Current density operator in systems with non-parabolic, position-dependent energy bands

The present manuscript was written in 1994 and was not published. It addresses the form that the quantum-mechanical current density must take in mesoscopic treatments of semiconductor heterostructures, in which the electron dispersion relations are non-parabolic and position dependent, rendering the...

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Bibliographic Details
Published in:arXiv.org 2015-09
Main Author: Frensley, William R
Format: Article
Language:English
Subjects:
Continuity equation
Current density
Domains
Energy bands
Formulations
Heterostructures
Mathematical models
Online Access:Get full text
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Summary:The present manuscript was written in 1994 and was not published. It addresses the form that the quantum-mechanical current density must take in mesoscopic treatments of semiconductor heterostructures, in which the electron dispersion relations are non-parabolic and position dependent, rendering the textbook expressions inapplicable. The approach is to derive the continuity equation for the specific model under consideration, using generalizations of Green's identities to higher-order derivatives and to discrete models of different topological structure. A new addendum addresses two issues of more current interest: the use of irregular meshes in discrete formulations, and the identification of the Heisenberg velocity operator to evaluate current density. It is demonstrated that on discrete domains the velocity operator fails to satisfy a sensible continuity equation, and therefore cannot be identified with the current density.
ISSN:2331-8422