Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits

Abstract

Non-Hermitian skin-edge states emerge only at one edge in one-dimensional nonreciprocal chains, where all states are localized at the edge irrespective of eigenvalues. The bulk topological number is the winding number associated with the complex energy spectrum, which is well defined for metals. We study non-Hermitian nonreciprocal systems in higher dimensions, and propose to realize them with the use of electric diode circuits. We first investigate one-dimensional interface states between two domains carrying different topological numbers, where all states are localized at the interface. They are a generalization of the skin-edge states. Then we generalize them into higher dimensions. We show that there emerge a rich variety of boundary states and interface states including surface, line and point states in three-dimensional systems. They emerge at boundaries of several domains carrying different topological numbers. The resulting systems are the first-order, second-order and third-order topological metals. Such states may well be observed by measuring the two-point impedance in diode circuits.

arXiv comment4 pages, 4 figures

References in corpus (38)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Edge states and topological invariants of non-Hermitian systems
• Complex Extension of Quantum Mechanics
• Higher-Order Topological Insulators
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Topolectrical circuits
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Edge states and topological phases in non-Hermitian systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Topologically protected midgap states in complex photonic lattices
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Non-Hermitian Delocalization and Eigenfunctions
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Topological invariance and global Berry phase in non-Hermitian systems
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• Minimal model for higher-order topological insulators and phosphorene
• Parity-time-symmetric topological superconductor
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Probing the Berry Curvature and Fermi Arcs of a Weyl Circuit
• Boundary Green functions of topological insulators and superconductors
• Edge states at the interface of non-Hermitian systems
• Topological nodal states in circuit lattice
• Effects of Non-Hermiticity on Su-Schrieffer-Heeger Defect States
• Nodal Manifolds Bounded by Exceptional Points on Non-Hermitian Honeycomb Lattices and Electrical-Circuit Realizations

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