Ginzburg-Landau Approach to the Vortex-Glass Transitions due to Line-Like Disorder

Vortex-glass transitions induced by a line-like disorder, the so-called Bose-glass (BG) transition and two types of Gaussian-splayed-glass (GSG) transitions, are studied on the basis of the lowest Landau level (LLL) approach to the Ginzburg-Landau (GL) model. For each of these transitions, we estimate the transition point and derive critical properties of response quantities just above the transition. A particular attention is paid to the scaling behaviors near GSG transitions of response quantities to a gauge disturbance δ A ⊥ perpendicular to the applied magnetic field B , which are difficult to be derived without explicit calculation. As an example, it is found for the case of planar GSG transition with a well-defined splay plane that the tilt modulus for a tilt parallel to the splay plane has no critical divergence, as in the vortex-glass (VG) transition due to a point disorder, while the corresponding modulus for an out-of-plane tilt is divergent as in BG case and proportional to the correlation length of this transition. The responses to a gauge disturbance δ A z parallel to B are also briefly discussed. It is pointed out that, as a result of a field dependence of glass transition temperature, any glass transition can suppress the first order freezing transition at sufficiently low fields but within LLL approach.