Weak localization of disordered quasiparticles in the mixed superconducting state

Starting from a random-matrix model, we construct the low-energy effective-field theory for the noninteracting gas of quasiparticles of a disordered superconductor in the mixed state. The theory is a nonlinear $\sigma$ model, with the order-parameter field being a supermatrix whose form is determined solely on symmetry grounds. The weak-localization correction to the field-axis thermal conductivity is computed for a dilute array of s-wave vortices near the lower critical field $H_{\mathrm{c}1}.$ We propose that weak-localization effects, cut off at low temperatures by the Zeeman splitting, are responsible for the field dependence of the thermal conductivity seen in recent high-$T_{\mathrm{c}}$ experiments by Aubin et al.