Critical non-Hermitian skin effect induced by boundary defects

The non-Bloch band theory, which gives the conditions for obtaining the generalized Brillouin zone, has been proven to be effective in one-dimensional (1D) non-Hermitian systems. On the other hand, the generalization of the non-Bloch band theory to two- and higher-dimensional non-Hermitian systems is nontrivial. In this work, we study a class of representative two-dimensional models for which the non-Bloch band theory can be constructed by reducing the problem to that for 1D models. In particular, we show that the energy spectrum of this class of models undergoes discontinuous transitions when a few lattice sites are removed from the boundaries of the system to slightly change its geometry, and importantly, this process accompanies the modification of the non-Bloch band theory. We apply the non-Bloch band theory to elaborate the mechanism of this new type of critical non-Hermitian skin effect, which distinguishes it from the critical non-Hermitian skin effect induced by transverse couplings between two chains studied in previous work.