EFFECT OF SUPERCONDUCTING CORRELATION ON THE LOCALIZATION OF QUASI-PARTICLES IN LOW DIMENSIONS

Localization lengths of superconducting quasiparticles lambda(s) are e valuated and compared with the corresponding normal-state values lambd a(n) in one-dimensional (1D) and two-dimensional lattices. The effect of superconducting correlation on the localization of quasiparticles i s generally stronger in an off-site pairing state than in an on-site p airing state. The modification of superconducting correlation to lambd a is strongly correlated with the density of states (DOS) of supercond ucting quasiparticles. lambda(s) drops within the energy gap but is la rgely enhanced around energies where DOS peaks appear. For a gapless p airing state in 1D or a d-wave pairing state in 2D, lambda(s)/lambda(n ) at the Fermi energy E(F) is of order 1 and determined purely by the value of gap parameter not by the random potential. For the d-wave pai ring state, the localization effect is largely weakened compared with the corresponding normal state and quasiparticles with energies close to E(F) are more strongly localized than other low-energy quasiparticl es.