Spin-orbit coupling (SOC) plays an important role in generating novel quantum phases in condensed matter physics. We investigated the electron systems with strong SOC on the pyrochlore lattice based on the Kramers doublet, formed by the interplay between strong atomic SOC and crystal field. This doublets’ pseudospin is the mixture of electronic spin and orbital momentum so that it does not conserve when an electron hops between sites. This effect is described by the SU(2) hopping matrix that rotates the pseudospins. We vary its rotation angle as a parameter and discovered a flat band [1] and a chiral symmetry [2] for particular angles. To understand their origin, we pay attention to the SU(2) gauge degrees of freedom; there is a gauge redundancy in the representation of the Hamiltonian and the wave function in that we can freely change the pseudospin quantization axis at each site. The intrinsic physical quantities such as energy bands are invariant under such a local gauge transformation. We introduce the gauge invariants related to the Wilson loop operator and show that they characterize the band structures. These invariants are also used to construct the gauge transformation and the chiral operator to prove analytically the existence and mechanism of the flat band and chiral symmetry.
[1] HN and C. Hotta, Nat. Commun. 13, 579 (2022). [2] HN, M. Kawano, and C. Hotta, Phys. Rev. B 108, L081106 (2023).
SU(2) gauge field and band structures in strongly spin-orbit coupled electronic systems
Host: Hae-Young Kee