The Joint Condensed Matter Seminar (JCMS) series is organised by KTH Royal Insitute of Technology, Nordita, and Stockholm University.
On Friday, November 18th, 2022 from 11 am to 12 am we will host a seminar by Patrick Lenggenhager from ETH, Zurich.
From a hyperbolic drum towards hyperbolic topological insulators
The recent development of hyperbolic band theory, which describes energy spectra of particles on hyperbolic lattices, revived interest in crystalline models embedded in negatively curved spaces and led to the emergence of hyperbolic lattices as a new paradigm of synthetic matter. A salient feature of hyperbolic band theory is the unusually large dimension of the momentum space: a two-dimensional hyperbolic lattice leads to an at least four-dimensional Brillouin zone. This potentially leads to novel types of topological matter. The theoretical interest has also sparked the search for suitable experimental realizations in different metamaterial platforms.
In this seminar, I will first give an introduction to the basic ideas of hyperbolic lattices and some of the subtleties arising before discussing two of our recent works. In the first, we experimentally realize an artificial hyperbolic space with constant negative curvature in an electric-circuit network and develop a set of methods to verify the effective hyperbolic metric [1]. More specifically, we consider the low-energy modes of a disk-shaped sample of a hyperbolic lattice, which we call “hyperbolic drum”, and reveal evidence of the negative curvature in both static and dynamical experiments. In the second, purely theoretical work, we take a first step towards analyzing topology in hyperbolic synthetic matter [2]. We formulate hyperbolic versions of two paradigmatic models of topological insulators, namely of (1) the Haldane model of a Chern insulator, and of (2) the Kane-Mele model of a time-reversal-symmetric topological insulator. Their non-trivial topology is revealed both in momentum space and real space invariants and we observe robust propagating metallic in-gap states at the boundary.
[1] P. M. Lenggenhager, A. Stegmaier, L. K. Upreti, T. Hofmann, T. Helbig, A. Vollhardt, M. Greiter, C. H. Lee, S. Imhof, H. Brand, T. Kießling, I. Boettcher, T. Neupert, R. Thomale, and T. Bzdušek, Nat. Commun. 13, 4373 (2022).
[2] D. M. Urwyler, P. M. Lenggenhager, I. Boettcher, R. Thomale, T. Neupert, and T. Bzdušek, arXiv:2203.07292 (2022).