Charged fixed point in the Ginzburg–Landau superconductor and the role of the Ginzburg parameter κ Original Research Article

We present a semi-perturbative approach which yields an infrared-stable fixed point in the Ginzburg–Landau for N=2, where N/2 is the number of complex components. The calculations are done in d=3 dimensions and below Tc, where the renormalization group functions can be expressed directly as functions of the Ginzburg parameter κ which is the ratio between the two fundamental scales of the problem, the penetration depth λ and the correlation length ξ. We find a charged fixed point for κ>1/2, that is, in the type II regime, where Δκ≡κ−1/2 is shown to be a natural expansion parameter. This parameter controls a momentum space instability in the two-point correlation function of the order field. This instability appears at a non-zero wave-vector p0 whose magnitude scales like ∼Δκβ̄, with a critical exponent β̄=1/2 in the one-loop approximation, a behavior known from magnetic systems with a Lifshitz point in the phase diagram. This momentum space instability is argued to be the origin of the negative η-exponent of the order field.