skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Andreev reflection and geometrical resonance effects for a gradual variation of the pair potential near the normal-metal--superconductor interface

Abstract

The probability of Andreev reflection is calculated as a function of the energy for quasiparticles that are incident on a normal-metal--superconductor (N-S) interface with a gradual variation of the pair potential. These calculations are an extension of the work of Blonder, Tinkham, and Klapwijk (Phys. Rev. B 25, 4515 (1982)), who assumed a step function for the position dependence of the pair potential. We integrate the Bogoliubov equations numerically in the region in which the pair potential varies with position and apply boundary conditions to find the quantities of interest. This approach is also used to calculate the geometrical resonances in the transmission of a tunnel junction on an N-S bilayer. For a steplike variation of the pair potential, the same expression for the transmission is found as with the usual density-of-states approach. Also results are given for a gradual variation of the pair potential at the interface. Both the probability of Andreev reflection and the geometrical resonance effects begin to change if the region in which the pair potential varies with position becomes of the order of the coherence length of the superconductor.

Authors:
; ;
Publication Date:
Research Org.:
Research Institute for Materials, University of Nijmegen, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands
OSTI Identifier:
5435995
Resource Type:
Journal Article
Journal Name:
Phys. Rev. B: Condens. Matter; (United States)
Additional Journal Information:
Journal Volume: 37:10
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; SUPERCONDUCTING JUNCTIONS; QUASI PARTICLES; BOGOLYUBOV METHOD; BOUNDARY CONDITIONS; INTERFACES; METALS; NUMERICAL SOLUTION; REFLECTION; ELEMENTS; JUNCTIONS; 656100* - Condensed Matter Physics- Superconductivity

Citation Formats

van Son, P C, van Kempen, H, and Wyder, P. Andreev reflection and geometrical resonance effects for a gradual variation of the pair potential near the normal-metal--superconductor interface. United States: N. p., 1988. Web. doi:10.1103/PhysRevB.37.5015.
van Son, P C, van Kempen, H, & Wyder, P. Andreev reflection and geometrical resonance effects for a gradual variation of the pair potential near the normal-metal--superconductor interface. United States. https://doi.org/10.1103/PhysRevB.37.5015
van Son, P C, van Kempen, H, and Wyder, P. Fri . "Andreev reflection and geometrical resonance effects for a gradual variation of the pair potential near the normal-metal--superconductor interface". United States. https://doi.org/10.1103/PhysRevB.37.5015.
@article{osti_5435995,
title = {Andreev reflection and geometrical resonance effects for a gradual variation of the pair potential near the normal-metal--superconductor interface},
author = {van Son, P C and van Kempen, H and Wyder, P},
abstractNote = {The probability of Andreev reflection is calculated as a function of the energy for quasiparticles that are incident on a normal-metal--superconductor (N-S) interface with a gradual variation of the pair potential. These calculations are an extension of the work of Blonder, Tinkham, and Klapwijk (Phys. Rev. B 25, 4515 (1982)), who assumed a step function for the position dependence of the pair potential. We integrate the Bogoliubov equations numerically in the region in which the pair potential varies with position and apply boundary conditions to find the quantities of interest. This approach is also used to calculate the geometrical resonances in the transmission of a tunnel junction on an N-S bilayer. For a steplike variation of the pair potential, the same expression for the transmission is found as with the usual density-of-states approach. Also results are given for a gradual variation of the pair potential at the interface. Both the probability of Andreev reflection and the geometrical resonance effects begin to change if the region in which the pair potential varies with position becomes of the order of the coherence length of the superconductor.},
doi = {10.1103/PhysRevB.37.5015},
url = {https://www.osti.gov/biblio/5435995}, journal = {Phys. Rev. B: Condens. Matter; (United States)},
number = ,
volume = 37:10,
place = {United States},
year = {1988},
month = {4}
}