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23 April 2024 |
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Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases | | Anffany Chen
; Hauke Brand
; Tobias Helbig
; Tobias Hofmann
; Stefan Imhof
; Alexander Fritzsche
; Tobias Kießling
; Alexander Stegmaier
; Lavi K. Upreti
; Titus Neupert
; Tomáš Bzdušek
; Martin Greiter
; Ronny Thomale
; Igor Boettcher
; | | Date: |
10 May 2022 | | Abstract: | We introduce and experimentally realize hyperbolic matter as a novel paradigm
for topological states, made of particles moving in the hyperbolic plane with
negative curvature. Curvature of space is emulated through a hyperbolic lattice
using topolectrical circuit networks relying on a newly developed complex-phase
circuit element. This original method creates an effectively infinite
hyperbolic space without the typical extensive holographic boundary -- our
system consists of pure bulk matter instead. The experiment is based on
hyperbolic band theory, which implies that momentum space of two-dimensional
hyperbolic matter is four-, six- or higher-dimensional, as we confirm here in
an unprecedented numerical survey of hyperbolic lattices with both open and
periodic boundary conditions. We experimentally realize hyperbolic graphene as
an example of topologically nontrivial hyperbolic matter. Our work sets the
stage to realize interacting hyperbolic matter to challenge our established
theories of physics in curved space, while the tunable complex-phase element
developed here can be a key ingredient for future experimental simulation of
various Hamiltonians with topological ground states. | | Source: | arXiv, 2205.05106 | | Services: | Forum | Review | PDF | Favorites | |
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