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.
Highlights
The nature of the static phase transition in superconductors was an open question for decades, since due to the large correlation length of the available superconducting materials the effect of critical fluctuations was hard to observe in the vicinity of the critical temperature Tc
As it was pointed out in [17] the equation for the gauge field (GF) in (5) can be derived from Maxwell’s equations in their low-frequency form. In this case the inverse transverse coefficientΓ−A1 for the GF can be identified with the bare normal electrical conductivity. We study this critical dynamics by using the Bausch-Janssen-Wagner approach [21] of dynamical field-theoretical renormalization group (RG)
For the dynamical model suggested by Lannert, Vishveshwara and Fisher [17] we have demonstrated that the order parameter (OP) dynamical exponent is gauge dependent
Summary
The nature of the static phase transition in superconductors was an open question for decades, since due to the large correlation length of the available superconducting materials the effect of critical fluctuations was hard to observe in the vicinity of the critical temperature Tc. A dynamical FP, w finite, implying strong scaling with a common dynamical critical exponent z for the OP and the GF in the Feynman gauge (one adds a quadratic term in the divergence of the GF to the static functional) has been found in one loop order. Even if for the uncharged FP, the dynamics would be in the universality class of model E, it is the weak scaling FP which is stable [19] One of these dynamical exponents is observable, namely zA entering the frequency dependent diverging electric conductivity σ(ξ, k = 0, ω) ∼ ξ(zA−2+ηA),. The description of dynamical vertex functions structure is given
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