Helical damping and dynamical critical skin effect in open quantum systems

Non-Hermitian skin effect and critical skin effect are unique features of non-Hermitian systems. In this work, we explore novel phenomena associated with the Z₂ skin effect and critical skin effect in open quantum systems. For the open system with the corresponding damping matrix exhibiting Z₂ skin effect, we identify the existence of helical damping, characterized by the evolution of relative particle number with exponentially and algebraically decreasing intervals distinguished by sharp wave fronts with opposite propagation directions. When the time-reversal symmetry is broken by adding perturbations, we find the occurrence of dynamical critical skin effect, which causes the disappearance of the helical damping in the thermodynamic limit although it can survive in small size systems. We also demonstrate the existence of anomalous critical skin effect when we couple two identical systems with Z₂ skin effect. With the help of non-Bloch band theory, we unveil that the change of generalized Brillouin zone equation is the origin of critical skin effect.