Josephson effect in quantum dots

master thesis

Abstract

In this master's thesis, I am considering the problem of two superconducting electrodes connected by a weak link. In such systems, a phenomenon known as the Josephson effect occurs. The Josephson effect is the flow of the direct electrical current through the non-biased system or the flow of the alternating current through the system which is biased by a constant voltage. That current is called the Josephson current and systems like those are known as Josephson junctions. In this thesis, the weak link between the superconducting electrodes consists of one or two quantum dots. In such cases, the Josephson current is carried by the discrete states known as Andreev bound states, formed through the Andreev reflection mechanism: electrons impinging on the interface between the superconductor and the normal metal are reflected back into the normal metal as holes, while pairs of electrons (the Cooper pairs) are formed in the superconductor. The Andreev bound states are visible as resonant peaks in the density of states of quantum dots. Here I search for those states in three different approximations: the case of no Coulomb repulsion between electrons in the dots, the case of electrons interacting through an infinite interaction and the case of infinite superconducting gap.

Keywords

quantum mechanics;quantum dots;superconductors;Josephson effect;

Data

Language:	English
Year of publishing:	2018
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[A. Alić]
UDC:	350.145
COBISS:	3243108
Views:	861
Downloads:	423
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Josephsonov pojav v kvantnih pikah
Secondary abstract:	V tej magistrski nalogi obravnavam problem dveh superprevodnih elektrod, povezanih s šibko povezavo. V takšnih sistemih pride do pojava, znanega kot Josephsonov pojav. Josephsonov pojav pomeni pretok enosmernega električnega toka skozi sistem, ki ni povezan z napetostnim virom, ali pretok izmeničnega toka skozi sistem, ki je priključen na konstantno napetost. Ta tok se imenuje Josephsonov tok in tovrstni sistemi so znani kot Josephsonovi spoji. V tem delu šibko povezavo med superprevodnimi elektrodami predstavljata ena ali dve kvantni piki. V takih primerih Josephsonov tok prenašajo diskretna stanja, ki se imenujejo Andreevova vezana stanja in ki nastanejo prek mehanizma Andreevovih odbojev: elektroni, ki vpadajo na vmesnik med superprevodnikom in normalno kovino, se odbijejo nazaj v normalno kovino kot vrzeli, medtem ko v superprevodniku nastanejo pari elektronov (Cooperjevi pari). Andreevova vezana stanja so vidna kot resonančni vrhovi v gostoti stanj kvantnih pik. V magisteriju iščem ta stanja v treh različnih približkih: primer, ko med elektroni v kvantni piki ni Coulombovega odboja, potem primer, ko je Coulombov odboj med elektroni neskončen, in primer, ko je energijska reža neskončna.
Secondary keywords:	kvantna mehanika;kvantne pike;superprevodniki;Josephsonov pojav;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za fiziko
Pages:	65 str.
ID:	10961997