1. flat bands and band touching in hyperbolic lattices

Joseph Maciejko

University of Alberta, Canada

5 July 2022 Tue 10 am

                                      IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and in classical electric-circuit networks, we study flat bands and band-touching phenomena in such lattices [1]. We analyze noninteracting nearest-neighbor hopping models on hyperbolic analogs of the kagome and dice lattices with heptagonal and octagonal symmetry. We show that two characteristic features of the energy spectrum of those models, namely the fraction of states in the flat band as well as the number of touching points between the flat band and the dispersive bands, can both be captured exactly by a combination of real-space topology arguments and a reciprocal-space description via the formalism of hyperbolic band theory [2,3].

[1] T. Bzdušek and J. Maciejko, arXiv:2205.11571

[2] J. Maciejko and S. Rayan, Sci. Adv. 7, eabe9170 (2021)

[3] J. Maciejko and S. Rayan, Proc. Natl. Acad. Sci. U.S.A. 119, e2116869119 (2022)