The effect of Coulomb charging energy on states inside the superconducting gap

Pavešić, Luka (author), Žitko, Rok (mentor)

We 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.

• Language: English
• Keywords: subgap states, Yu-Shiba-Rusinov states, Andreev bound states, superconductor, charging energy, Richardson model, quantum dot, Anderson impurity model
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-151832
• COBISS.SI-ID: 169709315
• Publication date in RUL: 21.10.2023

PAVEŠIĆ, Luka, 2023, The effect of Coulomb charging energy on states inside the superconducting gap [online]. Doctoral dissertation. [Accessed 31 March 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=151832

Secondary language

• Language: Slovenian
• Title: Vpliv energije Coulombskega odboja na stanja znotraj superprevodne reže

Abstract

V delu raziskujemo diskretna stanja znotraj superprevodne reže v modelih kvantnih pik sklopljenih s superprevodnimi otočki, kjer je energija Coulombskega odboja med elektroni v slednjih pomembna. V ta namen modeliramo superprevodne otočke z Richardsonovim modelom, posplošitvijo modela BCS, ki ohranja število delcev. Tekmovanje med Coulombskim odbojem in superprevodnim parjenjem vpliva na stanja v reži na dva načina. Spremeni naravo vzbuditev v superprevodnem otočku, hkrati pa preferira določeno porazdelitev naboja med komponentami sistema. V razširjenem sistemu, kjer je kvantna pika vgrajena med dva superprevodnika, to pripelje do nepričakovanih mnogodelčnih stanj, ki so zanimiva z vidika aplikacij v kvantnih tehnologijah. Predstavljeno metodo uporabimo za interpretacijo novih eksperimentalnih rezultatov, pridobljenih v režimu, kjer je učinek Coulombskega odboja primerljiv z velikostjo superprevodne reže. Predlagamo tudi poenostavljen Richardsonov model v limiti ravnega pasu kot preprost model, koristen za kvalitativne napovedi nizkoenergijskih stanj. Poenostavitev zmanjša Hilbertov prostor do te mere, da so določeni izračuni analitično obvladljivi. Ker zajema tako elektrostatične efekte kot tudi Josephsonov pojav, pa tudi spinsko fiziko na kvantni piki, predlagamo dvokanalno razširitev modela z ravnim pasom kot model kvantne pike, vgrajene v Josephsonov spoj transmonskega kubita.

• Keywords: stanja znotraj reže, stanja Yu-Shiba-Rusinova, vezana stanja Andreeva, superpre- vodnik, Coulombska interakcija, Richardsonov model, kvantna pika, Andersonov model nečistoče