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

In this work, the authors implement a crystalline rank-2 chiral modes by employing non-Hermitian dynamics. They showed the momentum-resolved dynamics and non-Hermitian skin effect associated with the rank-2 chirality both theoretically and experimentally. 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.

Automated summary

In this work, the authors successfully implement a crystalline rank-2 chiral modes using non-Hermitian dynamics. They demonstrate the momentum-resolved dynamics and non-Hermitian skin effect associated with rank-2 chirality both theoretically and experimentally. This study provides a circuit-based approach to explore higher-rank chiral physics and has potential applications in systems where momentum resolution is necessary.