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arXiv:0810.4149

Pairing instability driven by macroscopically degenerate collective modes in two-dimensional rotating fermion liquids near unitarity

Predrag Nikolić

Published Oct 22, 2008• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0810.4149

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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.
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.
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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.
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.
We study two-dimensional massless Dirac fermions at neutrality, coupled to bosonic modes through a Yukawa interaction. We then examine the intriguing possibility that such a system, devoid of carriers at zero temperature, might nevertheless exhibit superconductivity. Remarkably, we find that superconductivity emerges in the vicinity of Gross-Neveu quantum criticality, provided the fermions cease to behave as well-defined quasiparticles, that is, once their anomalous dimension in the normal state becomes sufficiently large. In other words, well-defined fermions do not superconduct, whereas ill-defined ones do. We analyze four symmetry-distinct bosonic modes, each capable of driving normal-state criticality and, in three of the four cases, giving rise to a distinct superconducting phase. While phase fluctuations are strong in this regime, we argue that they do not destroy the superconducting state. We further characterize the resulting pairing states for a concrete Dirac model of spin-orbit coupled systems with orbitals of different parity. Our results are obtained using the Sachdev-Ye-Kitaev (SYK)-inspired framework for Dirac systems introduced by Kim [Dirac fast scramblers, ], which provides a controlled approach to the strongly coupled regime of Dirac fluids near Gross-Neveu criticality.
We established superfluidity in a two-state mixture of ultracold fermionic atoms with imbalanced state populations. This study relates to the long-standing debate about the nature of the superfluid state in Fermi systems. Indicators for superfluidity were condensates of fermion pairs and vortices in rotating clouds. For strong interactions, near a Feshbach resonance, superfluidity was observed for a broad range of population imbalances. We mapped out the superfluid regime as a function of interaction strength and population imbalance and characterized the quantum phase transition to the normal state, known as the Pauli limit of superfluidity.