Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders

Abstract

Non-Hermitian systems exhibit a distinctive phenomenon known as the non-Hermitian skin effect, where an extensive number of eigenstates become localized at the boundaries of a lattice with open boundaries. While the spectral winding number under periodic boundary conditions is a well-established topological indicator for predicting the skin effect in one-dimensional non-Hermitian systems, a suitable topological invariant to diagnose higher-order skin effects remains elusive. In this Letter, we propose a unified non-Hermitian multipole characterization framework that generalizes the concept of spectral winding to higher-order skin effects. Specifically, we develop a set of non-Hermitian multipole Bott indices capable of diagnosing skin effects of different orders. Our approach provides a comprehensive understanding of both first- and higher-order skin effects in non-Hermitian systems, offering new perspectives for exploring topological phenomena in non-Hermitian systems.

arXiv commentpublished in Phys. Rev. B 111, 155121 (2025)

References in corpus (57)

• Topological Insulators in Three Dimensions
• Topological Photonics
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Edge states and topological invariants of non-Hermitian systems
• Quantized Electric Multipole Insulators
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Topological phases of non-Hermitian systems
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Origin of Non-Hermitian Skin Effects
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Spawning rings of exceptional points out of Dirac cones
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• The Quantum-Mechanical Position Operator in Extended Systems
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Non-Hermitian Topological Invariants in Real Space
• Universal non-Hermitian skin effect in two and higher dimensions
• Reciprocal skin effect and its realization in a topolectrical circuit
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Higher-order non-Hermitian skin effect
• Observation of higher-order non-Hermitian skin effect
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Effective operator formalism for open quantum systems
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• A review of progress in the physics of open quantum systems: theory and experiment
• Observation of resonance trapping in an open microwave cavity
• PT-symmetric scattering in flow duct acoustics
• Experimental demonstration of an anisotropic exceptional point
• Effective non-Hermitian Hamiltonian and continuum shell model
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Hybrid skin-topological modes without asymmetric couplings
• Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
• Anomalous topological edge states in non-Hermitian piezophononic media
• Quantized classical response from spectral winding topology
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Detecting non-Bloch topological invariants in quantum dynamics
• Real-space representation of winding number for one-dimensional chiral-symmetric topological insulator
• Non-Hermitian physics without gain or loss: the skin effect of reflected waves
• Dimensional transmutation from non-Hermiticity
• Direct Measurement of Topological Properties of an Exceptional Parabola
• Non-Hermitian Chiral Skin Effect
• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Non-Hermitian Squeezed Polarons
• Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
• Bulk-boundary correspondence in point-gap topological phases
• Edge theory of non-Hermitian skin modes in higher dimensions
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Universal scalefree non-Hermitian skin effect near the Bloch point
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number