Topological Insulators with Commensurate Antiferromagnetism

Abstract

We study the topological features of non-interacting insulators subject to an antiferromangetic (AFM) Zeeman field, or AFM insulators, the period of which is commensurate with the lattice period. These insulators can be classified by the presence/absence of an emergent anti-unitary symmetry: the combined operation of time-reversal and a lattice translation by vector $\mathbf{D}$. For AFM insulators that preserve this combined symmetry, regardless of any details in lattice structure or magnetic structure, we show that (i) there is a new type of Kramers' degeneracy protected by the combined symmetry; (ii) a new $Z_2$ index may be defined for 3D AFM insulators, but not for those in lower dimensions and (iii) in 3D AFM insulators with a non-trivial $Z_2$ index, there are odd number of gapless surface modes if and only if the surface termination also preserves the combined symmetry, but the dispersion of surface states becomes highly anisotropic if the AFM propagation vector becomes small compared with the reciprocal lattice vectors. We numerically demonstrate the theory by calculating the spectral weight of the surface states of a 3D TI in the presence of AFM fields with different propagation vectors, which may be observed by ARPES in Bi${}_2$Se${}_3$ or Bi${}_2$Te${}_3$ with induced antiferromagnetism.

14 pages + 3 pages of appendix; 7 figures. Missing Refs. on SmB${}_6$ added

References in corpus (19)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Magnetic Order versus superconductivity in the Iron-based layered La(O1-xFx)FeAs systems
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Topological Surface States Protected From Backscattering by Chiral Spin Texture
• Experimental realization of a topological crystalline insulator in SnTe
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• Antiferromagnetic topological insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Bulk Band Gap and Surface State Conduction Observed in Voltage-Tuned Crystals of the Topological Insulator Bi${}_2$Se${}_3$
• Correlated Topological Insulators with Mixed Valence
• A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
• Odd-Parity Pairing and Topological Superconductivity in a Strongly Spin-Orbit Coupled Semiconductor
• Magnetic field induced localization in 2D topological insulators

Cited by in corpus (57)

• Correlated quantum phenomena in the strong spin-orbit regime
• Prediction and observation of the first antiferromagnetic topological insulator
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Topology of crystalline insulators and superconductors
• Progress and prospects in magnetic topological materials
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Axion Electrodynamics in Topological Materials
• Variety of magnetic topological phases in the (MnBi${}_2$Te${}_4$)(Bi${}_2$Te${}_3$)${}_m$ family
• Topological non-symmorphic crystalline insulators
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Magnetically Controllable Topological Quantum Phase Transitions in Antiferromagnetic Topological Insulator MnBi${}_2$Te${}_4$
• Enumeration of spin-space groups: Towards a complete description of symmetries of magnetic orders
• Topological Insulators from Group Cohomology
• Topological correspondence between magnetic space group representations
• Berry-phase description of Topological Crystalline Insulators
• Perspective on Metallic Antiferromagnets
• Axion Quasiparticles for Axion Dark Matter Detection
• MagneticTB: A package for tight-binding model of magnetic and non-magnetic materials
• Route Towards Dirac and Weyl Antiferromagnetic Spintronics
• Composite Dirac liquids: parent states for symmetric surface topological order
• Magnetic structure of GdBiPt: A candidate antiferromagnetic topological insulator
• Topological magnetic materials of the (MnSb${}_2$Te${}_4$)$\cdot$(Sb${}_2$Te${}_3$)${}_n$ van der Waals compounds family
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Topological magnetic crystalline insulators and co-representation theory
• Antiferromagnetic Chern insulators in non-centrosymmetric systems
• Topological classification and diagnosis in magnetically ordered electronic materials
• Tuning the magnetism and band topology through antisite defects in Sb doped MnBi4Te7
• Quantum phase transitions of a disordered antiferromagnetic topological insulator
• From an array of quantum wires to three-dimensional fractional topological insulators
• Model Hamiltonian and Time Reversal Breaking Topological Phases of Anti-ferromagnetic Half-Heusler Materials
• Interplay of local order and topology in the extended Haldane-Hubbard model
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Topology invisible to eigenvalues in obstructed atomic insulators
• Unusual change in the Dirac-cone energy band upon two-step magnetic transition in CeBi
• Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
• Coexistence of metallic edge states and anti-ferromagnetic ordering in correlated topological insulators
• Interplay of interactions, disorder and topology in the Haldane-Hubbard model
• Intrinsic magnetic topological insulators of the MnBi${}_2$Te${}_4$ family
• Transport properties of organic Dirac electron system α-(BEDT-TSeF)${}_2$I${}_3$
• Topological and magnetic phases with strong spin-orbit coupling on the hyperhoneycomb lattice
• Correlation Effects in Quadrupole Insulators: a Quantum Monte Carlo Study
• Antiferromagnetic topological insulator with selectively gapped Dirac cones
• Spontaneous symmetry breaking of an interacting Chern insulator on a topological square lattice
• Topological crystalline antiferromagnetic state in tetragonal FeS
• Aspects of symmetry and topology in the charge density wave phase of 1T-TiSe2
• Temperature-driven gapless topological insulator
• Interacting topological mirror excitonic insulator in one dimension
• Topological $Z_2$ invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group
• Dirac Fermions and Topological Phases in Magnetic Topological Insulator Films
• ${\mathcal{Z}}_2$ classification for a novel antiferromagnetic topological insulating phase in three-dimensional topological Kondo insulator
• $Z_2$ antiferromagnetic topological insulators with broken $C_4$ symmetry
• Magnetic and topological transitions in three-dimensional topological Kondo insulator
• Quantum spin Hall effect in bilayer honeycomb lattices with C-type antiferromagnetic order
• A New Magnetic Topological Quantum Material Candidate by Design
• Universal Role of Combined Symmetry for the Protection of the Dirac Cone in Antiferromagnetic Topological Insulators
• Topological properties of domain walls in antiferromagnetic topological insulators