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

We investigate the 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 K40 Fermi gas. Including pairing fluctuations within a strong-coupling T-matrix theory, we determine the px-wave superfluid phase transition temperature Tcpx, as well as the other phase transition temperature Tcpx+ipy(<Tcpx), below which the superfluid order parameter has the px+ipy-wave symmetry. In the normal state near Tcpx, 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 (Tcpx+ipy<T≤Tcpx), 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.