Manipulating the non-Hermitian skin effect via electric fields

In non-Hermitian systems, the phenomenon that the bulk-band eigenstates are accumulated at the boundaries of the systems under open boundary conditions is called the non-Hermitian skin effect (NHSE), which is one of the most iconic and important features of a non-Hermitian system. In this work, we investigate the fate of the NHSE in the presence of electric fields by analytically calculating the dynamical evolution of an initial bulk state and numerically computing the spectral winding number and the distributions of eigenstates, as well as the dynamical evolutions. We show abundant manipulation effects of dc and ac fields on the NHSE and that the physical mechanism behind these effects is the interplay between the Stark localization, dynamic localization, and the NHSE. In addition, the finite size analysis of the non-Hermitian system with a pure dc field shows the phenomenon of size-dependent NHSE. We further propose a scheme to realize the discussed model based on an electronic circuit. The results will help to deepen the understanding of the NHSE and its manipulation.