Chiral-symmetry breaking and degeneracy in Koch fractal geometries
Abstract
Fractal geometries provide a distinctive platform for controlling quantum interference, topology, and localization. We investigate the Su--Schrieffer--Heeger (SSH) model constructed on the Koch curve, where a triangular geometry enables additional same-sublattice hoppings that break chiral symmetry and modify the conventional topological behavior captured by a real-space local marker. Destructive interference within the triangular units produces a highly degenerate flat level at E=−t. Although this level originates from the local geometry, its degeneracy and spectral weight are controlled by the self-similar connectivity of the Koch curve. The hierarchy reduces the number of independent flat states and reorganizes the spectrum into an intricate distribution of energy levels. Our results reveal complementary roles for local triangular interference and global fractal connectivity in shaping the electronic properties of geometrically modified SSH chains.
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BibTeX
@misc{lage2026chiralsymmetry,
title = {{Chiral-symmetry breaking and degeneracy in Koch fractal geometries}},
author = {L. L. Lage and A. Latgé},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30007},
eprint = {2608.30007},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30007},
}
RIS
TY - UNPB
TI - Chiral-symmetry breaking and degeneracy in Koch fractal geometries
AU - L. L. Lage
AU - A. Latgé
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.30007
UR - https://arxiv.org/abs/2608.30007
AB - Fractal geometries provide a distinctive platform for controlling quantum interference, topology, and localization. We investigate the Su--Schrieffer--Heeger (SSH) model constructed on the Koch curve, where a triangular geometry enables additional same-sublattice hoppings that break chiral symmetry and modify the conventional topological behavior captured by a real-space local marker. Destructive interference within the triangular units produces a highly degenerate flat level at E=−t. Although this level originates from the local geometry, its degeneracy and spectral weight are controlled by the self-similar connectivity of the Koch curve. The hierarchy reduces the number of independent flat states and reorganizes the spectrum into an intricate distribution of energy levels. Our results reveal complementary roles for local triangular interference and global fractal connectivity in shaping the electronic properties of geometrically modified SSH chains.
ER -