Manifestly gauge independent formulations of the Z2 invariants

TL;DR

This paper introduces gauge-independent formulas for Z2 topological invariants in 2D and 3D topological insulators, simplifying calculations by relying solely on projectors onto occupied states, and validates these formulas through numerical tests.

Contribution

It provides the first gauge-independent expressions for Z2 invariants using a monodromy approach, applicable to models with broken inversion symmetry.

Findings

Derived explicit gauge-independent formulas for Z2 invariants.

Validated formulas with numerical tests on tight-binding models.

Applicable to systems with strong inversion symmetry breaking.

Abstract

We use a "monodromy" argument to derive new expressions for the ${\bm Z}_2$ 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.