Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions

Abstract

We introduce a novel class of interaction-enabled topological crystalline insulators in two- and three-dimensional electronic systems, which we call "topological crystalline magnet." It is protected by the product of the time-reversal symmetry $\mathcal{T}$ and a mirror symmetry or a rotation symmetry $\mathcal{R}$. A topological crystalline magnet exhibits two intriguing features: (i) it cannot be adiabatically connected to any Slater insulator and (ii) the edge state is robust against coupling electrons to the edge. These features are protected by the anomalous symmetry transformation property $(\mathcal{R}\mathcal{T}{)}^2=-1$ of the edge state. An anisotropic response to the external magnetic field can be an experimental signature.

arXiv comment5 pages, 4 figures; v2: minor revision, to appear in Phys. Rev. B (Rapid Communications)

References in corpus (42)

• Topological Insulators
• Topological insulators and superconductors
• Topological Insulators in Three Dimensions
• Classification of topological quantum matter with symmetries
• Topological Crystalline Insulators
• Topological Crystalline Insulators in the SnTe Material Class
• Entanglement spectrum of a topological phase in one dimension
• Experimental realization of a topological crystalline insulator in SnTe
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Classifying quantum phases using Matrix Product States and PEPS
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• Antiferromagnetic topological insulators
• Symmetry Protected Topological phases of Quantum Matter
• Topology of crystalline insulators and superconductors
• Hourglass Fermions
• Observation of Dirac node formation and mass acquisition in a topological crystalline insulator
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• The strong side of weak topological insulators
• Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
• Topological phases protected by point group symmetry
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topology of nonsymmorphic crystalline insulators and superconductors
• Topological non-symmorphic crystalline insulators
• Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain
• Topological Insulators from Group Cohomology
• Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators
• Phase Transitions Between Topologically Distinct Gapped Phases in Isotropic Spin Ladders
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Theory of interacting topological crystalline insulators
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• String order and adiabatic continuity of Haldane chains and band insulators
• Direct observation and temperature control of the surface Dirac gap in the topological crystalline insulator (Pb,Sn)Se
• Hourglass Fermion Surface States in Stacked Topological Insulators with Nonsymmorphic Symmetry
• Coupled-layer description of topological crystalline insulators
• Flux-fusion anomaly test and bosonic topological crystalline insulators
• Featureless quantum insulator on the honeycomb lattice
• Interaction Enabled Topological Crystalline Phases
• Bosonic symmetry protected topological phases with reflection symmetry
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum

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• A fractional corner anomaly reveals higher-order topology
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Space group constraints on weak indices in topological insulators
• General corner charge formulas in various tetrahedral and cubic space groups
• Observation of trapped fractional charge and topological states at disclination defects in higher-order topological insulators
• Theory of fractional corner charges in cylindrical crystal shapes
• From Frustrated to Unfrustrated: Coupling two triangular-lattice itinerant Quantum Magnets
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges