Gauge dependence of the critical dynamics at the superconducting phase transition

Abstract

The critical dynamics of superconductors in the charged regime is reconsidered within field-theory. For the dynamics, the Ginzburg-Landau model with complex order parameter coupled to the gauge field suggested earlier [Lannert et al. Phys. Rev. Lett. 92, 097004 (2004)] is used. Assuming relaxational dynamics for both quantities, the renormalization group functions within one loop approximation are recalculated for different choices of the gauge. A gauge independent result for the divergence of the measurable electric conductivity is obtained only at the weak scaling fixed point unstable in one loop order where the time scales of the order parameter and the gauge field are different.

Critical behavior ofU(n)-χ4-model with antisymmetric tensor order parameter coupled with magnetic field

“…Another interesting result is that anomalous dimension γ χ , and critical exponent η = 2γ χ (g * ) as well, appears to be gauge dependent (14). It is not surprising because just the same situation takes place in case of the vector order parameter [9]. However, η become gauge dependent only at charged fixed point (e 2 * 0).…”

“…This means that gauge α = 0 is the only gauge invariant with respect to renormalization (see [9] for more detailed explanation).…”

“…On the other hand it is expected that charged order parameter of superconductive phase transition should be also coupled with a magnetic field. Critical behavior of such model with n-component vector order parameter was studied in [8], [9], where it has been shown that charged fixed points at one-loop level exist only for sufficiently large n.…”

“…Since analogues model of a vector order parameter has been studied at one-loop level in [9] we have a way to check our results by comparing calculations in those particular cases.…”

“…Critical behavior of such model with n-component vector order parameter was studied in [8], [9], where it has been shown that charged fixed points at one-loop level exist only for sufficiently large n.…”