Josephson current through a single Anderson impurity coupled to BCS leads
C. Karrasch, A. Oguri, V. Meden
DOI 10.1103/PhysRevB.77.024517 · Physical Review B
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Abstract
We investigate the Josephson current ⟨J(ϕ)⟩ through a quantum dot embedded between two superconductors showing a phase difference ϕ. The system is modeled as a single Anderson impurity coupled to BCS leads, and the functional and the numerical renormalization group frameworks are employed to treat the local Coulomb interaction U. We reestablish the picture of a quantum phase transition occurring if the ratio between the Kondo temperature TK and the superconducting energy gap Δ or, at appropriate TK∕Δ, the phase difference ϕ or the impurity energy is varied. We present accurate zero- as well as finite-temperature T data for the current itself, thereby settling a dispute raised about its magnitude. For small to intermediate U and at T=0 the truncated functional renormalization group is demonstrated to produce reliable results without the need to implement demanding numerics. It thus provides a tool to extract characteristics from experimental current-voltage measurements.
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