Topological Transitions of Evanescent Waves
Abstract
We study the band structure of evanescent waves, that is, the decaying or growing solutions that live within the gaps of tight-binding Hamiltonians. Although the underlying Hamiltonian is Hermitian, these modes carry complex wavevectors and therefore exhibit a non-Hermitian dispersion. Using the transfer matrix formalism in one dimension, we show that, in addition to the standard exceptional points that appear at the band edges, a different type of exceptional point can arise inside the gap, protected by spinless time-reversal symmetry. Tuning model parameters drives a topological transition where such in-gap exceptional points are nucleated in pairs, mediated by a crossing between purely imaginary momentum branches. We show that this spectral structure is diagnosed by a ℤ2 index assigned to every energy inside the gap, with the in-gap exceptional points arising as its domain walls. A generic bound state in the system has a tail that is purely exponential when its energy lies between a band edge and the nearest exceptional point, but becomes oscillatory - with a wavevector differing from the band-edge momentum - when its energy lies between the pair of in-gap exceptional points. We illustrate these results using continuum and tight-binding models, as well as an anisotropic photonic crystal.
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BibTeX
@misc{pavez2026topological,
title = {{Topological Transitions of Evanescent Waves}},
author = {Ignacio Pavez and Tom Sheppard and Yoonseok Hwang and Hannah M. Price and Frank Schindler},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07038},
eprint = {2611.07038},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07038},
}
RIS
TY - UNPB
TI - Topological Transitions of Evanescent Waves
AU - Ignacio Pavez
AU - Tom Sheppard
AU - Yoonseok Hwang
AU - Hannah M. Price
AU - Frank Schindler
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07038
UR - https://arxiv.org/abs/2611.07038
AB - We study the band structure of evanescent waves, that is, the decaying or growing solutions that live within the gaps of tight-binding Hamiltonians. Although the underlying Hamiltonian is Hermitian, these modes carry complex wavevectors and therefore exhibit a non-Hermitian dispersion. Using the transfer matrix formalism in one dimension, we show that, in addition to the standard exceptional points that appear at the band edges, a different type of exceptional point can arise inside the gap, protected by spinless time-reversal symmetry. Tuning model parameters drives a topological transition where such in-gap exceptional points are nucleated in pairs, mediated by a crossing between purely imaginary momentum branches. We show that this spectral structure is diagnosed by a ℤ_2 index assigned to every energy inside the gap, with the in-gap exceptional points arising as its domain walls. A generic bound state in the system has a tail that is purely exponential when its energy lies between a band edge and the nearest exceptional point, but becomes oscillatory - with a wavevector differing from the band-edge momentum - when its energy lies between the pair of in-gap exceptional points. We illustrate these results using continuum and tight-binding models, as well as an anisotropic photonic crystal.
ER -