Emergence of Spin-Polarized Unconventional Skin Effect in Hatano-Nelson Model

Abstract: The non-Hermitian skin effect (NHSE), a hallmark of non-Hermitian systems, stems from the topological nature of complex energy spectra, typically characterized by a nonzero spectral winding number. By investigating a one-dimensional Hatano-Nelson model with spin-dependent Abelian gauge fields, we uncover a tunable, spin-polarized, unconventional NHSE with zero spectral winding, coexisting with a conventional one. These unconventional skin modes, emerging in the absence of pseudo time-reversal symmetry, display scale-restricted localization and non-Bloch spectral stability, distinguishing them from the Z2 and critical NHSEs. By introducing an external magnetic field that couples the spin degrees of freedom, these unconventional skin modes evolve into critical skin states. Meanwhile, conventional ones persist, but undergo a transition from bidirectional to unidirectional accumulation with increasing field strength. While distinct, remarkably, this unconventional NHSE manifests a more general behavior, with the Z2 and critical NHSEs emerging as specific limiting cases. Our results provide experimentally accessible predictions relevant to photonic lattices and ultracold atomic systems with synthetic gauge fields.