Liouvillian Skin Effects and Relaxation Dynamics in Two-Dimensional Electron Systems

In recent years, non-Hermiticity of open quantum systems has attracted considerable attention. Such systems are described by quantum master equations whose generator, the Liouvillian, is non-Hermitian. This non-Hermiticity gives rise to topological phenomena absent in Hermitian systems [1]. In particular, the Liouvillian skin effect, where eigenmodes localize at an edge according to the spectral topology of the Liouvillian [2,3], has been intensively studied, as it causes anomalous dependencies of relaxation times on the localization length and system size [4]. Although electron systems in solids are inherently open due to coupling with environments, previous studies have mainly focused on synthetic platforms [4].

In this talk, we analyze a quantum master equation for a 2D electron system and show that Z and Z₂ Liouvillian skin effects emerge from the interplay of dissipation, spin-orbit coupling, and a transverse magnetic field [5]. We further analyze how the localization length affects the relaxation dynamics, as well as clarifying the roles of the Fermi surface and temperature effects [5].

 

[1] Z. Gong et al., PRX 8, 031079 (2018).

[2] S. Yao and Z. Wang, PRL 121, 086803 (2018).

[3] N. Okuma et al., PRL 124, 086801 (2020).

[4] T. Haga et al., PRL 127, 070402 (2021).

[5] Y. Shigedomi and T. Yoshida, arXiv:2505.18001.