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Non-Hermitian Boundary Modes
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We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary co-dimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green functions, we outline a generic perspective on the appearance of such modes and generate corresponding dispersion relations. In the process, we explain the skin effect in both topological and non-topological systems, exhaustively generalizing bulk-boundary correspondence in the presence of non-Hermiticity. This is accomplished via a doubled Green's function, inspired by doubled Hamiltonian methods used to classify Floquet and, more recently, non-Hermitian topological phases. Our work constitutes a general tool, as well as, a unifying perspective for this rapidly evolving field. Indeed, as a concrete application we find that our method can expose novel non-Hermitian topological regimes beyond the reach of previous methods.
Forward citations
Cited by 7 Pith papers
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Reciprocal skin effect and its realization in a topolectrical circuit
A reciprocal non-Hermitian 2D lattice shows skin-mode localization on opposite edges for opposite momenta, demonstrated experimentally in a passive RLC circuit.
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Non-Hermitian losses in anomalous Floquet insulators let boundary states detach from bulk bands and be engineered independently, enabling new chiral and directional edge transport.
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Generalized bulk-edge correspondence for non-hermitian topological systems
A modified periodic boundary condition with a decay parameter b makes the bulk-edge correspondence work for a non-Hermitian SSH model in an enlarged parameter space.
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Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
Bulk wave-packet dynamics, through the drift-velocity dependence of the Lyapunov exponent, can reveal the non-Hermitian skin effect and non-Bloch symmetry-breaking transitions.
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Non-Hermitian Floquet topological phases in the double-kicked rotor
The non-Hermitian double kicked rotor hosts Floquet topological phases labeled by two winding numbers, detectable by a generalized mean chiral displacement, with edge states counted by the bulk invariants.
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Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems
The topology of certain one-dimensional non-Hermitian chains is captured by a Chern number of an effective two-dimensional Hermitian Hamiltonian, and this hidden Chern number predicts zero-real-energy end states.
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Perspective on topological states of non-Hermitian lattices
A perspective review that attributes defectiveness in non-Hermitian lattices to boundary conditions of a hypothetical Hermitian parent system.
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