Superfluidity and Superconductivity in Body-centred-cubic and Face-centred-cubic Systems

Adebanjo, Ganiyu D (2022). Superfluidity and Superconductivity in Body-centred-cubic and Face-centred-cubic Systems. PhD thesis The Open University.



The microscopic description of phases in strongly correlated systems such as the fullerides (A3C60) is a challenge. In particular, how these strong interactions become attraction leading to a superconducting state remains a mystery. Understanding the mechanism(s) that drive(s) unconventional superconductivity is one of the most sought-after goals in many-body physics and indeed very complex to solve.

The aim of this thesis is, firstly, to investigate the conditions in which pairing may take place between two electrons in both body-centred cubic (BCC) and face-centred cubic (FCC) systems, and secondly, to examine the possibility for the emergence of a superconducting or superfluid state from paired electrons in three-dimensional (3D) systems. Here, pair properties are studied both in the anti-adiabatic and adiabatic limits.

In the anti-adiabatic limit, we use a symmetrised approach, group theory analysis, and perturbation theory to exactly solve the two-body problem and analyse the properties of the electron pair. We also examine, using a continuous-time Monte Carlo algorithm (CTQMC), the effects of retarded electron-phonon interactions on the pair properties away from the anti-adiabatic limit. In the high-phonon frequency limit, the CTQMC also serves as a validation check for the anti-adiabatic analytic result and vice-versa (with both results showing perfect agreement). Our result predicts that superfluidity can occur in BCC optical lattices up to a few tens of nanokelvin for fermionic lithium-6 atoms. Additionally, we found that, in the high-frequency limit, a paired state in an FCC lattice can be extremely light and small as compared to paired states on other 3D lattices. Such superlight states are expected to yield high transition temperatures under favourable circumstances. However, when the retardation effects arising from the electron-phonon interaction become important, bound pairs in the BCC lattice become lighter by orders of magnitude in a wide region of the parameter space. We also found significant long-range effects due to the vibration of the alkali ions in the cesium-doped fulleride systems leading to the creation of light pairs in its BCC structure.

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