Superconductive transport in curved thin film ferromagnets
Master thesis
Permanent lenke
https://hdl.handle.net/11250/3139170Utgivelsesdato
2024Metadata
Vis full innførselSamlinger
- Institutt for fysikk [2712]
Sammendrag
I denne avhandlingen tar vi for oss en teoretisk behandling av superleder-ferromagnet (SF) og superleder-ferromagnet-superleder (SFS) proksimitetssystemer for en krummet geometri. Systemene som undersøkes er diffusive og behandles med en kvasiklassisk tilnærming. Vi demonstrerer genereringen av tripletter med lang rekkevidde (LRTer) i SF-systemer med et Rashba-Dresselhaus spinn-bane-felt i xy-planet og i systemer med spinn-bane-felt i z-retningen. Vi introduserer deretter den kurvilineære formalismen og diskuterer muligheten for å generere LRTer med geometrisk krumning. Systemet for en krummet SF nanoledning løses numerisk, og det vises at systemet kan gi opphav til LRTer. En krumningsindusert 0-pi-overgang for en SFS nanoledning demonstreres også numerisk. Deretter introduseres differensialgeometrien for todimensjonale (2D) overflater, hvor vi utleder Christoffel-symbolene for en overflate plassert i tre dimensjoner. Flere 2D overflater behandles analytisk. Overflatene som behandles er en tunnel-overflate, en boomerang-overflate og en Gaussisk hump, og vi utleder analytiske grunnlag for at disse overflatene kan generere LRTer. Formalismen for 2D krummede overflater vises å fungere bra for numeriske utregninger for SF- og SFS- systemer. Vi plotter tilstandstettheten for et SF tunnel-system og viser at dette systemet er kvalitativt ekvivalent til en 1D nanoledning. For SFS boomerang-systemet ser vi indikasjoner på at ladningstrømmen er tettere langs den indre krumningen. Vi demonstrerer også muligheten for å ha virvling i ladningsstrømmen for et boomerang SFS-system, noe som kan indikere muligheten for superledende virvlinger. In this thesis, we are looking at the theoretical treatment of superconductor - ferromagnet (SF) and superconductor - ferromagnet - superconductor (SFS) proximity systems within a curved geometry. The systems considered are diffusive and treated in the quasiclassical approximation. We demonstrate the generation of long-range triplets (LRTs) in SF systems with a Rashba-Dresselhaus spin-orbit field in the xy-plane and in systems with a spin-orbit field in the z-direction. We then introduce the curvilinear formalism and discuss the potential for generating LRTs with geometric curvature. The system of an SF curved nanowire is solved numerically and demonstrated to generate LRTs. A curvature induced 0-pi transition for an SFS nanowire is demonstrated numerically as well. We then give an introduction to the differential geometry of two dimensional (2D) surfaces, where an expression for the Christoffel symbols of a surface embedded in 3D space is derived. Several 2D surfaces are treated analytically within this formalism, including a tunnel surface, a boomerang surface and a Gaussian bump. The analytical results for these surfaces predict the generation of LRTs in these systems. The formalism for 2D curved surfaces is shown to work well for the numerical treatment of SF- and SFS- proximity systems. We plot the density of states of an SF tunnel system and show that this system is qualitatively equivalent to the 1D nanowire. For the SFS boomerang, we see indications that the charge current tends to be denser along the inner curvature of the system. We also demonstrate the possibility of having a vortex in the charge current for a boomerang SFS system, which could be indicative of a superconducting vortex.