ARPES study on the quasi-symmetry protected gap of GdBiTe

During the past decades, the infusion of topological concepts into the realm of electronic dispersions has ignited the curiosity of condensed-matter physics, unleashing a surge of novel research avenues. Given the intricate interplay between crystalline symmetry and band topology, it stands to reason that symmetry should serve as our guiding compass in the quest for new materials. In an effort to underscore the significance of approximate symmetries as an additional concept, Guo et al. adopt the term ‘quasi-symmetry’ to denote a special type of approximate symmetry of electronic band structures that emerges from the hierarchy of a k∙p type of perturbation expansion around a high-symmetry point. As shown in Figure 1, the Hamiltonian itself does not commute with the symmetry operation, yet its first-order perturbation does. Although the quasi-symmetry is broken by the higher-order perturbation terms, the resulting gap size is negligible, which is sufficient to depict the essential physics and gives rise to exotic physical properties. For instance, in the case of the semimetal CoSi, quasi-symmetry bestows stability upon a nearly degenerate nodal plane (below 2 meV), engendering substantial Berry curvatures. Nonetheless, the direct spectroscopic evidence of the quasi-symmetry protected Dirac cone is still absent.