Abstract
AbstractIn this chapter, we establish the non-Bloch band theory in a one-dimensional non-Hermitian tight-binding system. We show how to determine the generalized Brillouin zone for the complex Bloch wave number. From the generalized Brillouin zone, we can calculate the energy spectra, which reproduce the band structure in an open chain of this system. As examples, we apply our theory to some models, and we explain remarkable features of the generalized Brillouin zone. Furthermore, we also show the bulk-edge correspondence in the non-Hermitian Su-Schrieffer-Heeger model from the topological invariant defined by the generalized Brillouin zone.KeywordsNon-Bloch band theoryGeneralized Brillouin zoneBulk-edge correspondence
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