Nonlinear material equation and its application in MgB2

Abstract The nonlinear material equation and longitudinal resistivity equation of mixed state of type-II superconductors are derived starting from the free-energy functional of vortex system, in which the additional contribution due to dissipation is taken into account. Applying the longitudinal resistivity equation to transverse case we obtain an analytical expression for the Hall resistivity ρ xy . This equation fits well the recently reported experimental data of MgB 2 and successfully reproduces the empirical scaling relations for ρ xy proposed in the present paper.