Two-Dimensional Quantum Walk with Non-Hermitian Skin EffectsSupported by the National Natural Science Foundation of China (Grant Nos. 11974331, 11674306, and 61590932), and the National Key R&D Program (Grant Nos. 2016YFA0301700 and 2017YFA0304100).

Abstract

We construct a two-dimensional, discrete-time quantum walk, exhibiting non-Hermitian skin effects under open-boundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states is consistent with the Floquet winding number, calculated using a non-Bloch band theory, invoking time-dependent generalized Brillouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined via the local biorthogonal eigenwave functions of a non-unitary Floquet operator. Our work aims to stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.