Nonlocal Andreev transport through a quantum dot in a magnetic field: Interplay between Kondo, Zeeman, and Cooper-pair correlations

Abstract

We study the nonlocal magnetotransport through a strongly correlated quantum dot, connected to multiple terminals consisting of two normal and one superconducting (SC) leads. Specifically, we present a comprehensive view on the interplay between the crossed Andreev reflection (CAR), the Kondo effect, and the Zeeman splitting at zero temperature in the large SC gap limit. The ground state of this network shows an interesting variety, which varies continuously with the system parameters, such as the coupling strength ΓS between the SC lead and the quantum dot, the Coulomb repulsion U, the impurity level ɛd, and the magnetic field b. We show, using the many-body optical theorem which is derived from the Fermi-liquid theory, that the nonlocal conductance is determined by the transmission rate of the Cooper pairs TCP=14sin2Θsin2(δ↑+δ↓) and that of the Bogoliubov particles TBG=12∑σsin2δσ. Here, δσ is the phase shift of the renormalized Bogoliubov particles, and Θ≡cot−1(ξd/ΓS) is the Bogoliubov-rotation angle in the Nambu pseudospin space, with ξd=ɛd+U/2. It is also demonstrated, using Wilson's numerical renormalization group approach, that the CAR is enhanced in the crossover region between the Kondo regime and the SC-proximity-dominated regime at zero magnetic field. The magnetic fields induce another crossover between the Zeeman-dominated regime and the SC-dominated regime, which occurs when the renormalized Andreev resonance level of majority spin crosses the Fermi level. We find that the CAR is enhanced and becomes less sensitive to magnetic fields in the SC-dominated regime close to the crossover region spreading over the angular range of π/4≲Θ≲3π/4. At the level crossing point, a spin-polarized current flows between the two normal leads, and it is significantly enhanced in the directions of Θ≃0 and Θ≃π where the SC proximity effect is suppressed.

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