  It is known from the solution of the two-body problem that an anisotropic
dipolar interaction can give rise to s-wave scattering resonances, which are
named as dipolar interaction induced resonaces (DIIR). In this letter, we study
zero-temperature many-body physics of a two-component Fermi gas across a DIIR.
In the low-density regime, it is very striking that the resulting pairing order
parameter is a nearly isotropic singlet pairing and the physics can be well
described by an s-wave resonant interaction potential with finite range
corrections, despite of the anisotropic nature of dipolar interaction. The
pairing energy is as strong as a unitary Fermi gas nearby a magnetic Feshbach
resonance. In the high density regime, the anisotropic effect plays an
important role. We find phase transitions from singlet pairing to a state with
mixed singlet and triplet pairing, and then from mixed pairing to pure triplet
pairing. The state with mixed pairing spontaneously breaks the time-reversal
symmetry.
