Tunneling processes between Yu-Shiba-Rusinov bound states

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 analogue in single-impurity junctions and they are manifested as current peaks with negative differential conductance for subgap voltages.

16 pages, 9 figures. arXiv admin note: text overlap with arXiv:2005.06491

References in corpus (5)

• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Orbital Picture of Yu-Shiba-Rusinov Multiplets
• Scaling of Yu-Shiba-Rusinov energies in the weak-coupling Kondo regime
• The Andreev states of a superconducting quantum dot: mean field vs exact numerical results
• Interplay Between Yu-Shiba-Rusinov States and Multiple Andreev Reflections

Cited by in corpus (13)

• Magnetic impurity in a one-dimensional few-fermion system
• Direct Transport between Superconducting Subgap States in a Double Quantum Dot
• Locking of magnetization and Josephson oscillations at ferromagnetic resonance in ${\phi }_0$ junction under external radiation
• Universal scaling of tunable Yu-Shiba-Rusinov states across the quantum phase transition
• Boosting the STM's spatial and energy resolution with double-functionalized probe tips
• Intermediate states in Andreev bound state fusion
• Full Counting Statistics of Yu-Shiba-Rusinov Bound States
• Effect of Van Hove singularities on Shiba states in two-dimensional $s$-wave superconductors
• Robust Spin Polarization of Yu-Shiba-Rusinov States in Superconductor/Ferromagnetic Insulator Heterostructures
• RKKY interaction in triplet superconductors: Dzyaloshinskii-Moriya-type interaction mediated by spin-polarized Cooper pairs
• Spectral properties of fractionalized Shiba states
• DC Josephson effect between two Yu-Shiba-Rusinov bound states
• Yu-Shiba-Rusinov States in Ising Superconductors