2024/09/04 by A. Dagnino, Alberto Corticelli, Dagnino, A. K. +8 · 1 citation
Biochemistry, Genetics and Molecular Biology · Materials Science · Mathematics · Neuroscience · #DNA and Nucleic Acid Chemistry #FOS: Physical sciences #Geometry #Materials Science (cond-mat.mtrl-sci) #Mathematics #Photoreceptor and optogenetics research #Physics #Statistical physics #Strongly Correlated Electrons (cond-mat.str-el) #Supramolecular Self-Assembly in Materials #Symmetry (geometry) #Theoretical physics
paper · pdf · doi:10.48550/arxiv.2409.02999
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.