Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits

Abstract

Exploring topological phases in non-Hermitian systems has attracted significant recent attention. One intriguing question is how topological edge states compete with the non-Hermitian skin effect. Here, we report the experimental observation of corner states in a two-dimensional non-reciprocal rhombus honeycomb electric circuit. We construct non-reciprocal and non-Hermitian circuits by introducing current-direction resolved capacitance between two nodes depends on the current direction. Skin effect thus emerges due to the non-reciprocity and prevails in dragging the corner state into the bulk. The non-Bloch winding number defined in generalized Brillouin zone is adopted to characterize the topological phase transition. Interestingly, we find that the non-Bloch $Z_2$ Berry phase can serve as an invariant to describe the non-Hermitian topology. By tuning the non-reciprocal parameter, we observe unbalanced distribution of corner states emerging on two acute angles of the rhombus lattice, with the localization length of the left corner state increasing exponentially with the degree of non-reciprocity.

9 pages, 8 figures; Accepted by PRB

References in corpus (21)

• Topological Origin of Non-Hermitian Skin Effects
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Non-reciprocal phase transitions
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Topological phase transition in non-Hermitian quasicrystals
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Higher-order non-Hermitian skin effect
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Second-order topological non-Hermitian skin effects
• Gain and loss induced topological insulating phase in a non Hermitian electrical circuit
• Realization of the square-root higher-order topological insulator in electric circuits
• Topological insulators and semimetals in classical magnetic systems
• Square-root higher-order Weyl semimetals
• Observation of symmetry protected zero modes in topolectrical circuits
• Floquet second-order topological insulators in non-Hermitian systems
• System size dependent topological zero modes in coupled topolectrical chains
• Experimental realization of two-dimensional weak topological insulators
• Wannier-type photonic higher-order topological corner states induced solely by gain and loss
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry