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arXiv:cond-mat/0008415 · Physical review. B, Condensed matter

Transport properties near the z=2 insulator-superconductor transition

Denis Dalidovich, Philip Phillips

Published May 7, 2001• 6 citations
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Abstract

We consider here the fluctuation conductivity near the point of the insulator-superconductor transition in a system of Josephson junction arrays in the presence of particle-hole asymmetry and Ohmic dissipation. The transition is characterized by the dynamical critical exponent $z=2,$ opening the possibility of the perturbative renormalization-group treatment. The coupling to the Ohmic heat bath, giving the finite quasiparticle lifetime, leads to the nonmonotonic behavior of the dc conductivity as a function of temperature in the leading logarithmic approximation.

DOI
10.1103/physrevb.63.224503

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We consider the scaling properties of the linear ac and nonlinear dc conductivities of a superconductor near the transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​. We first review a scaling theory of the conductivity near a critical point recently proposed by Fisher, Fisher, and Huse. By combining these scaling assumptions with causality arguments, we show that the phase ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{\ensuremath{\sigma}}}$ of the linear ac conductivity takes on a universal value near the critical point, ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{\ensuremath{\sigma}}}$=\ensuremath{\pi}(2-d+z)/2z, where d is the spatial dimension and z is the dynamic critical exponent. Hence, a measurement of the phase lag between the current and the voltage near the critical point provides a measurement of the exponent z. Then, using relaxational dynamics, we calculate these conductivities for 2d4, using (a) a Gaussian approximation, in which the quartic term in the Ginzburg-Landau Hamiltonian is neglected, and (b) an O(2n) generalization of the Ginzburg-Landau Hamiltonian, which for n\ensuremath{\rightarrow}\ensuremath{\infty} produces a Hartree approximation for the quartic term. These results agree with the scaling theory, and provide explicit expressions for the universal scaling functions. In addition, it is possible to study the crossover behavior from Gaussian to critical fluctuations as the critical temperature is approached. The prospects for going beyond the mean-field level by using renormalization-group methods are discussed, along with possible applications to the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors.
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