Classification of topological quantum matter with symmetries

2016/08/31 by Ching-Kai Chiu, Ching‐Kai Chiu, Jeffrey C. Y. Teo +3 · 149 citations
Physics and Astronomy · #Topological Materials and Phenomena #Quantum many-body systems #Advanced Condensed Matter Physics

paper · doi:10.1103/revmodphys.88.035005

Abstract

In recent years an increasing amount of attention has been devoted to quantum materials with topological characteristics that are robust against disorder and other perturbations. In this context it was discovered that topological materials can be classified with respect to their dimension and symmetry properties. This review provides an overview of the classification schemes of both fully gapped and gapless topological materials and gives a pedagogical introduction into the field of topological band theory.

Citations

• Topological Insulator Materials
• Berry's Phase and Absence of Back Scattering in Carbon Nanotubes
• Solitons in conducting polymers
• Topological Stability of Majorana Zero Modes in Superconductor–Topological Insulator Systems
• Anyons in an exactly solved model and beyond
• Non-Abelian anyons and topological quantum computation
• Light-induced gauge fields for ultracold atoms

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• Higher-Dimensional Information Lattice: Quantum State Characterization through Inclusion-Exclusion Local Information
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• Field-free Josephson diode and tunable ϕ₀-junction in chiral kagome antiferromagnets
• Dynamical Scarring from Scrambling in Two Dimensional Topological Materials
• Current switching behaviour mediated via hinge modes in higher order topological phase using altermagnets
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• Many-body symmetry-protected zero boundary modes of synthetic photo-magnonic crystals
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• Topological superconductivity and superconducting diode effect mediated via unconventional magnet and Ising spin-orbit coupling
• Size optimization for observeing Majorana fermions
• Nonlinear Hall responses in tunable nodal Dirac semimetals
• Observation of topological phases without crystalline counterparts
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• Inhomogeneous SSH models and the doubling of orthogonal polynomials
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Hidden wallpaper fermion and third-order topological insulator
• Parametric resonance in a spin-1/2 chain: dynamical effects of nontrivial topology
• Ordinary lattice defects as probes of topology
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• Non-Fermi-liquid transport phenomena in bilayer nickelates: Impact of quasi-quantum metric
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• Continuum Landau surface states in a non-Hermitian Weyl semimetal
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• Nonlinear Optical Spectroscopy of Nodal-Line Semimetals
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• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
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• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
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• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Quantum Spin Hall Effect with Extended Topologically Protected Features in Altermangetic Multilayers
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• Explicit equivalence between the spectral localizer and local Chern and winding markers
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• Two-dimensional Disordered Projected Branes: Stability and Quantum Criticality via Dimensional Reduction
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• Quantum metric and localization in a quasicrystal
• Emergent topology in thin films of nodal line semimetals
• Hierarchical Topological States without Dimension Reduction
• Dynamically stable topological edge states in an extended Su-Schrieffer-Heeger ladder with balanced perturbation
• Delicate Wannier insulators
• Quantum spin liquids in a square lattice subject to an Abelian flux
• Intra-unit-cell singlet pairing mediated by altermagnetic fluctuations
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• Robustness of topological edge states in alternating spin chains against environment
• Emergence of Diverse Topological States in Ge Doped MnBi2Te4
• Effective potential of scalar Lee-Wick pseudo-electrodynamics
• From Chern to Winding: Topological Invariant Correspondence in the Reduced Haldane Model
• A many-body marker for three-dimensional topological insulators with inversion symmetry
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
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Related

• Topological Classification of Insulators: I. Non-interacting Spectrally-Gapped One-Dimensional Systems
• Classification and Construction of Topological Phases of Quantum Matter
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• Two-dimensional Topological Quantum Chemistry and Catalog of Topological Materials
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