Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice II. impurities, confinement and Bloch oscillations

Authors:
Laurent Gosse
Affiliations:
IAC-CNR "Mauro Picone" (sezione di Bari), Via Amendola 122/I, 70126 Bari, Italy
Venue:
Journal of Computational Physics
Year:
2004

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Abstract

We present a computational approach for the WKB approximation of the wavefunction of an electron moving in a periodic one-dimensional crystal lattice by means of a nonstrictly hyperbolic system whose flux function stems from the Bloch spectrum of the Schrödinger operator. This second part focuses on the handling of the source terms which originate from adding a slowly varying exterior potential. Physically, relevant examples are the occurrence of Bloch oscillations in case it is linear, a quadratic one modelling a confining field and the harmonic Coulomb term resulting from the inclusion of a "donor impurity" inside an otherwise perfectly homogeneous lattice.