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dc.contributor.advisorBraunecker, Bernd
dc.contributor.authorCarroll, Christopher James
dc.coverage.spatial107 p.en_US
dc.description.abstractIn this thesis a Green’s function based, analytical formalism is developed to describe dense chains of spiral ordered classical magnetic moments embedded in superconducting substrates. I demonstrate that an understanding of the dimensional mismatch between the substrate and impurity chain is crucial to understand the physics at play. Renormalised gap closures are discovered by exact, analytic solution for a ferromagnetic chain and insights gleaned are used to understand the spiral ordered case to which it can be smoothly tuned. I investigate the topological characteristics of this model and find an ambiguity in defining effective Hamiltonians due to the dimensional embedding of the chain in the substrate. To aid in resolving this ambiguity I develop formalism which allows one to write down Green’s functions for bounded, semi infinite systems in terms of more easily attainable, exact solutions for infinite systems. I derive simple expressions to identify the presence of topological bound states which agrees with purely one dimensional models and changes suggestively when applied to the aforementioned two dimensional model. I then work to extend the formalism to allow the exact solution of two or three parallel chains, taking into account all possible interactions with the classical magnetic impurities. The solutions are decoupled so that they can be written in terms of the 𝑇 matrices for a single chain, with additional levels of resummation. I find that the induced sub-gap spectrum for the two chain solution completely replaces those from each individual chain, leading to oscillating, helix like band structures. I use the complicated solution of the three chain solution to inform a potential ansatz to solve the 𝑁 chain case.en
dc.description.sponsorship"This work was supported by the EPSRC under grant number EP/M506631/1." -- Fundingen
dc.publisherUniversity of St Andrews
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.subjectGreen's functionen
dc.subjectAnalytic solutionen
dc.subjectT matrixen
dc.subjectMajorana fermionen
dc.subjectYu-Shiba-Rusinov statesen
dc.subjectTopological superconductivityen
dc.subjectSelf consistent numericsen
dc.subject.lcshGreen's functionsen
dc.titleDesigned topological states from hybrid spiral magnet-superconductor heterostructuresen_US
dc.contributor.sponsorEngineering and Physical Sciences Research Council (EPSRC)en_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US

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