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arXiv · 2303.01966

Upper bound of a band complex

Si Li·Zeying Zhang·Xukun Feng·Weikang Wu·Zhi-Ming Yu·Y. X. Zhao·Yugui Yao·Shengyuan A. Yang
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Abstract

Band structure for a crystal generally consists of connected components in energy-momentum space, known as band complexes. Here, we explore a fundamental aspect regarding the maximal number of bands that can be accommodated in a single band complex. We show that in principle a band complex can have no finite upper bound for certain space groups. It means infinitely many bands can entangle together, forming a connected pattern stable against symmetry-preserving perturbations. This is demonstrated by our developed inductive construction procedure, through which a given band complex can always be grown into a larger one by gluing a basic building block to it. As a by-product, we demonstrate the existence of arbitrarily large accordion type band structures containing $N_C=4n$ bands, with $n\in\mathbb{N}$.

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Si Li, Zeying Zhang, Xukun Feng, Weikang Wu, Zhi-Ming Yu, Y. X. Zhao, Yugui Yao, Shengyuan A. Yang. 2023-03-03. Upper bound of a band complex. https://doi.org/10.1103/physrevb.107.235145

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