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.

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• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topology of density matrices
• From the adiabatic theorem of quantum mechanics to topological states of matter
• Effect of Strong Disorder on 3-Dimensional Chiral Topological Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of Topological Extended Bulk States
• A Non-Commutative Formula for the Isotropic Magneto-Electric Response
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
• Spontaneous loop-spin current with topological characters in the Hubbard model