Nobuyuki Okuma

Yukawa Institute for Theoretical Physics
Kyoto University
Japan

Physical interpretation of non-Hermitian topology

Non-Hermiticity gives a novel topological-insulator classification when the gap of a Hamiltonian H is defined as the point gap, i.e. det H≠0. Although the classification under fundamental symmetries has been completed, its physical meaning is still unclear. In light of the situation, we give physical interpretations of the non-Hermitian topology. We find that there are two types of point-gap topological invariants; one detects the conventional bulk-boundary correspondence, while the other one does the non-Hermitian skin effect, in which the bulk spectrum depends on the boundary condition. Our analysis based on the spectral theory of semi-infinite space, including the Toeplitz index theorem, gives a unified understanding of seemingly different phenomena. As a benefit of our theory, we find the ℤ₂ skin effect protected by the time-reversal symmetry.