Cooper pairing of fermions is a profound phenomenon that has become very important in many different areas of physics in the recent past. This book brings together, for the first time, experts from various fields involving Cooper pairing, at the level of BCS theory and beyond, including the study of novel states of matter such as ultracold atomic gases, nuclear systems at the extreme, and quark matter with application to neutron stars. Cross-disciplinary in nature, the book will be of interest to physicists in many different specialties, including condensed matter, nuclear, high-energy, and astrophysics. The emphasis is on novel issues beyond ordinary BCS theory such as pairing in asymmetric systems, the polarization effect, and higher spin pairing. These topics are rarely treated at the textbook level and all of them are the subjects of intensive ongoing research. The book also considers various new techniques widely used in current research that differ significantly from the conventional condensed matter approaches described in the standard literature. Sample Chapter(s). Chapter 1: Color Superconductivity in Dense, but not Asymptotically Dense, Quark Matter (1,976 KB). Contents: Color Superconductivity in Dense, But Not Asymptotically Dense, Quark Matter (M Alford & K Rajagopal); Larkin-Ovchinnikov-Fulde-Ferrell Phases in QCD (G Nardulli); Phase Diagram of Neutral Quark Matter at Moderate Densities (S B Rster et al.); Spontaneous Nambu-Goldstone Current Generation Driven by Mismatch (M Huang); The CFL Phase and m s: An Effective Field Theory Approach (T Schnfer); Nuclear Superconductivity in Compact Stars: BCS Theory and Beyond (A Sedrakian & J W Clark); Pairing Properties of Dressed Nucleons in Infinite Matter (W H Dickhoff & H Mther); Pairing in Higher Angular Momentum States: Spectrum of Solutions of the 3 P 2 - 3 F 2 Pairing Model (M V Zverev et al.); Four-Particle Condensates in Nuclear Systems (G RApke & P Schuck); Realization, Characterization, and Detection of Novel Superfluid Phases with Pairing Between Unbalanced Fermion Species (K Yang); Phase Transition in Unbalanced Fermion Superfluids (H Caldas). Readership: Researchers and graduate students in the areas of condensed matter, nuclear and particle physics."

In this thesis we study the spin or pseudospin singlet pair condensation of two diRTMerent 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.

The rapidly developing topic of ultracold atoms has many actual and potential applications for condensed-matter science, and the contributions to this book emphasize these connections. Ultracold Bose and Fermi quantum gases are introduced at a level appropriate for first-year graduate students and non-specialists such as more mature general physicists. The reader will find answers to questions like: how are experiments conducted and how are the results interpreted? What are the advantages and limitations of ultracold atoms in studying many-body physics? How do experiments on ultracold atoms facilitate novel scientific opportunities relevant to the condensed-matted community? This volume seeks to be comprehensible rather than comprehensive; it aims at the level of a colloquium, accessible to outside readers, containing only minimal equations and limited references. In large part, it relies on many beautiful experiments from the past fifteen years and their very fruitful interplay with basic theoretical ideas. In this particular context, phenomena most relevant to condensed-matter science have been emphasized. - Introduces ultracold Bose and Fermi quantum gases at a level appropriate for non-specialists - Discusses landmark experiments and their fruitful interplay with basic theoretical ideas - Comprehensible rather than comprehensive, containing only minimal equations

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.

This thesis presents a theoretical study of Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) pairing states in inhomogeneous systems of cold atoms and of electrons. Features of spatially separated phases are explored, with particular focus on the behavior of the condensed phase and its experimental measures. Three specific systems are addressed below. First, we study bosonic atoms in three-dimensional optical lattices in the presence of an external spherical harmonic trapping potential. We investigate the critical value associated with the lattice depth and interaction strength below which the system undergoes a quantum phase transition from a global BEC phase to a coexistence of local BEC and Mott-insulating phases. We discuss the ground state properties, excitations, and experimental signatures of the condensate surrounded by the Mott-insulators. BCS pairing in fermionic atoms of two spin species that are confined to spatially separated trapping potentials is investigated next. We investigate the one-dimensional limit and find that, with increasing separation between the spin-dependent traps, the fermions undergo a transition from a global fully-paired phase to a coexistence of a fully-paired phase, a spin-imbalanced phase with oscillatory pairing, the so-called Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, and an unpaired completely spin-polarized phase. We present numerical profiles of key parameters of the phase diagram as well as observable signatures of the oscillatory pairing phase. The third topic is that of transport physics in a superconductor-ferromagnetic-metal (S/F) hybrid in which superconducting phases and ferromagnetic normal phases are artificially combined. We model the interface between the S and F regions and discuss possible scattering processes at the interface. We apply the Blonder-Tinkham-Klapwijk treatment with the interfacial model to calculate resistance of the system. These results explain recent experimental observations.

Recent experimental and theoretical progress has elucidated the tunable crossover, in ultracold Fermi gases, from BCS-type superconductors to BEC-type superfluids. The BCS-BEC Crossover and the Unitary Fermi Gas is a collaborative effort by leading international experts to provide an up-to-date introduction and a comprehensive overview of current research in this fast-moving field. It is now understood that the unitary regime that lies right in the middle of the crossover has remarkable universal properties, arising from scale invariance, and has connections with fields as diverse as nuclear physics and string theory. This volume will serve as a first point of reference for active researchers in the field, and will benefit the many non-specialists and graduate students who require a self-contained, approachable exposition of the subject matter.