Dynamical topological invariant for non-Hermitian Rice-Mele model

Abstract

We study a non-Hermitian Rice-Mele model without breaking time-reversal symmetry, with the non-Hermiticity arising from imbalanced hopping rates. The Berry connection, Berry curvature and Chern number are introduced in the context of biorthonormal inner product. It is shown that for a bulk system, although the Berry connection can be complex numbers, the Chern number is still quantized, as topological invariant. For an opened chain system, the mid-gap edge modes are obtained exactly, obeying the bulk-edge correspondence. Furthermore, we also introduce a local current in the context of biorthonormal inner product to measure the pumping charge generated by a cyclic adiabatic evolution. Analytical analysis and numerical simulation of the time evolution of the mid-gap states show that the pumping charge can be a dynamical topological invariant in correspondence with the Chern number. It indicates that the geometric concepts for Hermitian topological insulator can be extended to the non-Hermitian regime.

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• Topological pumping of edge states via adiabatic passage
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• Topological Anderson insulators in two-dimensional non-Hermitian disordered systems
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• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Unravelling the edge spectra of non-Hermitian Chern insulators
• Quantum mold casting for topological insulating and edge states
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• Nonadiabatic nonlinear non-Hermitian quantized pumping
• Semi-localization transition driven by a single asymmetrical tunneling
• A Hermitian bypass to the non-Hermitian quantum theory
• Topological quantum slinky motion in resonant extended Bose-Hubbard model
• Recurrence method in Non-Hermitian Systems