Hidden quasi-symmetries stabilize non-trivial quantum oscillations in CoSi

Unlocking the exotic properties promised to occur in topologically non-trivial semi-metals requires significant fine-tuning. The scarcity of materials in which the topological anomalies occur at the chemical potential is a major obstacle towards their applications.

Here we show how quasi-symmetries stabilize near-degeneracies of bands over extended region in the Brillouin zone. Specifically, a quasi-symmetry is an exact symmetry of a lower-order Hamiltonian yet broken by higher-order terms. Hence quasi-symmetric points are gapped with a parametrically small gap which does not influence the physical properties of the system.

We demonstrate that in the eV-bandwidth semi-metal CoSi an internal quasi-symmetry stabilizes gaps below 2 meV over eight large near-degenerate planes (2D) [1]. This quasi-symmetry is key to explaining the surprising simplicity of the experimentally observed quantum spectrum. Untethered from the limitations of crystalline symmetry, quasi-symmetries eliminate the need for fine-tuning as the sources of large Berry curvature are pinned at the chemical potential, and thereby lead to new Wigner-Von Neumann classifications of solids. These results demonstrate a hidden classification framework for symmetry groups and materials in which quasi-symmetries are critical to understand the low-energy physics.