Exact mobility edges in finite-height Wannier-Stark ladders

Xingbo Wei, Liangqing Wu, Kewei Feng, Tong Liu, Yunbo Zhang
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)
2023-08-28 16:00:00
We investigate the single-particle localization transition in one-dimensional Wannier-Stark ladders with either a linear potential or a mosaic potential with spacing $\kappa=2$. In both cases, we exactly determine the mobility edges separating the Wannier-Stark localized states from extended states for a finite potential height. Especially in the latter case, we obtain mobility edges through a revised Lyapunov exponent, and demonstrate a rich phase diagram with extended states, weakly Wannier-Stark localized states, and strongly Wannier-Stark localized states. Our results also exhibit that mobility edges are highly dependent on the height of the ladder and extended states only survive at $E\approx0$ for the high ladder. Finally, we perform the simulation of the dynamical evolution for possible experimental observations. These interesting features will shed light on the study of localization phenomena in disorder-free systems.
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