Anomalous time-reversal symmetric non-Hermitian systems

The conditions for the emergence of the non-Hermitian skin effect, as a unique physical response of non-Hermitian systems, have now become one of the hot research topics. In this paper, we study the novel physical responses of non-Hermitian systems with anomalous time-reversal symmetry, in both one dimension and two dimensions. Specifically, we focus on whether the systems will exhibit a non-Hermitian skin effect. We employ the theory of generalized Brillouin zone and also numerical methods to show that the anomalous time-reversal symmetry can prevent the skin effect in one-dimensional non-Hermitian systems, but is unable to exert the same effectiveness in two-dimensional cases.