf/0907.2239","abstract":"We show that a film of a semiconductor such as GaAs, in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect, supports zero-energy Majorana fermion modes in the ordinary vortex excitations. The key to the topological order is the existence of spin-orbit coupling, coexisting with proximity-induced s-wave superconductivity. Since time reversal symmetry is explicitly broken, the edge of the film constitutes a chiral Majorana wire. The heterostructure we propose -- a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator -- is a generic system which can be used as the platform for topological quantum computation by virtue of the existence of non-Abelian Majorana fermions.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1008.1792","kind":"article","title":"Floquet topological insulator in semiconductor quantum wells","authors":["Netanel H. Lindner","Gil Refael","Victor M. Galitski"],"author_count":3,"year":2011,"published":"2011-03-13","venue":"Nature Physics","cited_by":1817,"doi":"10.1038/nphys1926","arxiv_id":"1008.1792","nct_id":null,"source_url":"https://doi.org/10.1038/nphys1926","archive_url":"https://space-kitty.com/papers/arxiv:1008.1792","updated":"2010-09-07","pmid":null,"pmcid":null,"openalex_id":"W2102030996","pdf_url":"https://arxiv.org/pdf/1008.1792","abstract":"Topological phase transitions between a conventional insulator and a state of matter with topological properties have been proposed and observed in mercury telluride - cadmium telluride quantum wells. We show that a topological state can be induced in such a device, initially in the trivial phase, by irradiation with microwave frequencies, without closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. The velocity of the edge states can be tuned by adjusting the intensity of the microwave radiation. We discuss the necessary experimental parameters for our proposal. This proposal provides an example and a proof of principle of a new non-equilibrium topological state, Floquet topological insulator, introduced in this paper.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2406.09591","kind":"article","title":"Ferromagnetism and Topology of the Higher Flat Band in a Fractional Chern Insulator","authors":["Heonjoon Park","Jiaqi Cai","Eric Anderson","Xiao-Wei Zhang","Xiaoyu Liu","William Holtzmann","Weijie Li","Chong Wang","Chaowei Hu","Yuzhou Zhao","Takashi Taniguchi","Kenji Watanabe","Jihui Yang","David Cobden","Jiun-Haw Chu","Nicolas Regnault","B. Andrei Bernevig","Liang Fu","Ting Cao","Di Xiao","Xiaodong Xu"],"author_count":21,"year":2024,"published":"2024-06-13","venue":"Nature Physics","cited_by":63,"doi":"10.1038/s41567-025-02804-0","arxiv_id":"2406.09591","nct_id":null,"source_url":"https://arxiv.org/abs/2406.09591","archive_url":"https://space-kitty.com/papers/arxiv:2406.09591","updated":"2024-12-16","pmid":null,"pmcid":null,"openalex_id":"W4408672945","pdf_url":"https://arxiv.org/pdf/2406.09591","abstract":"The recent observation of the fractional quantum anomalous Hall effect in moiré fractional Chern insulators provides an opportunity to investigate zero magnetic field anyons. To potentially realize non-Abelian anyons, one approach is to engineer higher flat Chern bands that mimic higher Landau levels. Here, we investigate the interaction, topology, and ferromagnetism of the second moiré miniband in twisted MoTe2 bilayers. At half filling of the second miniband, we observe spontaneous ferromagnetism and an incipient Chern insulator state. The Chern numbers of the top two moiré flat bands exhibit opposite signs for twist angles above 3.1°, but share the same sign near 2.6°, consistent with theoretical predictions. In the 2.6° device, increasing magnetic field induces a topological phase transition via band crossing between opposite valleys, resulting in an emergent state with Chern number C = -2. Additionally, an insulating state at half filling of the second valley-polarized band suggests a charge-ordered state is favored over the fractional Chern insulator state. These findings lay a foundation for understanding the higher flat Chern bands, crucial for the discovery of non-Abelian fractional Chern insulators.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":false,"retracted":false,"peer_reviewed":null,"categories":["cond-mat.mes-hall","cond-mat.str-el"],"details":null,"provenance":"arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1304.5693","kind":"article","title":"Topological Insulator Materials","authors":["Yoichi Ando"],"author_count":1,"year":2013,"published":"2013-09-12","venue":"Journal of the Physical Society of Japan","cited_by":1790,"doi":"10.7566/jpsj.82.102001","arxiv_id":"1304.5693","nct_id":null,"source_url":"https://doi.org/10.7566/jpsj.82.102001","archive_url":"https://space-kitty.com/papers/arxiv:1304.5693","updated":"2013-09-03","pmid":null,"pmcid":null,"openalex_id":"W1968721422","pdf_url":"https://arxiv.org/pdf/1304.5693","abstract":"Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on topological insulator materials with an emphasis on basic theory and materials properties. After presenting a historical perspective and basic theories of topological insulators, it discusses all the topological insulator materials discovered as of May 2013, with some illustrative descriptions of the developments in materials discoveries in which the author was involved. A summary is given for possible ways to confirm the topological nature in a candidate material. Various synthesis techniques as well as the defect chemistry that are important for realizing bulk-insulating samples are discussed. Characteristic properties of topological insulators are discussed with an emphasis on transport properties. In particular, the Dirac fermion physics and the resulting peculiar quantum oscillation patterns are discussed in detail. It is emphasized that proper analyses of quantum oscillations make it possible to unambiguously identify surface Dirac fermions through transport measurements. The prospects of topological insulator materials for elucidating novel quantum phenomena that await discovery conclude the review.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1904.11468","kind":"article","title":"Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi 2 Te 4","authors":["Yujun Deng","Yijun Yu","Meng Zhu Shi","Zhongxun Guo","Zihan Xu","Jing Wang","Xian Hui Chen","Yuanbo Zhang"],"author_count":8,"year":2020,"published":"2020-01-23","venue":"Science","cited_by":1684,"doi":"10.1126/science.aax8156","arxiv_id":"1904.11468","nct_id":null,"source_url":"https://doi.org/10.1126/science.aax8156","archive_url":"https://space-kitty.com/papers/arxiv:1904.11468","updated":"2019-04-25","pmid":"31974160","pmcid":null,"openalex_id":"W3000852548","pdf_url":"https://arxiv.org/pdf/1904.11468","abstract":"In a magnetic topological insulator, nontrivial band topology conspires with magnetic order to produce exotic states of matter that are best exemplified by quantum anomalous Hall (QAH) insulators and axion insulators. Up till now, such magnetic topological insulators are obtained by doping topological insulators with magnetic atoms. The random magnetic dopants, however, inevitably introduce disorders that hinder further exploration of quantum effects in the material. Here, we resolve this dilemma by probing quantum transport in MnBi$_2$Te$_4$ thin flake - a topological insulator with intrinsic magnetic order. In this layered van der Waals crystal, the ferromagnetic layers couple anti-parallel to each other, so MnBi$_2$Te$_4$ is an antiferromagnet. A magnetic field, however, aligns all the layers and induces an interlayer ferromagnetic order; we show that a quantized anomalous Hall response emerges in atomically thin MnBi$_2$Te$_4$ under a moderate magnetic field. MnBi$_2$Te$_4$ therefore becomes the first intrinsic magnetic topological insulator exhibiting quantized anomalous Hall effect. The result establishes MnBi$_2$Te$_4$ as an ideal arena for further exploring various topological phenomena.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Topological Materials and Phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."}],"next":"https://space-kitty.com/api/v1/topics/topological-matter/papers?sort=top&limit=25&offset=25"}