Quasiclassical approach to transport in the vortex state of type II superconductors and the Hall effect

Discovery of the high-temperature superconductors eleven years ago has once again propelled superconductivity into the forefront of condensed matter physics. Attempts to better understand the behavior of these novel materials has led to an effort to reexamine and gain further insight into phenomena that are ubiquitous to both low and high-{dollar}Tsb{lcub}c{rcub}{dollar} compounds.; One of the theoretical puzzles that has remained unanswered for over thirty years is the strongly nonlinear behavior of the Hall angle in the vortex state of both conventional and high-temperature superconductors. Microscopic calculations that explain qualitatively the behavior of the Hall angle in the dirty limit, when the quasiparticle mean free path l is much shorter than the superconducting coherence length {dollar}xisb0{dollar}, cannot be extended to the clean regime {dollar}lggxisb0{dollar}, and the predictions of existing phenomenological and semiphenomenological theories are at variance with experimental results.; We develop an approach to the calculation of the transport coefficients of clean type-II superconductors in the vortex state. This approach is based on the quasiclassical approximation to the microscopic theory, generalized to include the terms responsible for the Hall Effect in a charged superfluid. We use linear response theory to solve the quasiclassical equations and obtain the longitudinal and transverse resistivities in the mixed state in high magnetic fields. We find that below the superconducting transition the contribution to the conductivity due to dynamical fluctuations of the order parameter is compensated by the modification of the quasiparticle contribution. In this regime the nonlinear behavior of the Hall conductivity and the Hall angle is governed by the change in the effective quasiparticle scattering rate due to the reduction in the density of states at the Fermi level. The connection with experimental results on high purity Niobium is discussed.