Gapless Criterion for Crystals from Effective Axion Field

Abstract

Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a sufficient gapless criterion for three-dimensional non-interacting crystals, based on the simplified expressions for the bulk average value of the static axion field. The brief logic is that two different simplified expressions give the same value in an insulator, and thus the gapless phase can be detected by the mismatch of them. We demonstrate the effectiveness of the gapless criterion in the magnetic systems with space groups 26 and 13, where mirror, glide, and inversion symmetries provide the simplified expressions. In particular, the gapless criterion can identify gapless phases that are missed by the symmetry representation approach, as illustrated by space group 26. Our proposal serves as a guiding principle for future discovery of topological semimetals.

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References in corpus (56)

• Topological Insulators
• Topological insulators and superconductors
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Field Theory of Time-Reversal Invariant Insulators
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Type-II Weyl Semimetals
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Topological Materials: Weyl Semimetals
• Experimental discovery of Weyl semimetal TaAs
• Topological nodal semimetals
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• The (High Quality) Topological Materials In The World
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Catalogue of Topological Electronic Materials
• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Topological Semimetals
• Topological classification of crystalline insulators through band structure combinatorics
• Inversion Symmetric Topological Insulators
• Nodal-chain metals
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Exponential localization of Wannier functions in insulators
• Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator
• Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures
• Triple Point Topological Metals
• Topological Semimetals with Triply Degenerate Nodal Points in θ-phase Tantalum Nitride
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Non-Abelian band topology in noninteracting metals
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Surface States of Topological Crystalline Insulators in IV-VI Semiconductors
• Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state
• Tailoring tricolor structure of magnetic topological insulator for robust axion insulator
• Observation of the universal magnetoelectric effect in a 3D topological insulator
• Surfaces of Axion Insulators
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Spinless Topological Insulators without Time-Reversal Symmetry
• Equivalent topological invariants of topological insulators
• Diagnosis for topological semimetals in the absence of spin-orbital coupling
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• The Axion Insulator as a Pump of Fragile Topology
• Symmetry indicators of band topology
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• Pfaffian formalism for higher-order topological insulators
• Axion coupling in the hybrid Wannier representation
• Magnetic-Resonance-Induced Pseudo-electric Field and Giant Current Response in Axion Insulators
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Saddle-like topological surface states on the TT'X family of compounds (T, T' = Transition metal, X= Si, Ge)
• Weyl Semimetals with $S_4$ symmetry

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• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Simulating Higher-Order Topological Insulators in Density Wave Insulators