标题： 非厄米拓扑零模在平滑域壁上：精确解 显示英文标题

标题： Nonhermitian topological zero modes at smooth domain walls: Exact solutions

摘要： 体-边界对应关系预测了拓扑非平凡系统边缘处局域化的边界模式的存在。 厄米边界模式的波函数可以作为修改后的杰基夫-雷比方程的本征态获得。 最近，体-边界对应关系已被扩展到非厄米系统，这些系统描述了开放和非平衡系统中的增益和损耗等物理现象。 非厄米能谱可以是复数值的，并且在复平面上表现出点隙或线隙，无论这些间隙是否可以分别连续变形为点或线。 具体来说，线隙非厄米系统可以连续变形为厄米隙谱。 在这里，我们通过在非厄米区域内求解广义的杰基夫-雷比方程，找到了位于拓扑不同相之间平滑区域边界上零能量非厄米边界模式的波函数的解析形式。 此外，我们揭示了标量场与边界模式的衰减率和振荡波长之间的普遍关系。 这种关系以实验上可测量的物理量来量化非厄米线隙系统中的体-边界对应关系，并且不受标量场空间依赖性的细节影响。 这些发现为非厄米和拓扑非平凡物质状态中边界模式的局域化特性提供了一些新的见解。 显示英文摘要

摘要： The bulk-boundary correspondence predicts the existence of boundary modes localized at the edges of topologically nontrivial systems. The wavefunctions of hermitian boundary modes can be obtained as the eigenmode of a modified Jackiw-Rebbi equation. Recently, the bulk-boundary correspondence has been extended to nonhermitian systems, which describe physical phenomena such as gain and loss in open and non-equilibrium systems. Nonhermitian energy spectra can be complex-valued and exhibit point gaps or line gaps in the complex plane, whether the gaps can be continuously deformed into points or lines, respectively. Specifically, line-gapped nonhermitian systems can be continuously deformed into hermitian gapped spectra. Here, we find the analytical form of the wavefunctions of nonhermitian boundary modes with zero energy localized at smooth domain boundaries between topologically distinct phases, by solving the generalized Jackiw-Rebbi equation in the nonhermitian regime. Moreover, we unveil a universal relation between the scalar fields and the decay rate and oscillation wavelength of the boundary modes. This relation quantifies the bulk-boundary correspondence in nonhermitian line-gapped systems in terms of experimentally measurable physical quantities and is not affected by the details of the spatial dependence of the scalar fields. These findings shed some new light on the localization properties of boundary modes in nonhermitian and topologically nontrivial states of matter.