Three-body Fermi-liquid effects on the crossed Andreev reflection through quantum dots

We study the crossed Andreev reflection (CAR) through quantum dots connected to one superconducting (SC) lead and two normal leads at low temperatures. Specifically, we derive an exact formula for the T² conductance in the large SC gap limit [1]. Our formulation is based on the latest version of the Fermi-liquid theory for the Anderson impurity model [2-4], which has clarified that the quasiparticle energy shifts of order ω² and T², i.e., corrections of the same order as those due to the damping of quasiparticles, can be exactly described in terms of three-body correlations of impurity electrons. Using the numerical renormalization group (NRG) approach, we also demonstrate how the three-body contributions evolve and affect the CAR as the Andreev level moves away from the Fermi level.

[1] Y. Tanaka, N. Kawakami, and A. Oguri, JPSJ 76, 074701 (2007).

[2] C. Mora, C. P. Moca, J. von Delft, and G. Zarand, PRB 92, 075120 (2015).

[3] M. Filippone, C. Moca, A. Weichselbaum, J. von Delft, and C. Mora, PRB 98, 075404 (2018).

[4] A. Oguri and A. C. Hewson, PRL 120, 126802 (2018).