For topologically nontrivial Bloch bundles, the paper constructs Wannier functions with optimal decay O(|x|^{-2}) in 2D (Thouless's conjecture, with full asymptotics) and new uniform decay O(|x|^{-7/3}) in 3D.
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Wannier decay and the Thouless conjecture
For topologically nontrivial Bloch bundles, the paper constructs Wannier functions with optimal decay O(|x|^{-2}) in 2D (Thouless's conjecture, with full asymptotics) and new uniform decay O(|x|^{-7/3}) in 3D.