We investigate the diffusion behavior of quasiparticles in two-dimensional (2D) disordered systems with $s$-wave pairing by using the finite-size scaling analysis and transfer-matrix method. The disorder is introduced by random site energies, and the spatial fluctuations of the pairing potential due to this randomness are determined self-consistently. From the size dependence of the Lyapunov exponents, we show that the quasiparticle state in every channel is localized in such a 2D system. The calculated size dependence of the total transmittance of quasiparticles through all possible channels, however, shows a different scaling behavior that suggests the existence of a critical point. The associated critical behavior is studied and the relationship of the results to the Meissner effect and supercurrent is discussed.

• Received 11 August 2004

DOI:https://doi.org/10.1103/PhysRevB.71.174514