  The bulk-boundary correspondence is among the central issues of non-Hermitian
topological states. We show that a previously overlooked `non-Hermitian skin
effect' necessitates redefinition of topological invariants in a generalized
Brillouin zone. The resultant phase diagrams dramatically differ from the usual
Bloch theory. Specifically, we obtain the phase diagram of non-Hermitian
Su-Schrieffer-Heeger model, whose topological zero modes are determined by the
non-Bloch winding number instead of the Bloch-Hamiltonian-based topological
number. Our work settles the issue of the breakdown of conventional
bulk-boundary correspondence and introduces the non-Bloch bulk-boundary
correspondence.
