## Pair condensation in polarized fermion systems

##### Abstract

In this thesis we study the spin or pseudospin singlet pair condensation of
two different kinds of polarized fermion systems. Using generalized BCS mean-field
theories we study how pairing adapts to unequal spin or pseudospin populations.
After briefly reviewing the basic physics of superconductivity in Chapter 2, in Chapter
3 the mean-field theory for electron-hole bilayer systems is derived to describe
the condensation of excitons which is analogous to the Cooper pair condensation in
superconductors. Self-consistent solution of the exciton system gap equation shows
that the excitation energy spectrum is qualitatively the same as in superconductors.
In Chapter 4 the role of the spin degree of freedom in the bilayer system is investigated
by generalizing the two-component mean-field theory developed in Chapter
3 to four-component cases. The main consequence is that population polarization
leads to ferromagnetism. The interplay between exciton condensation and spontaneous
spin-order is the most important consequence of the presence of both spin
and pseudospin degrees of freedom in excitonic condensates. In a sense that we
explain in this Chapter, both normal and condensed fluids are present in the ferromagnetic
excitonic state. Using the Rashba spin-orbit interaction model derived
in the appendix, we show that an external electric field can alter the characteristics
of the ferromagnetic condensate phase. The spin splitting by the spin-orbit
interaction and its different spin state structures lead to qualitatively different magnetic
properties for electron and hole layers. In Chapter 5 we turn our attention
to a second class of polarized fermion systems that is of great current interest. A
fully quantum mechanical treatment of a rotating fermion atom cloud is developed
and implicit equations determining the critical temperatures for all center-of-mass
Landau level pairings are obtained. In Chapter 6 the condition for the realization
of higher center-of-mass Landau level pairing, which corresponds to FFLO state in
spin split superconductors, is determined by calculating the critical temperatures
for all possible pairing channels. It is shown that FFLO states can be realized in
the strong interaction and low rotation frequency regimes in parameter space, where
the pairing energy can survive the high polarization.

##### Department

##### Description

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