Supercurrent through a multilevel quantum dot close to singlet-triplet degeneracy

C. Karrasch, S. Andergassen, and V. Meden
Phys. Rev. B 84, 134512 – Published 13 October 2011

Abstract

We investigate two serially aligned quantum dots in the molecular regime of large tunnel couplings t. A Zeeman field B is used to tune the energy difference of singlet and triplet spin configurations. Attaching this geometry to BCS source and drain leads with gap Δ and phase difference φ gives rise to an equilibrium supercurrent J. To compute J in the presence of Coulomb interactions U between the dot electrons, we employ the functional renormalization group (FRG). For Bt, where the singlet and (one out of a) triplet spin states are equal in energy, the current exhibits characteristics of a 0-π transition similar to a single impurity. Its magnitude in the π phase, however, jumps discontinuously at B=t, being smaller on the triplet side. By exploiting the flexibility of the FRG, we demonstrate that this effect is generic and calculate J for realistic experimental parameters Δ, U, and gate voltages ε. To obtain a more thorough understanding of the discontinuity, we analytically treat the limit Δ=, where one can access the exact many-particle states. Finally, carrying out perturbation theory in the dot-lead couplings substantiates the intuitive picture that Cooper-pair tunneling is favored by a singlet spin configuration while inhibited by a triplet one.

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  • Received 28 July 2011

DOI:https://doi.org/10.1103/PhysRevB.84.134512

©2011 American Physical Society

Authors & Affiliations

C. Karrasch1,2, S. Andergassen2, and V. Meden2

  • 1Department of Physics, University of California, Berkeley, California 95720, USA
  • 2Institut für Theorie der Statistischen Physik and JARA–Fundamentals of Future Information Technology, RWTH Aachen University, DE-52056 Aachen, Germany

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Vol. 84, Iss. 13 — 1 October 2011

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