Generalized Brillouin zone of non-Hermitian continuum systems

Recently, it has been found that the principle of bulk-boundary correspondence is dramatically revised in non-Hermitian systems. According to the conventional bulk-boundary correspondence, the topological boundary modes of a Hermitian band insulator are generally determined by topological invariants defined in the Brillouin zone; the non-Hermitian bulk-boundary correspondence, however, relies on topological invariants defined in the generalized Brillouin zone (GBZ). While the GBZ has been successfully applied to characterize various non-Hermitian lattice models, its formulation and significance in non-Hermitian continuum systems have been unclear so far. Here, we generalize the GBZ theory to continuum systems and demonstrate its applications. As an illustration, we show an efficient GBZ-based calculation of the band gaps.