Splitting of Andreev levels in a Josephson junction by spin-orbit coupling

Abstract

We consider the effect of spin-orbit coupling on the energy levels of a single-channel Josephson junction below the superconducting gap. We investigate quantitatively the level splitting arising from the combined effect of spin-orbit coupling and the time-reversal symmetry breaking by the phase difference between the superconductors. Using the scattering matrix approach we establish a simple connection between the quantum mechanical time delay matrix and the effective Hamiltonian for the level splitting. As an application we calculate the distribution of level splittings for an ensemble of chaotic Josephson junctions. The distribution falls off as a power law for large splittings, unlike the exponentially decaying splitting distribution given by the Wigner surmise -- which applies for normal chaotic quantum dots with spin-orbit coupling in the case that the time-reversal symmetry breaking is due to a magnetic field.

arXiv comment6 pages, 3 figures

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• Superconducting Spin Qubits
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• Anomalous Fraunhofer Interference in Epitaxial Superconductor-Semiconductor Josephson Junctions
• Singularities of Andreev spectrum in multi-terminal Josephson junction
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• Spontaneous Edge Accumulation of Spin Currents in Finite-Size Two-Dimensional Diffusive Spin-Orbit Coupled SFS Heterostructures
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• Tuning Topological Superconductivity in Phase-Controlled Josephson Junctions with Rashba and Dresselhaus Spin-Orbit Coupling
• Current-phase relations of InAs nanowire Josephson junctions: from interacting to multi-mode regimes
• Josephson Current through a Semiconductor Nanowire: effect of strong spin-orbit coupling and Zeeman splitting
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• Signatures of time-reversal-invariant topological superconductivity in the Josephson effect
• Energy spectrum and current-phase relation of a nanowire Josephson junction close to the topological transition
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• Control of Josephson current by Aharonov-Casher Phase in a Rashba Ring
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• Andreev spin qubit protected by Franck-Condon blockade
• Effects of electron-electron interaction and spin-orbit coupling on Andreev pair qubits in quantum dot Josephson junctions