Non-Ohmic Electrical Transport in the Vicinity of the Superconducting Transition: Implications for the Study of the Phase Diagram of the Underdoped Cuprate Superconductors

In this paper, we present a theoretical discussion of the non-ohmic regime of the electrical conductivity of a type-II planar superconductor near its superconducting transition, focusing mainly in the region between the phase-coherence and the pair-condensation critical temperatures, T phase < T < T cond. For that purpose, we extend down to those temperatures existing calculations for the so-called Aslamazov-Larkin conductivity in presence of finite electric fields, and the resulting exponent α of the fluctuation voltage-current characteristics E∼j α . These results are then discussed by considering two possible scenarios for the phase diagram of the superconducting fluctuations in the underdoped high-temperature superconductors. Our results suggest that the strong phase fluctuations scenario (i.e., large T cond−T phase) leads to a plateau in the T-dependence of the exponent α near T phase, and that the T-region over which this plateau extends becomes wider when the applied electric field is increased. These features are much smaller in the conventional fluctuations scenario (i.e., small T cond−T phase).