Biorthogonal topological charge pumping in non-Hermitian systems

Abstract

We study charge pumping in generic non-Hermitian settings and show that quantized charge pumping is only guaranteed under a biorthogonal formalism therein, where the charge transport is evaluated using the left and right eigenvectors of the non-Hermitian Hamiltonian. Specifically, for biorthogonal charge pumping in generic one-dimensional non-Hermitian models, we demonstrate how quantized transport is related to the Chern number in the parameter space. When the non-Hermitian model possesses the non-Hermitian skin effect, under which Bloch states in the bulk are deformed and localize toward boundaries, we propose a scenario where the pumped charge is related to the non-Bloch Chern number defined in the parameter space involving the generalized Brillouin zone. We illustrate the validity of our analytic results using concrete examples and, in the context of the biorthogonal charge pumping, discuss in detail a recent experiment where quantized charge pumping was observed in a lossy environment.

arXiv commentAccepted for publication in Physical Review B

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• Characterizing topological pumping of charges in exactly solvable Rice-Mele chains of the non-Hermitian variety
• Adiabatic charge transport through non-Bloch bands
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Survival of Hermitian Criticality in the Non-Hermitian Framework