Pairing And Condensation In Fermionic Systems PDF Download

This dissertation covers my theoretical work in the field of pairing of fermions and BCS-BEC crossover behavior in various condensed matter systems. High temperature superconductors, heavy fermion systems, 2D semiconductors undergoing a semiconductor-superconductor transition, and ultracold atomic Fermi gases are examples of novel systems that provide us with a rich playground to study pairing phenomena such as superconductivity or superfluidity. In this dissertation, with ultracold fermions in mind, I attempt to address some of the outstanding theoretical issues regarding pairing of fermions for arbitrary interactions, and for arbitrary population and mass imbalance. In so doing, I explore pairing in Bose-Einstein condensation EC) and Bardeen-Cooper-Schrieffer CS) regimes, and the behavior at the BEC-BCS crossover. I investigate the stability of paired many-fermion ground states, e.g., superfluidity and phase separated states; and possible phase transitions between these ground states. The specific projects that I undertake at the mean-field level are: interplay of intra- and inter- species pairing correlations in determining s-wave pairing in spin-population imbalanced Fermi systems; p-wave pairing in systems with mismatched fermi surfaces; stability of "breached pairs" states with p-wave symmetry in BEC and BCS regimes; use of Bogoliubov-de Gennes equations to study spatial variation of the pairing order parameter; and superconductivity with unconventional pairing symmetries in 2D systems with an "inherent" gaps, such as in semiconducting systems. In the case of s-wave pairing in a spin-population imbalanced system, while the system phase separates into normal and superfluid components, I show that the inclusion of intra-species correlation stabilizes a supefluid phase, up to a critical polarization, on the BCS side. For S=1, ms=0 triplet p-wave pairing in a population imbalanced system, I obtain a rich phase diagram. In addition to the states Δ"1 propto Y1"1, a multitude of "mixed" SF states formed of linear combinations of Y1m's give global energy minimum under a phase stability condition. States with local minimum are also obtained. With increased polarization, the global minimum SF states may undergo a quantum phase transition to the local minimum SF states. I also study effects of finite temperature (T) and of mass imbalance (r) between the species. Though the features of the phase diagram are not changed qualitatively from the equal mass (r=1) case, the critical temperature Tc shows some interesting behavior for large polarization. Our p-wave pairing provides an arena to study "breached pairing" P), i.e., phase separation in momentum space. While this is not stable in BCS regime for s-wave pairing, I find that p-wave BP phases may be stable in both BCS and BEC regimes for arbitrary mass ratio, r. To explore many-body effects beyond mean-field, I study the effects of quantum fluctuations on equilibrium and pairing properties in BEC and BCS regimes and near the crossover (unitarity limit). I apply this to systems subjected to p-wave Feshbach resonance and compare with the results for the s-wave case. I also study the effects of these fluctuations on possible suppression of the superfluid transition temperature from dilute to dense regimes and at unitarity, and find the suppression factor of 2.2 to be quite robust, except close to unitarity. Specific systems to which my work may apply are population imbalanced cold atomic systems, 2D systems with "inherent gap", such as semiconducting systems, and strongly correlated Fermi systems close to the unitarity limit at the BEC-BCS crossover. My research utilizes method of many-body quantum field theory, quantum statistical mechanics, diagrammatic perturbation theory, notions of superconductivity and superfluidity at and beyond mean-field level. In many instances, I have developed detailed and reliable computer codes relevant to my work.