Systems showing resonant superfluidity, driven by an exchange coupling of strength g between uncorrelated pairs of itinerant fermions and tightly bound ones, undergo a first-order phase transition as g increases beyond some critical value gc. The superfluid phase for g<or=gc is characterized by a gap in the fermionic single-particle spectrum and an acoustic sound-wave-like collective mode of the bosonic resonating fermion pairs inside this gap. For g>gc this state gives way to a phase-uncorrelated bosonic liquid with a q2 spectrum.
We consider systems where the amplitude and the phase of a superfluid order parameter are controlled independently by local, respectively non-local phase correlations of the internal degrees of freedom of quasi-particles which characterize the different phases of such fermionic systems. A possible realization of such a situation is when pairing into the bosonic entities occurs via resonant scattering of itinerant fermionic particles. Examples for that are the ultracold fermionic gases in optical traps and lattices, the correlated electronic systems and strongly coupled electron-phonon systems, such as seen in the high Tc cuprates. We demonstrate the occurrence of a quantum phase transition from a superfluid to a phase uncorrelated boson liquid state in such systems, which is controlled by the competing effects of long and short range phase correlations of the constituents of composite quasi-particles.
We study the ground-state properties of one-dimensional mixtures of bosonic and fermionic atoms resonantly coupled to fermionic Feshbach molecules. When the particle densities of fermionic atoms and Feshbach molecules differ, the system undergoes various depletion transitions between binary and ternary mixtures as a function of the detuning parameter. However, when the particle densities of fermionic atoms and Feshbach molecules are identical, the molecular conversion and disassociation processes induce a gap in a sector of low-energy excitations, and the remaining system can be described by a two-component Tomonaga-Luttinger liquid. Using a bosonization scheme, we derive the effective low-energy Hamiltonian for the system, which has a similar form as that of the two-chain problem of coupled Tomonaga-Luttinger liquids. With the help of improved perturbative renormalization group analysis of the latter problem, we determine the ground-state phase diagram and find that it contains a phase dominated by composite superfluid or pairing correlations between the open and closed resonant channels.
The change-over from phase- to amplitude-fluctuation-driven superconductivity is examined for a composite system of free electrons (fermions with concentration
nF) and localized electron pairs (hard-core bosons with concentration
nB) as a function of doping---changing the total concentration of charge carriers
(ntot=nF+2nB). The coupling together of these two subsystems via a charge exchange term induces electron pairing and ultimately superconductivity in the fermionic subsystem. The difference in statistics of the two species of charge carriers has important consequences on the doping mechanism, showing an onset temperature
T∗ of incoherent electron pairing in the fermionic subsystem (manifest in form of a pseudogap), which steadily decreases with decreasing
ntot. Below
T∗ this electron pairing leads, in the normal phase, to electron-pair resonant states (Cooperons) with quasiparticle features which strongly depend on
ntot. For high concentrations, where ${n}_{B}\ensuremath{\simeq}0.5,$ correlation effects between the hard-core bosons lead to itinerant Cooperons having a heavy mass
mp, but are long lived. Upon reducing the concentration of charge carriers and consequently
nB, the mass as well as the lifetime of those Cooperons is considerably reduced. As a result, for high values of
nB, a superconducting state below
T∗ sets in at a
Tc, being controlled by the phase stiffness ${D}_{\ensuremath{\varphi}}={\ensuremath{\Elzxh}}^{2}{n}_{p}{/m}_{p}$ of those Cooperons, where
np denotes their density. Upon reducing
ntot, the phase stiffness steadily increases, and eventually exceeds the pairing energy
kBT∗. There, the Cooperons loose their well defined itinerant quasi-particle features and superconductivity gets controlled by amplitude fluctuations. The resulting phase diagram with doping is reminiscent of that of the phase fluctuation scenario for high-
Tc superconductivity, except that in our scenario the determinant factors are the mass and the lifetime of the Cooperons rather than their density.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
After a short review of the different physics in the weak and strong coupling regime, resulting in amplitude fluctuation controlled Cooper pair superconductivity and phase fluctuation controlled superfluidity of tightly bound local polaron pairs, we suggest a scenario for the cross-over regime between those two. It is based on the idea of resonating Bipolarons inside a Fermi sea of uncorrelated electrons, similar to the Feshbach resonance in Fermionic gases in optical traps. Due to the competition between amplitude and phase correlations such systems in the cross-over regime can exhibit a superconductor to insulator transition upon varying the strength of that resonance.