Seminar "Coherence-Correlations-Complexity", Dept. of Theoretical Physics, Wrocław University of Technology
Sala 320a bud. A-1, Politechnika Wrocławska
Analysis of superconducting quantum dot made simple(r)
dr Martin Žonda
Department of Condensed Matter Physics, Charles University in Prague
Theoretical studies of realistic single-level quantum dots with local Coulomb repulsion attached to two generally different superconducting leads largely rely on heavy numerics. We will demonstrate two methods which make such otherwise lengthy and resources-consuming analyses significantly easier. First, we will argue that for a broad range of parameters can be methods such as the NRG or QMC reliably substituted by a simple second-order perturbation theory. Then we will prove that any system with asymmetric coupling to the leads can be related to a symmetricone via trivial analytical relation. Counter-intuitively, the symmetric setup is the most general one and its knowledge allows full description of the equivalent asymmetric system for any value of the asymmetry. This is a very handy discovery as the asymmetric coupling is ubiquitous in the experimental reality while theorists usually just consider symmetric setups for simplicity and viability. To demonstrate their usefulness we use both above mentioned methods to analyze the recent experiments on a carbon nano-tube quantum dot focused on the 0-pi transition controlled by the the superconducting phase difference [1].
[1] Delagrange et al., Phys. Rev. B 91, 241401(R) (2015); Phys. Rev. B 93, 196437 (2016)
