Condensation of Cooper pairs and Cooper quartets in fermionic systems with multiple internal degrees of freedom is studied. In this thesis work, I work on two major projects. On the first project I discuss Cooper pair condensation and while on the second I discuss Cooper quartet condensation.
Due to the restrictions imposed by Pauli's principle, no two identical fermions can occupy a single quantum state. Therefore for electronic systems with two internal states, the maximum number of electrons that could be bound together is two. However; for a fermionic system having more than two internal states, it is possible that the bound state structure could be quite different. On my thesis I focus on systems that have four internal states. On one hand it is possible that the system will still undergo some types of pairing condensation, but there is also a possibility that the fermions will form a more complex structure where four fermions are bound together which we call a quartet. Physical systems where fermions can have four internal states
include a system of spin-3/2 fermionic atoms and a two band electronic system. I look at possible two and four particle bound state structures in such systems.
First I discuss pairing condensation in the system. I extend the original Cooper problem to the pairing of two quasiparticles excited out of two decoupled superconductors. I show that two quasiparticles can form a bound state but can't destabilize the underlying system. I derive the Landau Ginzberg free energy for the system and use it to describe the pairing structure that will exist under different limits of the interaction among the fermions.
In the second work, I discuss quartet condensation in the system. I modify the Landau Ginzberg approach to include fluctuations in the order parameters and to allow for a quartet order parameter. We show that under the special SU(4) symmetric limit of interaction, the system has a tendency to undergo a quartet instability which will suppress the pair instability. More importantly, the same tendency can be seen even if the interaction is tuned away from the SU(4) limit.