Abstract.
In the framework of the theory of an electron in a periodic potential, we reconsider the longstanding problem of the existence of smooth and periodic quasi-Bloch functions, which is shown to be equivalent to the triviality of the Bloch bundle. By exploiting the time-reversal symmetry of the Hamiltonian and some bundle-theoretic methods, we show that the problem has a positive answer in any dimension d ≤ 3, thus generalizing a previous result by G. Nenciu. We provide a general formulation of the result, aiming at the application to the Dirac equation with a periodic potential and to piezoelectricity.
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Communicated by Vincent Rivasseau.
Submitted: October 5, 2006. Accepted: November 11, 2006.
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Panati, G. Triviality of Bloch and Bloch–Dirac Bundles. Ann. Henri Poincaré 8, 995–1011 (2007). https://doi.org/10.1007/s00023-007-0326-8
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DOI: https://doi.org/10.1007/s00023-007-0326-8