Quasi-symmetry protected topology in semi-metal

The crystal symmetry dictates the type of topological band structures it may host, hence it is the principle guiding the search for topological materials. Here we present a different type of topological matter, in which approximate symmetries stabilize near-degeneracies of bands. Specifically, we coin “quasi-symmetry” as a term for an exact symmetry of a Hamiltonian to lower-order yet is broken by higher-order perturbation terms. This enforces finite but parametrically small gaps at low-symmetry k-points across the whole Brillouin zone, eliminating the need for fine-tuning as the sources of large Berry curvature will occur at any arbitrary chemical potentials.



We demonstrate that in the eV-bandwidth semi-metal CoSi an internal quasi-symmetry stabilizes gaps below 2 meV on eight large near-degenerate planes (2D) [1]. The true, symmetry-protected topological degeneracies of CoSi [2] are easily gapped by weak strain, evidenced by new magnetic breakdown orbits. In contrast, the quasi-symmetry does not depend on spatial symmetries and therefore transmission remains fully coherent.



This remarkable resilience of quasi-symmetry to perturbations may lead to more robust topological applications. Thereby, it promises to extend the scope of topology to materials beyond the usual crystalline symmetry classifications.

[1] C. Y. Guo, L. Hu, C. Putzke et al., Nat. Phys. 18, 813–818 (2022).

[2] N. Huber, K. Alpin, G. L. Causer et al., Phys. Rev. Lett. 129, 026401 (2022).