Skin effect in Non-Hermitian systems with spin

TL;DR

This paper investigates the influence of magnetic fields on the non-Hermitian skin effect in spinful systems, revealing magnetic control over skin modes and uncovering spin-dependent symmetry transitions.

Contribution

It introduces a comprehensive study of spinful non-Hermitian systems with magnetic fields, demonstrating magnetic induction of skin effects and spin-dependent symmetry transitions.

Findings

Magnetic fields induce a transition from bidirectional to unidirectional skin effect.

Magnetic fields can anomalously induce skin modes in topologically trivial systems.

Transition between non-Bloch PT and anti-PT symmetries depending on spin and magnetic field.

Abstract

The skin effect, where bulk modes collapse into boundary modes, is a key phenomenon in topological non-Hermitian systems, has been predominantly studied in spinless systems. Recent studies illustrate the magnetic suppression of the first-order skin effect while ignoring spin. However, the physical significance of a magnetic field in non-Hermitian skin effect with spin remains elusive. Here, we systematically explore non-Hermitian spinful systems based on generalized Hatano-Nelson models with SU(2) gauge potential fields. In an open one-dimensional lattice, the spin-up and spin-down states can be uniquely separated and localized at the two boundaries without magnetic field. When an external magnetic field is applied, the skin effect exhibits a smooth transition from bidirectional to unidirectional. Remarkably, we demonstrate that the first-order skin effect can be anomalously induced by a magnetic field in a topologically trivial non-Hermitian spinful system without any skin effect at zero field. The direction of such magnetically induced skin modes can be controlled by simply changing the amplitude and polarity of the magnetic field. In addition, we demonstrate a transition between non-Bloch PT and anti-PT symmetries in the system, and uncover the spindependent mechanism of non-Bloch PT symmetry. Our results pave the way for the investigation of non-Hermitian skin effect with spin degrees of freedom.