Tunneling processes between Yu-Shiba-Rusinov bound states

Year: 2021

Authors: Villas A., R. Klees R.L., Morrbs G., Huang H., Ast C.R., Rastelli G., Belzig W., Cuevas J.C.

Autors Affiliation: Univ Autonoma Madrid, Dept Fis Teor Mat Condensada, E-28049 Madrid, Spain; Univ Autonoma Madrid, Condensed Matter Phys Ctr IFIMAC, E-28049 Madrid, Spain; Univ Konstanz, Fachbereich Phys, D-78457 Constance, Germany; Max Planck Inst Festkorperforsch, Heisenbergstr 1, D-70569 Stuttgart, Germany; Univ Konstanz, Zukunftskolleg, D-78457 Constance, Germany; Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy.

Abstract: Very recent experiments have reported the tunneling between Yu-Shiba-Rusinov (YSR) bound states at the atomic scale. These experiments have been realized with the help of a scanning tunneling microscope where a superconducting tip is functionalized with a magnetic impurity and is used to probe another magnetic impurity deposited on a superconducting substrate. In this way it has become possible to study for the first time the spin-dependent transport between individual superconducting bound states. Motivated by these experiments, we present here a comprehensive theoretical study of the tunneling processes between YSR bound states in a system in which two magnetic impurities are coupled to superconducting leads. Our theory is based on a combination of an Anderson model with broken spin degeneracy to describe the impurities and nonequilibrium Green?s function techniques to compute the current-voltage characteristics. This combination allows us to describe the spin-dependent transport for an arbitrary strength of the tunnel coupling between the impurities. We first focus on the tunnel regime and show that our theory naturally explains the experimental observations of the appearance of current peaks in the subgap region due to both the direct and thermal tunneling between the YSR states in both impurities. Then, we study in detail the case of junctions with increasing transparency, which has not been experimentally explored yet, and predict the occurrence of a large variety of (multiple) Andreev reflections mediated by YSR states that give rise to a very rich structure in the subgap current. In particular, we predict the occurrence of multiple Andreev reflections that involve YSR states in different impurities. These processes have no analog in single-impurity junctions, and they are manifested as current peaks with negative differential conductance for subgap voltages. Overall, our work illustrates the unique physics that emerges when the spin degree of freedom is added to a system with superconducting bound states.

Journal/Review: PHYSICAL REVIEW B

Volume: 103 (15)      Pages from: 155407  to:

More Information: The authors would like to thank Alfredo Levy Yeyati, Joachim Ankerhold, Ciprian Padurariu, and Bjorn Kubala for insightful discussions. A.V. and J.C.C. acknowledge funding from the Spanish Ministry of Economy and Competitiveness (MINECO) (Contract No. FIS2017-84057-P). This work was funded in part by the ERC Consolidator Grant AbsoluteSpin (Grant No. 681164) and by the Center for Integrated Quantum Science and Technology (IQST). R.L.K., W.B., and G.R. acknowledge support by the DFG through SFB 767 and Grant No. RA 2810/1. J.C.C. also acknowledges support via the Mercator Program of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in the frame of the SFB 767.
KeyWords: mesoscopic superconductivity, Andreev Reflection, Josephson effect, quantum dots
DOI: 10.1103/PhysRevB.103.155407

Citations: 12
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