Angle-dependent Hall resistivity and longitudinal resistivity of type-II superconductor

We use time-dependent Ginzburg–Landau theory in a three-dimensional model, including thermal noise, to analyze angle-dependent Hall resistivity and longitudinal resistivity of type-II superconductor. The Hall resistivity and longitudinal resistivity are calculated as functions of temperature, magnetic field and the angle $\theta$ between the magnetic field and the ab-plane in the vortex-liquid regime. Our theoretical calculations within a self-consistent fluctuation approximation for MgB₂ and HgBa₂CaCu₂O₆ materials are in good agreements with the experimental findings for both below and above the critical temperature $T_c$. We observe that when the field angle decreases, the transition temperature increases and the magnitude of longitudinal resistivity decreases, which is qualitatively comparable to decrease of the perpendicular field component. However, when the magnetic field direction approaches the layer surface, it shows a clear different effect from that of a perpendicular field with the same normal component.