A delta barrier in a well and the exact time evolution of its eigenstates

The analytic nature of the transmission coefficient for a δ-function barrier makes it a useful tool to examine a variety of technologically important applications, such as photoemission from semiconductors with an alkali coating, the examination of tunneling times for wave packets incident on a barr...

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Bibliographic Details
Published in:Journal of applied physics 2023-05, Vol.133 (17)
Main Authors: Jensen, Kevin L., Riga, Jeanne, Shabaev, Andrew, Osofsky, Michael, Prestigiacomo, Joseph C.
Format: Article
Language:English
Subjects:
Applied physics
Delta function
Eigenvectors
Evolution
Mathematical analysis
Photoelectric emission
Point contact
Wave packets
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Summary:The analytic nature of the transmission coefficient for a δ-function barrier makes it a useful tool to examine a variety of technologically important applications, such as photoemission from semiconductors with an alkali coating, the examination of tunneling times for wave packets incident on a barrier, and for parameterizing tunneling through the narrow barrier of a normal-superconducting point contact. The analytic model of a δ-function barrier inside a confining well is extended to the finite height and width rectangular barrier (a delta-function sequence). Methods to exactly evaluate the eigenstates are given and their dependencies are examined. The time evolution of a superposition of the lowest eigenstates is considered for barriers having comparable Gamow tunneling factors so as to quantify the impact of barrier height and shape on time evolution in a simple and exact system and, therefore, serve as a proxy for tunneling time. Last, density profiles and associated quantum potentials are examined for coupled wells to show changes induced by weaker and wider barriers.
ISSN:0021-8979
1089-7550
DOI:10.1063/5.0150385