Quantum dot attached to two supercondicting leads

Two quite different worlds meet at the quantum dot attached to two superconducting leads. Superconductor is a macroscopic quantum state with billions of electrons in the form of Cooper bound pairs, while quantum dot allows us to follow individual electrons and Cooper pairs. Quantum dot in a superconducting environment allows us to study exotic physical phenomena and simultaneously promises technological applications. Such a nanosclae system is ideal for investigating and understanding of the microscopic origin of a class of fundamental quantum phenomena including quantum phase transitions.
We investigated with colleagues from the Faculty of Mathematics and Physics of Charles University a model of such a quantum dot and used a dynamical perturbation theory to described the experimentally observed transition from a spin singlet to a spin doublet identified by a change of the sign of the supercurrent through the dot. Among other, we demonstrated that this rather complex phenomenon can be quantitatively well described and qualitatively understood in terms of a rather simple method. It is hence unnecessary in a number of realistic cases to use large-scale numerical simulations, as has been assumed so far.

A phase diagram for the 0- transition as a function of the dot energy level () and and the coupling of the dot to the right (R) and left . (L) superconducting leads in several approximations: Numerical renormalization group (NRG), dynamical perturbation theory (DC), stati hartree-Fock (HF), and generalized atomic limit (GAL). Results are shown for various strengths of the Coulomb repulsion on the dot (U) and for the phase difference between the righjt and left superconducting states  with asymmetric and symmetric attachment, L = 2R , L = R, respectively. Unprecedented precision of the DC solution in weak and intermediate interaction compared to the numerically exact NRG solution.

M. Žonda, V. Pokorný, V. Janiš, and T. Novotný: Perturbation theory of a superconducting 0 − π impurity quantum phase transition, Scientific Reports 5, 8821 (2015).

M. Žonda, V. Pokorný, V. Janiš, and T. Novotný: Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads, Phys. Rev. B 93, 024523 (2016).