Approximate symmetries and conservation laws in topological insulators and associated $\mathbb{Z}$-invariants

Abstract

Solid state systems with time reversal symmetry and/or particle-hole symmetry often only have ${\mathbb{Z}}_2$-valued strong invariants for which no general local formula is known. For physically relevant values of the parameters, there may exist approximate symmetries or almost conserved observables, such as the spin in a quantum spin Hall system with small Rashba coupling. It is shown in a general setting how this allows to define robust integer-valued strong invariants stemming from the complex theory, such as the spin Chern numbers, which modulo $2$ are equal to the ${\mathbb{Z}}_2$-invariants. Moreover, these integer invariants can be computed using twisted versions of the spectral localizer.

arXiv commentadded references, minor improvements, appeared in Annals of Physics

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Cited by in corpus (5)

• Local invariants identify topology in metals and gapless systems
• Local markers for crystalline topology
• Invariants of disordered semimetals via the spectral localizer
• Spectral localizer for line-gapped non-hermitian systems
• Real-space topological localizer index to fully characterize the dislocation skin effect