Unconventional superconductivity in nanoscopic junctions
Two quantum dots squeezed between superconductors: where does exotic four-electron pairing survive — and can a laptop-friendly approximation map it as reliably as methods that need cluster-scale computing?
A quantum dot is an artificial atom a few nanometres across. Trap one — or two — between superconducting electrodes and the pairing that makes superconductors special leaks into it, creating states bigger circuits can't host. The thesis maps where the most exotic of them, four-electron Cooper quartets, actually survive.
found
Recomputing the quartet phase diagram of an earlier study, I found a region where quartet correlations vanish exactly — missed by the original publication — and traced it to a doublet ground state.
verified
GAL tracks exact NRG almost perfectly in the strongly correlated regime and at weaker couplings, but cannot produce the triplet ground state NRG finds. Knowing where an approximation breaks is what makes it usable.
computed
Current–phase analysis of a three-lead junction, locating the “sweet line” of couplings where the OFF supercurrent vanishes and switching becomes ideal — calculations that grew into an article of its own.
method & toolkit
- model
- superconducting Anderson impurity model — one and two quantum dots
- method
- generalized atomic limit (GAL), benchmarked against numerically exact DM-NRG
- stack
- Python · TRIQS 3.3.1
- scripts
- zenodo.org/records/15300011 — Tutorial.py · Single_dot.py · Double_dot.py
- open thread
- impurity Green's function for a p-wave superconductor with Rashba spin–orbit coupling — groundwork for a follow-up study