Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases

TL;DR

This paper introduces hyperbolic matter in electrical circuits with tunable complex phases, experimentally realizing topological states in hyperbolic lattices and confirming hyperbolic band theory through numerical surveys.

Contribution

It presents the first experimental realization of hyperbolic matter using topolectrical circuits with complex-phase elements, advancing the simulation of curved space physics.

Findings

Successful implementation of hyperbolic graphene as topologically nontrivial hyperbolic matter

Confirmation of hyperbolic band theory in finite hyperbolic lattices

Development of tunable complex-phase circuit elements for simulating Hamiltonians

Abstract

Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be simulated with hyperbolic lattices. Here we introduce and experimentally realize hyperbolic matter as a paradigm for topological states through topolectrical circuit networks relying on a complex-phase circuit element. The experiment is based on hyperbolic band theory that we confirm here in an unprecedented numerical survey of finite hyperbolic lattices. We implement hyperbolic graphene as an example of topologically nontrivial hyperbolic matter. Our work sets the stage to realize more complex forms of 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.