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arXiv · 2409.02999

The landscape of symmetry enhancement in tight-binding models

A. K. Dagnino·A. Corticelli·M. Gohlke·A. Mook·R. Moessner·P. A. McClarty
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Abstract

Band structures are ubiquitous in condensed matter physics and their symmetries constrain possible degeneracies, topology and response functions across a broad range of different systems. Here we address the question: given a parent crystal, what is the symmetry of hopping models on that lattice at a given shell number? We find that the parent structure does not, in general, determine the symmetry of the tight-binding model. Instead, the symmetry is dependent on the hopping range. The key to symmetry breakdown on the lattice is the existence of different {\it bond equivalence classes} whose number is related to group-subgroup indices for a broad classes of cases. We find all bond equivalence classes for $s$-wave hopping out to 20th neighbor across the different space groups and Wyckoff positions and the symmetries of the associated tight-binding models. These observations naturally lead to the definition of a {\it bond complex} $-$ the possible classes of networks of bonds to which symmetries may be enhanced from a given parent structure.

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A. K. Dagnino, A. Corticelli, M. Gohlke, A. Mook, R. Moessner, P. A. McClarty. 2024-09-04. The landscape of symmetry enhancement in tight-binding models. https://arxiv.org/abs/2409.02999

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