Inhomogeneity driven by Higgs instability in a gapless superconductor

We derive the low energy effective action for the collective modes in systems of fermions interacting via a short-range s-wave attraction, featuring unequal chemical potentials for the two fermionic species (asymmetric systems). As a consequence of the attractive interaction, fermions form a condensate that spontaneously breaks the U(1) symmetry associated with total number conservation. Therefore at sufficiently small temperatures and asymmetries, the system is a superfluid. We reproduce previous results for the stability conditions of the system as a function of the four-fermion coupling and asymmetry. We obtain these results analyzing the coefficients of the low energy effective Lagrangian of the modes describing fluctuations in the magnitude (Higgs mode) and in the phase (Goldstone mode) of the difermion condensate. We find that for certain values of parameters, the mass of the Higgs mode decreases with increasing mismatch between the chemical potentials of the two populations, if we keep the scattering length and the gap parameter constant. Furthermore, we find that the energy cost for creating a position dependent fluctuation of the condensate is constant in the gapped region and increases in the gapless region. These two features may lead to experimentally detectable effects. As an example, we argue that if the superfluid is put in rotation, the square of the radius of the outer core of a vortex should sharply increase on increasing the asymmetry, when we pass through the relevant region in the gapless superfluid phase. Finally, by gauging the global U(1) symmetry, we relate the coefficients of the effective Lagrangian of the Goldstone mode with the screening masses of the gauge field.Comment: 41 pages, 6 figures. Expanded introduction, improved figures, conclusions unchanged. Version to match the published versio

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Collective modes in asymmetric ultracold Fermi systems

Gubankova

Mannarelli

Sharma

2010

Annals of Physics

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Interweaving chiral spirals

et al. 2012

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We elaborate how to construct interweaving chiral spirals in (2+1) dimensions, defined as a superposition of chiral spirals oriented in different directions. We divide a two-dimensional Fermi sea into distinct wedges, characterized by the opening angle 2Θ and depth Q p F , where p F is the Fermi momentum. In each wedge, the energy is lowered by forming a single chiral spiral. The optimal values for Θ and Q are chosen by balancing this gain in energy versus the cost of deforming the Fermi surface (which dominates at large Θ) and patch-patch interactions (dominant at small Θ). Using a non-local four-Fermi interaction model, we estimate the gain and cost in energy by expanding in terms of 1/N c (where N c is the number of colors), Λ QCD /Q, and Θ. Due to a form factor in our non-local model, at small 1/N c the mass gap (chiral condensate) is large, and the interaction among quarks and the condensate local in momentum space. Consequently, interactions between different patches are localized near their boundaries, and it is simple to embed many chiral spirals. We identify the dominant and subdominant terms at high density and catagorize formulate an expansion in terms of Λ QCD /Q or Θ. The kinetic term in the transverse directions is subdominant, so that techniques from (1+1)-dimensional systems can be utilized. To leading order in 1/N c and Λ QCD /Q, the total gain in energy is ∼ p F Λ 2 QCD with Θ ∼ (Λ QCD /p F ) 3/5 . Since Θ decreases with increasing p F , there should be phase transitions associated with the change in the wedge number. We also argue the effects of subdominant terms at lower density where the large-N c approximation is more reliable.

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An unconventional colour superconductor

Huang

2007

J. Phys. G: Nucl. Part. Phys.

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Superfluidity, or superconductivity with mismatched Fermi momenta, appears in many systems such as charge-neutral dense quark matter, asymmetric nuclear matter, and in imbalanced cold atomic gases. The mismatch plays the role of breaking the Cooper pairing, and the pair-breaking state cannot be properly described in the framework of standard BCS theory. I give a brief review on recent theoretical developments in understanding unconventional colour superconductivity, including a gapless colour superconductor, chromomagnetic instabilities and the Higgs instability in the gapless phase. I also introduce a possible new framework for describing an unconventional colour superconductor.

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Inhomogeneity driven by Higgs instability in a gapless superconductor

Cited by 11 publications

References 74 publications

Collective modes in asymmetric ultracold Fermi systems

Collective modes in asymmetric ultracold Fermi systems

Interweaving chiral spirals

An unconventional colour superconductor

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