Title: Non-Fermi liquid at the FFLO quantum critical point,
Abstract: When a 2D superconductor is subjected to a strong in-plane magnetic field,
Zeeman polarization of the Fermi surface can give rise to inhomogeneous FFLO
order with a spatially modulated gap. Further increase of the magnetic field
eventually drives the system into a normal metal state. Here, we perform a
renormalization group analysis of this quantum phase transition, starting from
an appropriate low-energy theory recently introduced by Piazza et al. (Ref.1).
We compute one-loop flow equations within the controlled dimensional
regularization scheme with fixed dimension of Fermi surface, expanding in
$\epsilon = 5/2 - d$. We find a new stable non-Fermi liquid fixed point and
discuss its critical properties. One of the most interesting aspects of the
FFLO non-Fermi liquid scenario is that the quantum critical point is
potentially naked, with the scaling regime observable down to arbitrary low
temperatures. In order to study this possibility, we perform a general analysis
of competing instabilities, which suggests that only charge density wave order
is enhanced in the vicinity of the quantum critical point.