Spectral Modelling of Quantum Superlattice and Application to the Mott-Peierls Simulated Transitions

Details Spectral Modelling of Quantum Superlattice and Application to the Mott-Peierls Simulated Transitions Spectral Modelling of Quantum Superlattice and Application to the Mott-Peierls Simulated Transitions

2003-11-19

arxiv.org/abs/cond-mat/0311468v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

14 pages, LaTex

Scientific paper

A local perturbation theory for the spectral analysis of the Schr\"odinger operator with two periodic potentials whose periods are commensurable has been constructed. It has been shown that the perturbation of the periodic 1D Hamiltonian by an additional small periodic potential leads to the following spectral deformation: all gaps in the spectrum of the unperturbed periodic Hamiltonian bear shifts while any band splits by arising additional gaps into a set of smaller spectral bands. The spectral shift, the position of additional gaps and their widths have been calculated explicitly. The applications to the operational regime of a nanoelectronic device based on Mott-Peierls stimulated transition have also been discussed.

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