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Hydrodynamics and Nonlocal Conductivities in Vortex States

A hydrodynamical description for vortex states in type II superconductors with no pinning is presented based on the time-dependent GL equation, and the nonlocal conductivities are examined in terms of Kubo formula. Typically, the nonlocal conductivities deviate from the usual vortex flow expressions as the nonlocality parallel to the field becomes weaker than that perpendicular to the field associated with the freezing to the vortex lattice, and, for instance, the dc Hall conductivity nonlocal only in directions perpendicular to the field becomes zero in the vortex lattice due to its infinite shear viscosity. Various situations are discussed on the basis of the resulting expressions.