In this research, the excess conductivity in 5 wt% nano carbon-doped MgB_2 superconductor was systematically studied as a function of magnetic field by measurements of the resistivity. The mean field temperature was calculated using two different methods. Two- and three-dimensional -2D and 3D- models were used to scale the excess conductivity caused by fluctuations. The mean field of the coherence length for the sample was obtained by using the Aslamazo-Lockerian model in the region of critical temperature. A transition from the 2D to the 3D region was observed in different fields at a crossover temperature as the temperature increased. The crossover temperatures were obtained by using the Maki-Thompson − Lawrence-Doniach -MT-LD- model. The results show that the crossover temperature decreases as the field increases. The phase-relaxation time of the fluctuation pairs was obtained by using the crossover temperature. The fluctuation pair lifetime, τϕ, and the coherence length were obtained by using the transition temperature and the reduced temperature crossover values as functions of magnetic field . The phase-relaxation time decreases with increasing field. It was found that the excess conductivity has 2D dimensionality behavior due to the Cooper pairs.

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