# Theory Meets Experiment in Low-Dimensional Structures with Correlated Electrons

## Prague, Czech Republic, July 1 – 4, 2019

#### Quantum Phase Transitions in Superconducting Quantum Dots

*(1) Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, CZ-121 16 Praha 2, Czech Republic, (2) Institute of Physics, Albert Ludwig University of Freiburg, Hermann-Herder-Strasse 3, 791 04 Freiburg, Germany*

A quantum dot attached to BCS superconducting leads exhibits a 0−π impurity quantum phase transition, which can be experimentally controlled either by the gate voltage or by the superconducting phase difference. From the theoretical point of view, the system is described by the single-impurity Anderson model, solving of which relies on heavy numerical methods. To enhance understanding and speed up characterization of the system, we aim to provide semi-analytical insight.

First, in the common case of the two leads having the same superconducting gap size, we explain the influence of asymmetric dot-lead coupling by relating the asymmetric system to a symmetric one. Surprisingly, it is the symmetric case, which is the most general, meaning that physical quantities in the case of asymmetric coupling are fully determined by their symmetric counterparts. We give ready-to-use conversion formulas for the 0−π phase transition boundary, on-dot quantities, and the Josephson current [1].

Next, we study the 0−π impurity quantum phase transition, clearly visible by a jump in the supercurrent in the ground state but smeared out to a crossover by finite temperature. For zero temperature, we present two simple analytical formulae describing the position of the phase boundary in parameter space for two opposing limits (the weakly correlated and Kondo regime). Furthermore, we show that the two-level approximation provides an excellent description of the low temperature physics near the phase transition. We discuss reliability and mutual agreement of available finite temperature numerical methods (the numerical renormalization group and quantum Monte Carlo) and suggest a novel approach for efficient determination of the quantum phase boundary from measured finite temperature data [2].

[1] A. Kadlecová, M. Žonda, T. Novotný, Phys. Rev. B 95(19), 195114 (2017).

[2] A. Kadlecová, M. Žonda, V. Pokorný, and T. Novotný, Phys. Rev. Applied 11, 044094 (2019).