We consider a gas of two species of fermions with population imbalance. Using the renormalization group in d=1+ϵ spatial dimensions, we show that for spinless fermions and 2>ϵ>0 a fixed point appears at finite attractive coupling where the quasiparticle residue vanishes, and identify this with the transition to Larkin-Ovchinnikov-Fulde-Ferrell order (inhomogeneous superconductivity). When the two species of fermions also carry spin degrees of freedom we find a fixed point indicating a transition to spin density wave order.
We study a dissipative gauge theory of nonrelativistic fermions in 2+1 dimensions at zero temperature by the Wilsonian renormalization-group method. In this theory, we incorporate in the fermion propagator a new term of the form $ i κ\cdot\sign(ω)$ (where
κ is a parameter and
ω is the fermion frequency), which is usually induced by impurity effects. In the previous papers, we studied this system for
κ=0, and showed that there exists a non-Fermi-liquid infrared fixed point. In this paper, we address the question whether this non-Fermi-liquid behavior remains stable or not in the presence of impurity effects, i.e., the
κ term. Our results show that the non-Fermi-liquid fixed point is unstable for
κ=0 and an effective gauge coupling constant tends to vanish at low energies. However, in intermediate energy scales, the behavior of correlation functions for
κ=0 is controlled by the non-Fermi-liquid fixed point at
κ=0, i.e., a crossover phenomenon appears. Physical implications of this phenomenon are discussed.
We consider the emergence of a non-Fermi liquid fixed point in two-dimensional metals at the onset of a quantum phase transition from a Fermi liquid state to an incommensurate charge density wave (CDW) ordered phase. The momentum of the CDW boson is centred at the wavevector Q, which connects a single pair of antipodal points on the Fermi surface with antiparallel tangent vectors. We employ the dimensional regularization technique in which the co-dimension of the Fermi surface is extended to a generic value, while keeping the dimension of Fermi surface itself fixed at one. Although the system is strongly coupled at dimension d=2, the interactions become marginal at the upper critical dimension d=dc, whose value is found to be 5/2. Using a controlled perturbative expansion in the parameter ϵ=dc−d, we compute the critical exponents of the stable infrared fixed point characterizing the quantum critical point. The scalings of the original theory are determined by setting ϵ=1/2, where the fermion self-energy is seen to scale with the frequency with a fractional power law of 2/3, which is the telltale signature of a typical non-Fermi liquid phase.