Liouvillian skin effects in two-dimensional electron systems at finite temperatures

TL;DR

This paper investigates Liouvillian skin effects in two-dimensional electron systems, revealing their dependence on temperature, dissipation, spin-orbit coupling, and magnetic fields, and highlighting their unique properties compared to previous skin effects.

Contribution

It demonstrates the existence of $ ext{Z}$ and $ ext{Z}_2$ Liouvillian skin effects in 2D electron systems and analyzes their temperature dependence and unique relaxation dynamics.

Findings

Liouvillian skin effects are observed due to dissipation, spin-orbit coupling, and magnetic fields.

Skin effects become prominent below the energy scale of band splitting.

Charge accumulation occurs under quench dynamics with size-independent relaxation time.

Abstract

Liouvillian skin effects, manifested as the localization of Liouvillian eigenstates around the boundary, are distinctive features of non-Hermitian systems and are particularly notable for their impact on system dynamics. Despite their significance, Liouvillian skin effects have not been sufficiently explored in electron systems. In this work, we demonstrate that a two-dimensional electron system on a substrate exhibits $\mathbb{Z}$ and $\mathbb{Z}_2$ Liouvillian skin effects due to the interplay among energy dissipations, spin-orbit coupling, and a transverse magnetic field. In addition, our analysis of the temperature dependence reveals that these Liouvillian skin effects become pronounced below the energy scale of band splitting induced by the spin-orbit coupling and the magnetic field. While our $\mathbb{Z}$ Liouvillian skin effect leads to charge accumulation under quench dynamics, its relaxation time is independent of the system size, in contrast to that of previously reported Liouvillian skin effects. This difference is attributed to the scale-free behavior of the localization length, which is analogous to non-Hermitian critical skin effects.