Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators

Abstract

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($\mathcal{T}$-) invariant (helical) 3D TCI$\unicode{x2014}$termed higher-order TCIs (HOTIs)$\unicode{x2014}$the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetals, and $\mathcal{T}$-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that $\beta$-MoTe${}_2$ realizes a spin-Weyl state and that $\alpha$-BiBr hosts both 3D QSHI and T-DAXI regimes.

arXiv commentFinal version: 22+146 pages, 8+44 figures. Nested and spin-resolved Wilson loop code with example scripts and documentation freely available at https://github.com/kuansenlin/nested_and_spin_resolved_Wilson_loop

References in corpus (83)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Anyons in an exactly solved model and beyond
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• WannierTools: An open-source software package for novel topological materials
• Quantum Spin Hall Effect
• Topological Crystalline Insulators
• Dissipationless Quantum Spin Current at Room Temperature
• Wannier90 as a community code: new features and applications
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Spin Transfer Torque Generated by the Topological Insulator Bi_2Se_3
• Topological Crystalline Insulators in the SnTe Material Class
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• 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
• The (High Quality) Topological Materials In The World
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Catalogue of Topological Electronic Materials
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Zoo of quantum-topological phases of matter
• Higher-Order Topology in Bismuth
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• High-throughput calculations of magnetic topological materials
• Hourglass Fermions
• Fermi level dependent charge-to-spin current conversion by Dirac surface state of topological insulators
• On A Proper Definition of Spin Current
• Fragile Topology and Wannier Obstructions
• Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator
• Robustness of the Spin-Chern number
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Layer Hall effect in a 2D topological Axion antiferromagnet
• Fractional topological insulators
• Quantitative mappings between symmetry and topology in solids
• Mapping topological order in coordinate space
• Magnetic Topological Quantum Chemistry
• Angle-resolved photoemission spectroscopy and its application to topological materials
• Towards a microscopic theory of toroidal moments in bulk periodic crystals
• Integer quantum Hall effect for bosons: A physical realization
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Topological Materials Discovery from Crystal Symmetry
• Material design with the van der Waals stacking of bismuth-halide chains realizing a higher-order topological insulator
• Surfaces of Axion Insulators
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Rotation Anomaly and Topological Crystalline Insulators
• The macroscopic monopolization in diagonal magnetoelectrics
• Experimental signature of parity anomaly in semi-magnetic topological insulator
• Evidence of Higher Order Topology in Multilayer WTe${}_2$ from Josephson Coupling through Anisotropic Hinge States
• Room-temperature quantum spin Hall edge state in a higher-order topological insulator Bi${}_4$Br${}_4$
• Edge modes in band topological insulators
• Observation of an edge supercurrent in the Weyl superconductor MoTe${}_2$
• Resolving the Topological Classification of Bismuth with Topological Defects
• Polar and phase domain walls with conducting interfacial states in a Weyl semimetal MoTe2
• Obstructed surface states as the origin of catalytic activity in inorganic heterogeneous catalysts
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Purely rotational symmetry-protected topological crystalline insulator $\alpha$-Bi4Br4
• Surface theorem for the Chern-Simons axion coupling
• Half quantum spin Hall effect on the surface of weak topological insulators
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Measurement of spin Chern numbers in quantum simulated topological insulators
• Axion coupling in the hybrid Wannier representation
• Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4
• Delocalization Transition of Disordered Axion Insulator
• Doubled Quantum Spin Hall Effect with High-Spin Chern Number in $\alpha$-Antimonene and $\alpha$-Bismuthene
• Spin-resolved electronic response to the phase transition in MoTe${}_2$
• Coincidence angle-resolved photoemission spectroscopy: Proposal for detection of two-particle correlations
• Spin Hall conductivity in insulators with non-conserved spin
• Distinguishing finite momentum superconducting pairing states with two-electron photoemission spectroscopy
• Twisted nodal wires and three-dimensional quantum spin Hall effect in distorted square-net compounds
• Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials
• Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Electromagnetic Response of Three-dimensional Topological Crystalline Insulators

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• Topological Nature of Orbital Chern Insulators
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• Quantum geometric bounds in spinful systems with trivial band topology
• Surface Reconstructions in Thin-Films of Magnetic Topological Insulator MnBi${}_2$Te${}_4$
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• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators
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• Coincidence detection techniques for direct measurement of many-body correlations in strongly correlated electron systems
• Non-magnetic layers with a single Dirac cone at high-symmetry point of the Brillouin zone
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure
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