Quasi-symmetry protected topology in a semi-metal

TL;DR

This paper introduces the concept of quasi-symmetry, a guiding principle for topological materials that is less dependent on crystal symmetry, demonstrated through its stabilization of gaps in a semi-metal and resilience to perturbations.

Contribution

It presents the novel concept of quasi-symmetry, showing how it stabilizes topological features in semi-metals independently of spatial symmetries.

Findings

Quasi-symmetry stabilizes small gaps in CoSi over a large momentum space region.

In-plane strain breaks crystal symmetry but preserves quasi-symmetry, maintaining coherence.

Quasi-symmetry enables topological features resilient to symmetry-breaking perturbations.

Abstract

The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we call 'quasi-symmetry'. This is the situation where a Hamiltonian has an exact symmetry at lower-order that is broken by higher-order perturbation terms. This enforces finite but parametrically small gaps at some low-symmetry points in momentum space. Untethered from the restraints of symmetry, quasi-symmetries eliminate the need for fine-tuning as they enforce that sources of large Berry curvature will occur at arbitrary chemical potentials. We demonstrate that a quasi-symmetry in the semi-metal CoSi stabilizes gaps below 2 meV over a large near-degenerate plane that can be measured in the quantum oscillation spectrum. The application of in-plane strain breaks the crystal symmetry and gaps the degenerate point, observable by new magnetic breakdown orbits. The quasi-symmetry, however, does not depend on spatial symmetries and hence transmission remains fully coherent. These results demonstrate a class of topological materials with increased resilience to perturbations such as strain-induced crystalline symmetry breaking, which may lead to robust topological applications as well as unexpected topology beyond the usual space group classifications.