Modeling long imperfect SNS junctions and Andreev bound states using two impurities and the $T$-matrix formalism

Pinon, Sarah and Kaladzhyan, Vardan and Bena, Cristina. (2020) Modeling long imperfect SNS junctions and Andreev bound states using two impurities and the $T$-matrix formalism. Physical Review B, 101 (20). p. 205136.

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Official URL: https://edoc.unibas.ch/85182/

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We provide an analytical tool to calculate the energies of Andreev bound states (ABSs) in long imperfect SNS junctions, which at present can only be described using numerical tools. We model an NS junction as a δ-function “Andreev” impurity, i.e., a localized potential that scatters an electron into a hole with opposite spin. We show using the scattering matrix formalism that, quite surprisingly, an “Andreev” impurity is equivalent to an NS junction characterized by both Andreev reflection and a finite amount of normal scattering. The ABS energies are then calculated using the T-matrix formalism applied to a system with two Andreev impurities. Our results lie between those for a perfect long SNS junction limit described by the Andreev approximation (ABS energies depend linearly on the phase and are independent of the chemical potential) and the particle-in-the-box limit (bound state energies are independent of the phase and have a linear dependence on the chemical potential). Moreover, we recover a closed-form expression for the ABS energies by expanding around the particle-in-the-box limit.
Faculties and Departments:05 Faculty of Science > Departement Physik
UniBasel Contributors:Kaladzhyan, Vardan
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Physical Society
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:19 Nov 2021 13:04
Deposited On:19 Nov 2021 13:04

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