Practical Guide to Quantum Phase Transitions in Superconducting Quantum Dots

Dong E. Liu, Shailesh Chandrasekharan A, Harold U. Baranger

Arturo Wong, William Brian Lane, Luis Dias +3 more

Sujit Sarkar

A. Kadlecová, Martin Žonda, Vladislav Pokorný +1 more

Superconducting quantum dots (SQDs), as generalized and tunable Josephson junctions, have potential for versatile components in electronic circuits and detectors. A key factor holding back their application is characterization, which often requires lengthy, impractical numerical methods. The authors offer simple analytical formulas that allow fast, reliable characterization of SQDs in different regimes, plus a straightforward and general method to locate the quantum phase transition from finite-temperature experimental data. These tools will dramatically speed up the characterization of real devices, and provide a handy framework to predict and refine the properties of these devices.

Alexander F. Andreev

Yu-Chun Hsu, Wu-Jing Chen, Chien‐Te Wu

We theoretically study the superconducting proximity effect in a quantum dot coupled to two superconducting leads when the intradot interaction between electrons is made attractive. Because of the superconducting proximity effect, the electronic states for the embedded quantum dot are either spin-polarized states with an odd occupation number or BCS-like states with an even occupation number. We show that in the presence of an external magnetic field, the system can exhibit quantum phase transitions of fermion parity associated with the occupation number. In this paper, we adopt a self-consistent theoretical method to extend our considerations beyond the so-called superconducting atomic limit in which the superconducting gap for the leads is assumed to be the largest energy scale. This method enables us to numerically investigate the electronic structure of the dot as a result of the attractive interaction. For energy phase diagrams in the regime away from the atomic limit, we find a reentrant behavior where a BCS-like phase of the dot exists in an intermediate range of the hybridization strength between the quantum dot and the leads. We also consider Josephson current-phase relations and identify a number of examples showing 0-$\ensuremath{\pi}$ phase transitions that may offer important switching effects.