Viscous flux motion in anisotropic type-II superconductors in low fields

The Bardeen-Stephen model of viscous flux motion in isotropic type-II superconductors is extended to the anisotropic case characterized by a phenomenological effective mass tensor m_ij. When the magnetic field is low and the vortex lines are aligned along one of the three principal axes, simple expressions for the viscosity tensor η_ij of the viscous flux motion are obtained as functions of m_ij and the normal state conductivity tensor σ_ij for temperature T close to the critical temperature T_c. For the high-temperature oxide superconductors, the theory predicts that η_b^(a):η_b^(c):η _c^(a)≈1:4γ:3γ², where η_i⁽ⁱ⁾ is the viscosity for the motion along the i-axis of a vortex parallel to the j-axis and γ=√m_c/m_a is the anisotropy parameter (m_i, i=a, b, c, are the principal values of the mass tensor satisfying m_a≈m_b≪m_c )