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arXiv:1211.1225 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Pairing fluctuation effects in a strongly coupled color superfluid/superconductor

Jin-Yi Pang, Jincheng Wang, Lianyi He

Published Sep 17, 2013• 1 citation

Abstract

We investigate the effects of pairing fluctuations in fermionic superfluids/superconductors where pairing occurs among three species (colors) of fermions. Such color superfluids/superconductors can be realized in three-component atomic Fermi gases and in dense quark matter. The superfluidity/superconductivity is characterized by a three-component order parameter which denotes the pairing among the three colors of fermions. Because of the SU(3) symmetry of the Hamiltonian, one color does not participate in pairing. This branch of fermionic excitation is gapless in the naive BCS mean-field description. In this paper, we adopt a pairing fluctuation theory to investigate the pairing fluctuation effects on the unpaired color in strongly coupled atomic color superfluids and quark color superconductors. At low temperature, a large pairing gap of the paired colors suppresses the pairing fluctuation effects for the unpaired color, and the spectral density of the unpaired color shows a single Fermi-liquid peak, which indicates the naive mean-field picture remains valid. As the temperature is increased, the spectral density of the unpaired color generally exhibits a three-peak structure: The Fermi-liquid peak remains but gets suppressed, and two pseudogaplike peaks appears. At and above the superfluid transition temperature, the Fermi-liquid peak disappears completely and all three colors exhibit pseudogaplike spectral density. The coexistence of Fermi liquid and pseudogap behavior is generic for both atomic color superfluids and quark color superconductors.

DOI: 10.1103/physrevd.88.054017

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We investigate the effects of pairing fluctuations in fermionic superfluids/superconductors where pairing occurs among three species (colors) of fermions. Such color superfluids/superconductors can be realized in three-component atomic Fermi gases and in dense quark matter. The superfluidity/superconductivity is characterized by a three-component order parameter which denotes the pairing among the three colors of fermions. Because of the SU(3) symmetry of the Hamiltonian, one color does not participate in pairing. This branch of fermionic excitation is gapless in the naive BCS mean-field description. In this paper, we adopt a pairing fluctuation theory to investigate the pairing fluctuation effects on the unpaired color in strongly coupled atomic color superfluids and quark color superconductors. At low temperature, a large pairing gap of the paired colors suppresses the pairing fluctuation effects for the unpaired color, and the spectral density of the unpaired color shows a single Fermi-liquid peak, which indicates the naive mean-field picture remains valid. As the temperature is increased, the spectral density of the unpaired color generally exhibits a three-peak structure: The Fermi-liquid peak remains but gets suppressed, and two pseudogaplike peaks appears. At and above the superfluid transition temperature, the Fermi-liquid peak disappears completely and all three colors exhibit pseudogaplike spectral density. The coexistence of Fermi liquid and pseudogap behavior is generic for both atomic color superfluids and quark color superconductors.

The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature

{T}_{\mathrm{c}}

decreases with pairing strength in the BEC regime, where it approaches asymptotically ${T}_{\mathrm{c}}=\ensuremath{\pi}an/2m$, with

a

being the

s

-wave scattering length, and

n

(

m

) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast-growing (absolute value of the) fermionic chemical potential $\ensuremath{\mu}$ and pairing gap $\mathrm{\ensuremath{\Delta}}$, which depends exponentially on the ratio

d/a

. Importantly,

{T}_{\mathrm{c}}

at unitarity increases with the lattice constant

d

and hopping integral

t

. The effect of the van Hove singularity on

{T}_{\mathrm{c}}

is identified. The superfluid density exhibits

{T}^{3/2}

power laws at low

T

, away from the extreme BCS limit. These predictions can be tested in future experiments.

We investigate the pairing symmetry of the superfluid state in repulsively interacting three-component (color) fermionic atoms in optical lattices. When two of the three color-dependent repulsions are much stronger than the other, pairing symmetry is an extended

s

wave, although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. On the other hand, when two of the three color-dependent repulsions are weaker than the other, pairing symmetry is a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave. This change in pairing symmetry is attributed to the change in the dominant quantum fluctuations from the density fluctuations of unpaired atoms and the color-density wave fluctuations to the color-selective antiferromagnet fluctuations. This phenomenon can be studied using existing experimental techniques.

Achieving room-temperature superconductivity has been a long-sought goal of both the physics community and the industry. The superfluid transition temperature

T_\mathrm{c}

of a Fermi system initially increases with increasing pairing strength between fermions following the mean-field prediction of the Bardeen-Cooper-Schrieffer (BCS) theory, and is then suppressed by pairing fluctuations as the strength increases further, which prevents

T_\mathrm{c}

from becoming high. Here we propose a mechanism for suppressing pairing fluctuations using the synergy between population imbalance and momentum space confinement in lattice systems, enabling an ultrahigh

T_\mathrm{c}

at moderately strong attraction. We show that in a three-dimensional optical lattice, strong Pauli exclusion between paired and excess majority fermions pushes up the pair excitation energy and suppresses finite-momentum pairing fluctuations. The mechanism is general to any lattice with a finite Brillouin zone; the optimal imbalance is modest (

p\lesssim 0.1

), keeping the Zeeman field small and avoiding orbital complications. The gapped pair dispersion at moderate imbalance exponentially suppresses thermal condensate depletion, providing a testable signature. The gapped dispersion, enhanced condensate fraction, and pseudogap reduction are all accessible in present-day experiments. This work opens new avenues toward room-temperature superconductivity.

We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase and amplitude fluctuations of the superfluid order parameter within a

T

-matrix theory, we calculate the superfluid density of states (DOS), as well as single-particle spectral weight, over the entire BCS-BEC crossover region below the superfluid transition temperature

{T}_{\mathrm{c}}

. We clarify how the pseudogap in the normal state evolves into the superfluid gap, as one passes through

{T}_{\mathrm{c}}

. While the pseudogap in DOS continuously evolves into the superfluid gap in the weak-coupling BCS regime, the superfluid gap in the crossover region is shown to appear in DOS after the pseudogap disappears below

{T}_{\mathrm{c}}

. In the phase diagram with respect to the temperature and interaction strength, we determine the region where strong pairing fluctuations dominate over single-particle properties of the system. Our results would be useful for the study of strong-coupling phenomena in the BCS-BEC crossover regime of a superfluid Fermi gas.

We investigate the

1/N

expansion proposed recently as a strategy to include quantum fluctuation effects in the nonrelativistic, attractive Fermi gas at and near unitarity. We extend the previous results by calculating the next-to-leading order corrections to the critical temperature along the whole crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation. We demonstrate explicitly that the extrapolation from the mean-field approximation, based on the

1/N

expansion, provides a useful approximation scheme only on the BCS side of the crossover. We then apply the technique to the study of strongly interacting relativistic many-fermion systems. Having in mind the application to color superconductivity in cold dense quark matter, we develop, within a simple model, a formalism suitable to compare the effects of order parameter fluctuations in phases with different pairing patterns. Our main conclusion is that the relative correction to the critical temperature is to a good accuracy proportional to the mean-field ratio of the critical temperature and the chemical potential. As a consequence, it is significant even rather deep in the BCS regime, where phenomenologically interesting values of the quark--quark coupling are expected. Possible impact on the phase diagram of color-superconducting quark matter is discussed.

We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. An effective attractive interaction is induced by density fluctuations of the third-color atoms. This superfluid state is stable against changes in filling close to half filling. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions.