Hall Angle of a Normal Current Flowing through the Core of a Vortex

Abstract

A calculation, based on the microscopic theory of superconductivity, is made of the Hall angle of a normal current flowing through the core of a single vortex. The magnetic vector potential is assumed uniform throughout the core region and the moments of the current are taken with the electric field. The ratio of these two quantities yields the tangent of the Hall angle. In agreement with a prediction of Bardeen, we find $tan\ensuremath{\alpha}=(\frac{e\ensuremath{\tau}}{\mathrm{mc}}){H}_{\mathrm{eff}}$, where $\ensuremath{\tau}$ is the relaxation time of the electrons, and the effective magnetic field ${H}_{\mathrm{eff}}$ is in part due to the depression in the order parameter at the core of the vortex and in part to the actual magnetic field in the core of the vortex. For niobium, ${H}_{\mathrm{eff}}$ is very nearly equal to ${H}_{c2}$. At 0\ifmmode^\circ\else\textdegree\fi{}K for niobium, our theory is valid for $\frac{l}{\ensuremath{\xi}}$ ranging from $\ensuremath{\infty}$ to about 10, where $l$ is the mean free path and $\ensuremath{\xi}$ the coherence length.