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arXiv:hep-ph/0502003

Phase Transition in Asymmetrical Superfluids

Heron Caldas, C. W. Morais, A. L. Mota

Published Jan 31, 2005• 0 citations
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Abstract

In this paper, we study phase transitions in asymmetrical fermion superfluids. In this scenario, the candidates to form pair are particles with mismatched masses and chemical potentials. We derive an expression for the critical temperature in terms of the gap and masses (or chemical potentials) when the constraint of equal Fermi surfaces $m_a\mu_a = m_b\mu_b$ is imposed.

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In this paper, we study phase transitions in asymmetrical fermion superfluids. In this scenario, the candidates to form pair are particles with mismatched masses and chemical potentials. We derive an expression for the critical temperature in terms of the gap and masses (or chemical potentials) when the constraint of equal Fermi surfaces maμa=mbμbm_a\mu_a = m_b\mu_bma​μa​=mb​μb​ is imposed.
In this chapter the recent theoretical work on phase transition in imbalanced fermion superfluids is reviewed. The imbalanced systems are those in which the two fermionic species candidate to form pairing have different Fermi surfaces or densities. We consider systems subjected to weak interactions. In this scenario two distinct phase transitions are predicted to occur. A thermodynamical phase transition, induced by the temperature (T), and a quantum phase transition as a function of the increasing chemical potentials asymmetry, that takes place at zero temperature. We also briefly discuss some recent experimental work at non-zero T with imbalanced Fermi gases in cold atomic traps.
We analytically investigate superfluid phase in two dimension at zero temperature for asymmetric Fermi gas. Analytic expressions for both gap and chemical potentials at mean-field level are obtained as a function of binding energy and population imbalance when mass of different types of fermions is equal. We identify regions corresponding to normal, Sarma phase for different polarization, or mass ratio and discuss topological phase diagram in the BCS-BEC crossover and find that energy gap and chemical potential behave differently in these topological quantum phase. We also obtain the low-frequency and long-wavelength collective excitation spectrum and find sound velocity has a maximum when two types of mass are equal.
We study the phase diagram of a two component Fermi system with a weak attractive interaction. Our analysis includes the leading order Hartree energy shifts and pairing correlations at finite temperature and chemical potential difference between the two fermion species. We show that in an asymmetric system, the Hartree shift to the single particle energies is important for the phase competition between normal and superfluid phase and can change the phase transition curve qualitatively. At large chemical potential asymmetry we find that a somewhat fragile superfluid state can be favored due to finite-temperature effects. We also investigate the transition between the normal phase and an inhomogeneous superfluid phase to study how gradient instabilities evolve with temperature and asymmetry. Finally, we adopt our analysis to study the density profiles of similar asymmetric Fermi systems that are being observed in cold-atom experiments.
We discuss the superfluid phase transition of a strongly interacting Fermi gas with unequal (asymmetric) chemical potentials in two pairing hyperfine states, and map out its phase diagram near the BCS-BEC crossover. Our approach includes the fluctuation contributions of "preformed Cooper pairs" to the thermodynamic potential at finite temperature. We show that, below a critical difference in chemical potentials between species, a normal gas is unstable towards the formation of either a finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov superconducting phase or a uniform superfluid, depending on the asymmetry and interaction strengths. We determine the value of critical chemical potential mismatch, and find that it is consistent with a recent measurement by Zwierlein et al. ( Science , 311 (2006) 492).