The effect of Coulomb charging energy on states inside the superconducting gapPavešić, Luka (Avtor) Žitko, Rok (Mentor) subgap statesYu-Shiba-Rusinov statesAndreev bound statessuperconductorcharging energyRichardson modelquantum dotAnderson impurity modelWe investigate discrete subgap states in models of quantum dots coupled to superconducting islands, where the Coulombic charging energy term in the latter is important. For this purpose, we model superconducting islands using the Richard- son model, a charge-conserving generalization of the BCS approximation. The competition of charging energy and superconducting pairing affects the subgap states in two ways. It alters the nature of the excitations in the superconducting island but also favours a certain charge distribution between components of the system. In an extended system where the quantum dot is embedded between two superconducting islands, the second effect produces unexpected emergent states, interesting from the standpoint of quantum technology applications. We used the method to interpret novel experimental results performed in the regime where the charging energy is comparable to the gap induced by superconducting pairing. Finally, we propose the flat-band limit of the Richardson model as a toy model useful for qualitative predictions of subgap states. The simplification reduces the Hilbert space to the point where certain calculations are analytically tractable. Be- cause it captures both the charging and Josephson effects, as well as the spin physics of the quantum dot, we propose the two-channel extension of the flat-band limit as a model of a quantum dot embedded in a Josephson junction of a transmon qubit.20232023-10-21 08:15:04Doktorsko delo/naloga151832VisID: 138405COBISS_ID: 169709315sl