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.

我们构建了一个二维、离散时间的量子行走，在开放边界条件下表现出非厄米特皮肤效应。作为非厄米体边界对应的确认，我们表明拓扑边缘状态的出现与使用非布洛赫带理论计算的 Floquet 绕组数一致，调用时间相关的广义布里渊区。此外，与准能带相关的非布洛赫拓扑不变量由真实空间中的非厄米局部陈标记捕获，该标记通过非酉 Floquet 算子的局部双正交特征波函数定义。我们的工作旨在激发对皮肤效应起关键作用的非 Hermitian Floquet 拓扑相的进一步研究。