Quantum Matter Study Group invited Prof. Nobuyuki Okuma to give an online seminar about non-Hermitian topological phases. The seminar started with a succinct introduction to non-Hermitian matrices. Different from Hermitian systems, the energy spectra now become complex numbers, the bra and ket states become inequivalent, and the Hamiltonians are not always diagonalizable, leading to the emergence of exceptional points. Taking the Hatano-Nelson model as an example, the speaker studied the 1D chain with the imaginary gauge transformation and showed that the spectra strongly depend on the boundary conditions (being periodic or open). Furthermore, distinct from end modes in Hermitian topological insulators, skin effect arises in non-Hermitian systems, with skin modes accumulating in one end of the chain. He further showed that this skin effect also exhibits topological nature and can be generalized to either higher-dimensional systems or to other non-Hermitian systems with Z2 topological invariants.

Reported by Chen-Hsuan Hsu (YITP) and Ching-Kai Chiu