Perfect flat band induced by strong spin-orbit coupling
Chisa Hotta
University of Tokyo
Friday, May 23, 2025
10:30 a.m.
In-person: QNC 1201
Abstract: We demonstrate that a perfect flat band can emerge in pyrochlore and kagome lattices when a strong spin-orbit coupling (SOC) is introduced. The SOC manifests as a spin-dependent hopping term, where electrons undergo rotations by an angle determined by the relative strengths of the spin-orbit-induced and ordinary transfer integrals. This type of hopping is described by an SU(2) gauge field. Using a spinor-line-graph framework, we prove the existence of a perfect flat band when the SU(2) gauge field takes specific values. Furthermore, we show that the wave function of the SOC-induced flat band stabilizes a trimerized charge ordering in the pyrochlore lattice when weak Coulomb interactions are present[1]. The driving mechanism behind this charge ordering is not Coulomb interaction itself but rather a destructive interference effect intrinsic to the flat band. This interference enforces 1/4 of the pyrochlore sites to become completely vacant, providing a natural explanation for the experimentally observed charge order in CsW2O4 [2]. Aside from flat bands, varying the SU(2) gauge field (i.e., the degree of SOC) can also give rise to a band structure with chiral symmetry. We explain the origin of this symmetry through the Wilson-loop operator, which characterizes the underlying gauge structure [3].
[1] H. Nakai and C. Hotta, Nature Comm. 13, 579 (2022)
[2] Y. Okamoto, et al., Nature Comm. 11, 3144 (2020)
[3] H. Nakai, M. Kawano, C. Hotta, Phys. Rev. B 108, L081106 (2023)