Higher rank chirality and non-Hermitian skin effect in a topolectrical circuit

TL;DR

This paper demonstrates the realization of higher-rank chirality and non-Hermitian skin effects in a 2D topolectric circuit, revealing new boundary-localized modes and momentum-position locking phenomena with potential technological applications.

Contribution

It introduces the concept of rank-2 chirality and skin effects in non-Hermitian systems and experimentally verifies these phenomena in a topolectric circuit.

Findings

Confirmation of rank-2 non-Hermitian skin effect in a circuit

Observation of edge- and corner-localized skin modes

Detection of momentum-position locking response

Abstract

While chirality imbalances are forbidden in conventional lattice systems, non-Hermiticity can effectively avoid the chiral-doubling theorem to facilitate 1D chiral dynamics. Indeed, such systems support unbalanced unidirectional flows that can lead to the localization of an extensive number of states at the boundary, known as the non-Hermitian skin effect (NHSE). Recently, a generalized (rank-2) chirality describing a 2D robust gapless mode with dispersion $\omega=k_{x}k_{y}$ has been introduced in crystalline systems. Here we demonstrate that rank-2 chirality imbalances can be established in a non-Hermitian (NH) lattice system leading to momentum-resolved chiral dynamics, and a rank-2 NHSE where there are both edge- and corner-localized skin modes. We then experimentally test this phenomenology in a 2-dimensional topolectric circuit that implements a NH Hamiltonian with a long-lived rank-2 chiral mode. Using impedance measurements, we confirm the rank-2 NHSE in this system, and its manifestation in the predicted skin modes and a highly unusual momentum-position locking response. Our investigation demonstrates a circuit-based path to exploring higher-rank chiral physics, with potential applications in systems where momentum resolution is necessary, e.g., in beamformers and non-reciprocal devices.