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arXiv · 2505.01999

Wannier decay and the Thouless conjecture

Simon Becker·Zhongkai Tao·Mengxuan Yang
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Abstract

Non-trivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions which provide natural bases for spectral subspaces. For non-trivial Bloch bundles, we obtain decay rates of Wannier functions in dimensions $d=2,3$. For $d=2$, we construct Wannier functions with full asymptotics and optimal decay rate $\mathcal{O}(|x|^{-2})$ as conjectured by Thouless; for $d=3$, we construct Wannier functions with the uniform decay rate $\mathcal{O}(|x|^{-7/3})$.

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Simon Becker, Zhongkai Tao, Mengxuan Yang. 2025-05-04. Wannier decay and the Thouless conjecture. https://arxiv.org/abs/2505.01999

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