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The Aharonov-Bohm effect for the stationary and coherent states of an electron in a homogeneous magnetic field

Vladislav G. Bagrov, Dmitri M Gitman, Vladimir D. Skarzhinsky

Published Jan 1, 1986• 1 citation
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We present a stationary state description of the Aharonov-Bohm effect in semiconductor quantum wells in terms of Landau wavefunctions and discuss electron injection into wells. This description explicitly shows that, if the potential drops between the quantum well interfaces are negligible, a net ballistic charge current in the direction perpendicular to the magnetic field and perpendicular to the axis of the wells is produced only by electrons which are injected into the structure in Aharonov-Bohm superposition states.
This work presents an analysis of the Aharonov-Bohm effect taking into account both regions where the electron is present and where it is excluded, and also the time variations of the magnetic vector potential and the magnetic induction field as they change between two of their stationary values. This analysis allows the identification of the electrical force field induced in the region where the electron is present by the time variation of the magnetic flux in the region where the electron is excluded, thus providing a classical explanation of the changes in the stationary properties of the electron when the magnetic potential and field change from one set of stationary values to another. Some apparent contradictions in attempts to interpret the A-B effect are also discussed and clarified.