Abstract

We have investigated analytically the nature of the transition to the Fulde–Ferrel–Larkin–Ovchinnikov (FFLO) superfluid phases in the vicinity of the tricritical point (TCP), where these phases begin to appear. Near the TCP, one can make an expansion of the free energy up to sixth order, both in the order parameter amplitude and wave vector. Restricting ourselves to the order parameter subspace (LO subspace) made of superposition of plane waves of the same wavelength, we obtain first order transitions and a cos( q · r ) form as the stablest FFLO phase. Moreover, going out of the LO subspace, combining analytical and numerical studies, we show that the actual order parameter at the transition is very close to the simple cos( q · r ) form.

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