Pair condensation in polarized fermion systems
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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.