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On optimal Wannier decay in dimension three
Simon Becker, Zhongkai Tao, Mengxuan Yang
For a Chern nontrivial Bloch bundle over the three torus, we construct an orthonormal Wannier basis with the optimal pointwise decay . All but one of the g…
Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap
Simon Becker, Mengxuan Yang
We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentiall…
Wannier decay and the Thouless conjecture
Simon Becker, Zhongkai Tao, Mengxuan Yang
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…
Fragile topology on solid grounds: a mathematical perspective
Simon Becker, Zhongkai Tao, Mengxuan Yang
This paper provides a mathematical perspective on fragile topology phenomena in condensed matter physics. In dimension , vanishing Chern classes of bundles of Bloch eigen…
Dirac cones and magic angles in the Bistritzer--MacDonald TBG Hamiltonian
Simon Becker, Solomon Quinn, Zhongkai Tao +2
We demonstrate the generic existence of Dirac cones in the full Bistritzer--MacDonald Hamiltonian for twisted bilayer graphene. Its complementary set, when Dirac cones are absent,…