Bulk-boundary correspondence is the cornerstone of topological physics. In some non-Hermitian topological system this fundamental relation is broken in the sense that the topological number calculated for the Bloch energy band under the periodic boundary condition fails to reproduce the boundary properties under the open boundary. To restore the bulk-boundary correspondence in such non-Hermitian systems a framework beyond the Bloch band theory is needed. We develop a non-Hermitian Bloch band theory based on a modified periodic boundary condition that allows a proper description of the bulk of a non-Hermitian topological insulator in a manner consistent with its boundary properties. Taking a non-Hermitian version of the Su-Schrieffer-Heeger model as an example, we demonstrate our scenario, in which the concept of bulk-boundary correspondence is naturally generalized to non-Hermitian topological systems.
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