Semiclassical analysis for a Schr\"odinger operator with a U(2) artificial gauge: the periodic case
Abstract
We consider a Schr\"odinger operator with a Hermitian 2x2 matrix-valued potential which is lattice periodic and can be diagonalized smoothly on the whole Rn. In the case of potential taking its minimum only on the lattice, we prove that the well-known semiclassical asymptotic of first band spectrum for a scalar potential remains valid for our model.
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