Manifestly gauge independent formulations of the Z2 invariants

Abstract

We use a "monodromy" argument to derive new expressions for the ${\mathbf{Z}}_2$ invariants of topological insulators with time-reversal symmetry in 2 and 3 dimensions. The derivations and the final expressions do not require any gauge choice and the calculation of the invariants is based entirely on the projectors onto the occupied states. Explicit numerical tests for tight-binding models with strongly broken inversion symmetry are presented in 2 and 3-dimensions.

References in corpus (31)

• 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
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Model Hamiltonian for Topological Insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Wannier representation of Z_2 topological insulators
• Well-localized edge states in two-dimensional topological insulators: ultrathin Bi films
• Half-Heusler Compounds as a New Class of Three-Dimensional Topological Insulators
• Quantum spin Hall effect in three dimensional materials: Lattice computation of Z${}_2$ topological invariants and its application to Bi and Sb
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Helical edge and surface states in HgTe quantum wells and bulk insulators
• Half-Heusler Topological Insulators: A First-Principle Study with the Tran-Blaha Modified Becke-Johnson Density Functional
• Three-Dimensional Topological Insulators in I-III-VI${}_2$ and II-IV-V${}_2$ Chalcopyrite Semiconductors
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Triviality of Bloch and Bloch-Dirac bundles
• Equivalent topological invariants of topological insulators
• Chern-Simons orbital magnetoelectric coupling in generic insulators
• Topological insulators beyond the Brillouin zone via Chern parity
• Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells
• Disorder-Induced Multiple Transition involving Z2 Topological Insulator
• Mapping the braiding properties of the Moore-Read state
• The edge spectrum of Chern insulators with rough boundaries
• Topological phonon modes in filamentous structures
• An edge index for the Quantum Spin-Hall effect

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• Time Reversal Symmetric Topological Exciton Condensate in Bilayer HgTe Quantum Wells
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• ${\mathbb{Z}}_2$ invariants of topological insulators as geometric obstructions
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• Effect of Strong Disorder on 3-Dimensional Chiral Topological Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of Topological Extended Bulk States
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• Proximity-induced topological phases in bilayer graphene
• A Non-Commutative Formula for the Isotropic Magneto-Electric Response
• Gauge-theoretic invariants for topological insulators: A bridge between Berry, Wess-Zumino, and Fu-Kane-Mele
• Spin Conductance and Spin Conductivity in Topological Insulators: Analysis of Kubo-like terms
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
• Spontaneous loop-spin current with topological characters in the Hubbard model