[행사/세미나] [Seminar] July 11(Tue.) SU(2) gauge field and band structures in strongly spin-orbit coupled systems
- 물리학과
- 조회수2440
- 2023-07-07
다체계이론연구실에서 University of Tokyo 의 Hiroki Nakai 연사님을 초청하여 아래와 같이 세미나를 개최합니다.
학과 구성원 여러분의 많은 참여를 부탁 드립니다.
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○ Topic: SU(2) gauge field and band structures in strongly spin-orbit coupled systems
○ Speaker: Hiroki Nakai (University of Tokyo)
○ Date/time: 2023. 7. 11(Tue) 3:00 PM
○ Place: Natural Science 1, Room No.31355
○ Abstract: Spin-orbit coupling (SOC) plays an important role in generating novel quantum phases in condensed matter physics. We investigated the SOC electronic Hamiltonian 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 spins by an angle θ that depends on the materials, namely on the atomic SOC and crystal field. We vary θ as a parameter and discovered a flat band [1] and a chiral symmetry [2] for particular values of θ. 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. A naive interpretation of these transformations is that they allow us to choose an appropriate site-dependent quantization axis that simplifies the description of the originally spin-mixed representation of wave functions.
[1] HN and C. Hotta, Nat. Commun. 13, 579 (2022).
[2] HN, M. Kawano, and C. Hotta, arXiv:2208.07171 (2022).