Disorder induced superconductivity in a Quasi one-dimensional strongly correlated system

Abstract

This thesis proposes two theoretical models. The first theory that is devised extends a modelsuggested by Karnaukhov [1] which suggests spontaneously broken time reversal symmetry(T- symmetry) in a superconductor, thus implying a non trivial topology with the system.The first contribution of this thesis provides an analytical derivation for such a system, incontrast to the original paper which relied on numerical techniques. The analytical solutionsconfirm the results of the original paper. Furthermore, the assumption of the translationallyinvariant gap field being homogeneous is checked. This yields the result that for zero chem-ical potential there is a degeneracy of ground states along the diagonals of the Brillouinzone, and thus it can not be claimed that the gap field is homogeneous in all cases [2]. Con-sequently, it is found thatT-symmetry may not be broken in the scenario for a zero chemicalpotential, but in all other cases it is.The other theory that is explored within this thesis is a quasi-1D model which is basedon Luttinger liquid wires which have superconducting coupling inbetween the wires. Fromthis a disorder term is added, and the relation between disorder and superconductivity isstudied. This was inspired by an experiment [3] which claimed that disorder could enhancesuperconductivity. To solve the model, renormalisation group (RG) theory is applied, andthe coupled differential equations were solved. For certain initial conditions, it is foundthat disorder could enhance superconductivity, which represents a novel piece of research.Moreover, different mechanisms of how this phenomenon occurs are studied, by lookingat the competition between charge density wave (CDW), spin density wave (SDW) and thenormal state. In an attempt to fully reconcile the experiment with the theory, different prop-erties of the resistivity are studied such that direct comparisons can be made between thepredictions of the theory and the experiment itself.Keywords: Disorder Induced Superconductivity, Topological Superconductors