We consider a generic two-dimensional system of fermionic particles with attractive interactions and no disorder. If time reversal symmetry is absent, it is possible to obtain incompressible insulating states in addition to the superfluid at zero temperature. The superfluid-insulator phase transition is found to be second order in type-II systems using a perturbative analysis of Cooper pairing instability in quantum Hall states of unpaired fermions. We obtain the pairing phase diagram as a function of chemical potential (density) and temperature. However, a more careful analysis presented here reveals that the pairing quantum phase transition is always preempted by another transition into a strongly correlated normal state which retains Cooper pairing and cannot be smoothly connected to the quantum Hall state of unpaired fermions. Such a normal phase can be qualitatively viewed as a liquid of vortices, although it may acquire conventional broken symmetries. Even if it did not survive at finite temperatures its influence would be felt through strong quantum fluctuations below a crossover temperature scale. These conclusions directly apply to fermionic ultracold-atom systems near unitarity, but are likely relevant for the properties of other strongly correlated superfluids as well, including high-temperature superconductors.
We consider a generic two-dimensional system of fermionic particles with attractive interactions and no disorder. If time reversal symmetry is absent, it is possible to obtain incompressible insulating states in addition to the superfluid at zero temperature. The superfluid-insulator phase transition is found to be second order in type-II systems using a perturbative analysis of Cooper pairing instability in quantum Hall states of unpaired fermions. We obtain the pairing phase diagram as a function of chemical potential (density) and temperature. However, a more careful analysis presented here reveals that the pairing quantum phase transition is always preempted by another transition into a strongly correlated normal state which retains Cooper pairing and cannot be smoothly connected to the quantum Hall state of unpaired fermions. Such a normal phase can be qualitatively viewed as a liquid of vortices, although it may acquire conventional broken symmetries. Even if it did not survive at finite temperatures its influence would be felt through strong quantum fluctuations below a crossover temperature scale. These conclusions directly apply to fermionic ultracold-atom systems near unitarity, but are likely relevant for the properties of other strongly correlated superfluids as well, including high-temperature superconductors.
Fermionic superfluids can undergo phase transitions into different kinds of normal regimes, loosely characterized by whether Cooper pairs remain locally stable. If the normal phase retains strong pairing fluctuations, it behaves like a liquid of vortices, which has been observed in cuprate superconductors. We argue that analogous strongly correlated normal states exist in two-dimensional neutral fermion liquids near unitarity, where superfluid is destroyed by fast rotation. These states have non-universal properties, and if they develop as distinct thermodynamic phases they can be characterized as quantum Hall states of Cooper pairs. The formal analysis is based on a model with SP(2N) symmetry that describes the quantum critical region in the vicinity of a broad Feshbach resonance. We explore the pairing phase diagram and demonstrate that the considered model has macroscopically degenerate bosonic modes in the normal phase, to all orders in 1/N. It takes finite-range interactions to lift this degeneracy, making the Abrikosov flux lattice of the superfluid particularly susceptible to quantum melting.
Ultracold atoms in an optical lattice provide a platform for realization of the superfluid (SF) state, a quantum order with paired charge-neutral fermions. In this paper, we study the SF state in the two-dimensional attractive Hubbard model with $\ensuremath{\pi}$ flux on each plaquette. The SF state in the $\ensuremath{\pi}$-flux lattice model suffers very strong quantum fluctuations and the ground state becomes a possible quantum phase liquid state. In this phase, there exists Cooper pairing together with a finite energy gap for the atoms, but no long-range SF phase coherence exists at zero temperature. In addition, we discuss the properties of the SF vortices.
By analyzing vortex lattices, re-entrant Cooper pairing, and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a single theoretical framework, we explore how vortices and spin textures join to protect superconductivity against large magnetic fields. We use a rapidly rotating ultracold gas of fermionic atoms near unitarity as a model system amenable to experimental exploration and discover a hierarchy of spin-polarized and FFLO phases in which a metal or a band insulator of unpaired particles coexists with a spatially modulated superfluid hosting a vortex lattice. Quantum fluctuations can transform these phases into strongly correlated ``vortex-liquid'' metals and insulators, respectively. We argue that vortex lattices significantly enhance the stability of FFLO states and discuss prospects for observing these states in cold-atom experiments.
We analyze the phase diagram of the spin-21 Yukawa--Sachdev-Ye-Kitaev model, which describes complex spin-21 fermions randomly interacting with real bosons via a Yukawa coupling, at finite temperatures and varying fermion density. A recent work [Wang and Chubukov, Phys. Rev. Res. 2, 033084 (2020).] showed that, upon varying the filling or chemical potential, a first-order quantum phase transition exists between a non-Fermi-liquid (NFL) phase and an insulating phase. Here we show that in such a model with time-reversal symmetry this quantum phase transition is preempted by a pairing phase that develops as a low-temperature instability. As a remnant of the would-be NFL-insulator transition, the superconducting critical temperature rapidly decreases beyond a certain chemical potential. On the other hand, depending on the parameters, the first-order quantum phase transition extends to finite temperatures and terminates at a thermal critical point, beyond which the NFL and the insulator become the same phase, similar to that of the liquid-gas and metal-insulator transition in real materials. We determine the pairing phase boundary and the location of the thermal critical point via combined analytic and quantum Monte Carlo numeric efforts. Our results provide a model realization of the transition of NFLs towards superconductivity and insulating states and therefore offer a controlled platform for future investigations of the generic phase diagram that hosts a NFL, insulator, and superconductor and their phase transitions.
We study the system of a dilute gas of fermions in 3-dimensions, with attractive interactions tuned to the unitarity point, using the non-perturbative Restricted Path Integral Monte Carlo (R-PIMC) method. The pairing and superfluid properties of this system are calculated at finite temperature. The total energy at very low temperature from our results agrees closely with that of previous ground-state Quantum Monte Carlo calculations. We identify the temperature T � � 0.70ǫF below which pairing correlations develop, and estimate the critical temperature for the superfluid transition Tc � 0.25ǫF from a finite size scaling analysis of the superfluid density. PACS numbers: The recent experiments, starting with generating a degenerate gas of cold atoms[3], the use of Feshbach resonance to tune the effective interaction between the fermions[4, 5], the measurements of the gap to identify a pairing scale[6] and the measurements of vortices[7] to identify the superfluid state, have all given an impetus to the study of superfluidity in the BCS-BEC crossover regime. The nature of superconductivity or superfluidity in a many-particle system with an increasing pairing attraction was shown [1, 2] to interpolate smoothly between the BCS regime for weak attraction between the fermions, and the Bose-Einstein condensation (BEC) regime for strong coupling. In the weak coupling regime, the Cooper pair size is much larger than the interparticle spacing, and the simultaneous pairing and condensation of fermions is well described by the BCS theory. In the strong coupling regime, fermions form strongly bound bosonic molecules at a pairing temperature scale T ∗ that is considerably higher than the BEC temperature Tc. In a two species system of fermions with an attractive interaction between them, the unitary point is defined by the divergence of the zero energy s-channel scattering length, as, for two particles in free space. The unitary point is interesting since it describes a strongly correlated system with universal properties[8]. In general, there are two length scales that define the system: the interparticle spacing ∝ n −1/3 , and the scattering length as which contains information about the interaction potential. At the unitary point however, since as diverges, all the properties of the system are described by a single length scale k −1
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.