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arXiv · 2504.07098

Nonhermitian topological zero modes at smooth domain walls: Exact solutions

Pasquale Marra·Angela Nigro
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Abstract

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 eigenmodes of a modified Jackiw-Rebbi equation. The bulk-boundary correspondence has also 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 through physical quantities that are experimentally measurable. Furthermore, this relation is not affected by the specific spatial variations of the scalar fields. These results offer new insights into the localization properties of boundary modes in nonhermitian and topologically nontrivial states of matter.

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Pasquale Marra, Angela Nigro. 2026-02-13. Nonhermitian topological zero modes at smooth domain walls: Exact solutions. https://doi.org/10.1093/ptep%2Fptaf158

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