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

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.

arXiv comment12+8 pages, 5+6 figures

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• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Percolation-induced PT symmetry breaking
• Kinked linear response from non-Hermitian cold-atom pumping
• Engineering topological states and quantum-inspired information processing using classical circuits
• Crystalline-electromagnetic responses of higher order topological semimetals
• Harnessing Nonlinearity to Tame Wave Dynamics in Nonreciprocal Active Systems
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Phase transitions of wave packet dynamics in disordered non-Hermitian systems
• Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices
• Proposal for realizing unpaired Weyl points in a three-dimensional periodically driven optical Raman lattice
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials