The BCS gap equation for spin-polarized fermions

Abstract

We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For $\cosh ({\delta }_{\mu }/T)\le 2$, with $T$ the temperature and ${\delta }_{\mu }$ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in \cite{FHNS,HHSS,HS}. For $\cosh ({\delta }_{\mu }/T)>2$ the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.

23 pages, 1 figure

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Direct Observation of the Superfluid Phase Transition in Ultracold Fermi Gases
• Finite temperature phase diagram of a polarised Fermi condensate
• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• The BCS Critical Temperature for Potentials with Negative Scattering Length
• Spectral properties of the BCS gap equation of superfluidity
• Temperature Effects in a Fermi Gas with Population Imbalance

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• Persistence of translational symmetry in the BCS model with radial pair interaction
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
• Another operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity
• An operator-theoretical study of the specific heat and the critical magnetic field in the BCS-Bogoliubov model of superconductivity
• A lower bound for the BCS functional with boundary conditions at infinity
• An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature
• Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature