In this paper, we present a theoretical discus- sion of the non-ohmic regime of the electrical conductivity of a type-II planar superconductor near its superconduct- ing transition, focusing mainly in the region between the phase-coherence and the pair-condensation critical temper- atures, Tphase <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 fluctu- ation 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 Tcond − Tphase) leads to a plateau in the T - dependence of the exponent α near Tphase, 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 Tcond − Tphase).
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