Disorder and spin imbalance induced exotic phases in weakly coupled s-wave superconductors

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The first part of our work deals with a smooth crossover from a Bardeen Cooper Schrieffer (BCS) phase comprising of largely overlapping pairs to a Bose superfluid (BEC) with short ranged tightly bound pairs induced by a random onsite disorder potential, as opposed to tuning the interparticle attraction which is largely seen in literature. At small disorder concentration, Anderson theorem is known to be valid and in the large disorder regime, an insulating phase is favoured. We have convincingly shown that the intermediate disorder regime holds key to a more interesting phase, a paired phase having long range order, resembling a BEC. Quantities such as participation ratio and ground state fidelity are computed which further strengthen the claim of crossover to a Bose phase, when the starting point is a weak coupling BCS superconductor. Many physical quantities which are of experimental significance e.g. superfluid stiffness, off diagonal long range order, spectral gap etc are computed to characterize the exotic phase which emerges at intermediate values of disorder strength. Thus a detailed study is carried out to elucidate different physical properties associated with a BCS-BEC crossover. The next problem deals with studying superfluidity in population imbalanced systems which are often thought to host an exotic Fulde-Ferrell-Larkin-Ovchinnikov phase (FFLO) characterized by finite momentum Cooper pairing. In spite of the extensive study of the phase, the unambiguous determination of the exotic phase both theoretically and experimentally, is still awaited. Recently, cursory evidences of the presence of FFLO phase has been obtained in trapped ultracold atoms in an optical lattice, which provided motivation for us to explore the FFLO phase in details. Our gap parameter and magnetization data show modulating profiles in real space, thereby providing support to the existence of FFLO phase, while we have noted the presence of various other ground states with close by energies. As confinement effects are technologically important for achieving the condensation phenomena in atomic systems, we have incorporated a harmonic trapping potential in our study and elaborately investigated the effects of harmonic confinement vis-a-vis the finite momentum pairing scenario. Further, we have computed different correlation functions that are of experimental importance. Finally, an interesting physics emerges that shows superfluid to insulator transition (SIT) as obtained by increasing the trapping potential, even in a model with attractive interactions...
Supervisor: Saurabh Basu