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Numerical Studies of Vortex Core States in Type II Superconductors
Umeå University, Faculty of Science and Technology, Department of Physics.
2012 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

In this thesis, we study an isolated vortex in an s-wave superconductor by solving the Bogoliubov-de Gennes equations self-consistently on a disc. We calculate the order parameter and supercurrent profiles, as well as the distribution of quasiparticle states. In contrast to quasi-classical treatments, the ratio Δ/EF between the order parameter and the Fermi energy is not assumed negligible. We study a regime where this ratio is on the order of 10-1, relevant to high-temperature superconductors. In this regime, we find a Friedel-like oscillation in the order parameter profile at low temperatures. This oscillation is attributed to an increased level spacing of the quasiparticle states, causing a decrease of the number of states present inside the superconducting energy gap. The results are in good agreement with previously published works. In future studies, the method used in this thesis will be generalized to d-wave superconductors.

Abstract [sv]

I detta examensarbete studeras en ensam virvel i en s-vågssupraledare genom att självkonsistent lösa Bogoliubov och de Gennes' ekvationer på en cylinderskiva. Vi beräknar ordningsparameter- och superströmsprofiler, samt fördelningen av kvasipartikeltillstånd. Till skillnad från i kvasiklassiska metoder så antas inte kvoten Δ/EF mellan ordningsparametern och Fermi-energin vara negligerbar. Vi studerar en regim där denna kvot är av storleksordningen 10-1, vilket är fallet i högtemperatur-supraledare. Vid låga temperaturer finner vi i denna regim en Friedelliknande oscillation i ordningsparameterprofilen. Denna oscillations förklaras genom att separationen mellan kvasipartikeltillstånd ökar, vilket får som effekt att färre tillstånd ryms innanför det supraledande energigapet. Våra resultat överensstämmer väl med tidigare publicerade artikler. I framtida studier kommer metoden vi använder i detta examensarbete att generaliseras till d-vågssupraledare.

Place, publisher, year, edition, pages
2012. , 53 p.
Keyword [en]
superconductivity, type II, vortex, s-wave, Bogoliubov-de Gennes
Keyword [sv]
supraledning, typ II, virvel, s-våg, Bogoliubov-de Gennes
National Category
Condensed Matter Physics
URN: urn:nbn:se:umu:diva-55159OAI: diva2:525873
External cooperation
Chalmers University of Technology, Department of Microtechnology and Nanoscience, Applied Quantum Physics Laboratory
Subject / course
Fysik D - examensarbete
Educational program
Masterprogrammet i fysik
2012-05-02, Physics department seminar room, 15:00 (English)
Physics, Chemistry, Mathematics
Available from: 2012-05-30 Created: 2012-05-09 Last updated: 2012-05-30Bibliographically approved

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