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.
Keywords
Cite
@article{arxiv.1804.09975,
title = {Dynamical topological invariant for non-Hermitian Rice-Mele model},
author = {R. Wang and X. Z. Zhang and Z. Song},
journal= {arXiv preprint arXiv:1804.09975},
year = {2018}
}