# Topological Phases & Anyons Domain: Fundamental & Quantum Physics · 249 papers indexed · newest 2026-10-29 Topological insulators and semimetals, fractional Chern insulators, the fractional quantum anomalous Hall effect in moire materials and non-Abelian anyons. Key concepts: fractional quantum anomalous Hall, fractional Chern insulator, topological insulator, anyons, non-Abelian, Weyl semimetal, topological order ## Most influential - **[Colloquium : Topological insulators](https://space-kitty.com/papers/arxiv:1002.3895)**. M. Zahid Hasan, C. L. Kane · 2010 · Reviews of Modern Physics (arXiv:1002.3895 · doi:10.1103/revmodphys.82.3045 · 19,951 citations). Source: > 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 HgCdT… - **[Topological insulators and superconductors](https://space-kitty.com/papers/arxiv:1008.2026)**. Xiao-Liang Qi, Shoucheng Zhang · 2011 · Reviews of Modern Physics (arXiv:1008.2026 · doi:10.1103/revmodphys.83.1057 · 14,414 citations). Source: > 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-dimensi… - **[Topological domains in mammalian genomes identified by analysis of chromatin interactions](https://space-kitty.com/papers/doi:10.1038/nature11082)**. Jesse R. Dixon, Siddarth Selvaraj, Feng Yue et al. · 2012 · Nature (doi:10.1038/nature11082 · 6,829 citations). Source: - **[Progress, Challenges, and Opportunities in Two-Dimensional Materials Beyond Graphene](https://space-kitty.com/papers/doi:10.1021/nn400280c)**. Sheneve Butler, Shawna Hollen, Linyou Cao et al. · 2013 · ACS Nano (doi:10.1021/nn400280c · 4,888 citations). Source: - **[Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates](https://space-kitty.com/papers/arxiv:1007.0016)**. Xiangang Wan, Ari M. Turner, Ashvin Vishwanath et al. · 2011 · Physical Review B (arXiv:1007.0016 · doi:10.1103/physrevb.83.205101 · 4,724 citations). Source: > 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… - **[Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator](https://space-kitty.com/papers/arxiv:1605.08829)**. Cui‐Zu Chang, Jinsong Zhang, Xiao Feng et al. · 2013 · Science (arXiv:1605.08829 · doi:10.1126/science.1234414 · 3,891 citations). Source: > 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… - **[Topological photonics](https://space-kitty.com/papers/arxiv:1408.6730)**. Ling Lü, John D. Joannopoulos, Marin Soljacic A · 2014 · Nature Photonics (arXiv:1408.6730 · doi:10.1038/nphoton.2014.248 · 3,655 citations). Source: > 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… - **[Photonic Floquet topological insulators](https://space-kitty.com/papers/arxiv:1212.3146)**. Mikael C. Rechtsman, Julia M. Zeuner, Yonatan Plotnik et al. · 2013 · Nature (arXiv:1212.3146 · doi:10.1038/nature12066 · 3,330 citations). Source: > 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… - **[The birth of topological insulators](https://space-kitty.com/papers/doi:10.1038/nature08916)**. Joel E. Moore · 2010 · Nature (doi:10.1038/nature08916 · 3,232 citations). Source: - **[WannierTools: An open-source software package for novel topological materials](https://space-kitty.com/papers/arxiv:1703.07789)**. Quansheng Wu, ShengNan Zhang, Haifeng Song et al. · 2017 · Computer Physics Communications (arXiv:1703.07789 · doi:10.1016/j.cpc.2017.09.033 · 2,737 citations). Source: > 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 momentu… - **[Weyl Semimetal in a Topological Insulator Multilayer](https://space-kitty.com/papers/arxiv:1105.5138)**. A. A. Burkov, Leon Balents · 2011 · Phys. Rev. Lett. 107, 127205 (2011) (arXiv:1105.5138 · doi:10.1103/physrevlett.107.127205 · 2,291 citations). Source: > 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 b… - **[Type-II Weyl semimetals](https://space-kitty.com/papers/arxiv:1507.01603)**. Alexey A. Soluyanov, Dominik Gresch, Zhijun Wang et al. · 2015 · Nature (arXiv:1507.01603 · doi:10.1038/nature15768 · 2,526 citations). Source: > 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 string… - **[Discovery of a Three-Dimensional Topological Dirac Semimetal, Na 3 Bi](https://space-kitty.com/papers/arxiv:1310.0391)**. Zhongkai Liu, B. Zhou, Yi Zhang et al. · 2014 · Science (arXiv:1310.0391 · doi:10.1126/science.1245085 · 2,334 citations). Source: > 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 … - **[Topological insulators and superconductors: tenfold way and dimensional hierarchy](https://space-kitty.com/papers/arxiv:0912.2157)**. Shinsei Ryu, Andreas P. Schnyder, Akira Furusaki et al. · 2010 · New Journal of Physics (arXiv:0912.2157 · doi:10.1088/1367-2630/12/6/065010 · 2,325 citations). Source: > 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 d… - **[Quantized Anomalous Hall Effect in Magnetic Topological Insulators](https://space-kitty.com/papers/arxiv:1002.0946)**. Rui Yu, Wei Zhang, Haijun Zhang et al. · 2010 · Science (arXiv:1002.0946 · doi:10.1126/science.1187485 · 2,273 citations). Source: > 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 fie… ## Newest - **[Magnetotransport experiments on side-contacted topological insulator three-terminal Josephson junctions](https://space-kitty.com/papers/arxiv:2610.40083)**. Christoph Wassmer, Ella Nikodem, Oliver Breunig et al. · 2026 (arXiv:2610.40083). Source: - **[Three-dimensional QCA that are not stably circuits](https://space-kitty.com/papers/arxiv:2610.40235)**. Bowen Yang · 2026 (arXiv:2610.40235). Source: - **[Transport in spinful non-Hermitian gauge lattices](https://space-kitty.com/papers/arxiv:2610.40317)**. Hamed Ghaemi-Dizicheh, Shahram Dehdashti, Janis Nötzel · 2026 (arXiv:2610.40317). Source: - **[Chiral $p$-Wave Superconductivity Proximate to a Fractional Chern Insulator and a Topological Charge Density Wave in a Moiré Chern Band](https://space-kitty.com/papers/arxiv:2610.40469)**. Yunze Ouyang, Fengcheng Wu · 2026 (arXiv:2610.40469). Source: - **[Toric codes all the way down: decoupling translation-invariant topological CSS codes in higher dimensions](https://space-kitty.com/papers/arxiv:2610.40592)**. Mingxin He, Yifei Wang, Hao Song et al. · 2026 (arXiv:2610.40592). Source: - **[Algebraic theory of abelian fractons and beyond](https://space-kitty.com/papers/arxiv:2610.40596)**. Wilbur Shirley, Evan Wickenden, Bowen Yang et al. · 2026 (arXiv:2610.40596). Source: - **[Variational wavefunctions for ideal anyon gas: superfluid and skyrmion Hall crystal](https://space-kitty.com/papers/arxiv:2610.40657)**. Ya-Hui Zhang · 2026 (arXiv:2610.40657). Source: - **[Time evolution in the multi-component dynamical Keldysh models](https://space-kitty.com/papers/arxiv:2610.38338)**. M. N. Kiselev · 2026 (arXiv:2610.38338). Source: - **[Exploring Fractional Quantum Hall States with Deep Learning: From Abelian to Non-Abelian Phases](https://space-kitty.com/papers/arxiv:2610.38533)**. Xiangyu Ma, Kehuang Chen, Yuntian Gu et al. · 2026 (arXiv:2610.38533). Source: - **[Gravitational anomaly spectroscopy of a Kitaev spin liquid](https://space-kitty.com/papers/arxiv:2610.38704)**. Kumar Ghosh · 2026 (arXiv:2610.38704). Source: --- Space Kitty Archive · https://space-kitty.com · API: https://space-kitty.com/api/v1 · MCP: https://space-kitty.com/mcp · Premium: $0.20/request via x402 (Base Sepolia (testnet)). Metadata: arXiv (CC0), OpenAlex (CC0), Europe PMC (CC BY/CC0 works), ClinicalTrials.gov.