Pairing fluctuations and anisotropic pseudogap phenomenon in an ultracold superfluid Fermi gas with plural p-wave superfluid phases

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We investigate superfluid properties of a one-component Fermi gas with a uniaxially anisotropic p-wave pairing interaction, Uₓ>Uy=Uz (where Uᵢ (i=x,y,z) is a pᵢ-wave pairing interaction). This type of interaction is considered to be realized in a ⁴⁰K Fermi gas. Including pairing fluctuations within a strong-coupling T-matrix theory, we determine the pₓ-wave superfluid phase transition temperature Tᵖˣ c, as well as the other phase transition temperature T cpₓ+ipy (<T cᵖˣ), below which the superfluid order parameter has the pₓ+ipy-wave symmetry. In the normal state near Tᵖˣ c, pₓ-wave pairing fluctuations are shown to induce an anisotropic pseudogap phenomenon, where a dip structure in the angle-resolved density of states around ω=0 is the most remarkable in the pₓ direction. In the pₓ-wave superfluid phase (T cpₓ+ipy<T≤ T cᵖˣ), while the pseudogap in the pₓ direction continuously changes to the superfluid gap, the pseudogap in the perpendicular direction to the pₓ axis is found to continue developing, because of enhanced py-wave and pz-wave pairing fluctuations around the node of the pₓ-wave superfluid order parameter. Since pairing fluctuations are always suppressed in the isotropic s-wave superfluid state, this phenomenon is peculiar to an unconventional Fermi superfluid with a nodal superfluid order parameter. Since the p-wave Fermi superfluid is the most promising non s-wave pairing state in an ultracold Fermi gas, our results would contribute to understanding how the anisotropic pairing fluctuations, as well as the existence of plural superfluid phases, affect many-body properties of this unconventional Fermi superfluid.