  We study the nature of superfluid pairing in imbalanced Fermi mixtures in two
spatial dimensions. We present evidence that the combined effect of Fermi
surface mismatch and order parameter fluctuations of the superfluid condensate
can lead to continuous quantum phase transitions from a normal Fermi mixture to
an intermediate Sarma-Liu-Wilczek superfluid with two gapless Fermi surfaces --
even when mean-field theory (incorrectly) predicts a first order transition to
a phase-separated "Bardeen-Cooper-Schrieffer plus excess fermions" ground
state. We propose a mechanism for non-Fermi liquid behavior from repeated
scattering processes between the two Fermi surfaces and fluctuating Cooper
pairs. Prospects for experimental observation with ultracold atoms are
discussed.
