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Therefore the localization length of quasiparticle decreases with the increase of disorder strength. The global critical temperature, computed by percolation techniques and neglecting phase fluctuations, is enhanced with respect to the clean limit only for very weakly coupled superconductors.

Energies are in unit of t. It is obvious that, in the superconducting phase, the localization effect of disorder is weakened by the off-diagonal superconducting order. Hudson, Nature Physics, Vol.

These results are used to construct a general algorithm for calculating the gauge invariant gradient expansion of the free energy density of an inhomogeneous superconductor at arbitrary temperatures. The lattice size scaling of the generalized inverse participation ratio for the quasiparticles with energy in the conditions with attractive interactions and different disorder strength W. The method is applicable to any pure bulk superconductor described by a pair potential with arbitrary spatial dependence, in the presence of supercurrents and external magnetic field. The foregoing solutions can be demonstrated by observing the evolution of Drude weight.

Atkinson Physical Review BLee Reports on Progress

There is growing evidence, from experiments and numerical simulations, that a key feature of sufficiently disordered superconductors is the spatial inhomogeneity of the order parameter. Berciu, Physical Review Letters, Vol. This method is based on the quasiclassical limit or Andreev approximation of the Bogoliubov-de Gennes or wave function formulation of the theory of weakly coupled superconductors. In summary, the localization effect of disorder has been investigated by applying the scaling of generalized inverse participation ratio.

Lee, Reports on Progress in Physics, Vol. Atkinson, Physical Review B, Vol.

Here we address this problem for disordered systems around an Anderson transition characterized by multifractal one-body eigenstates. We find that the density of optical conductivity in the low-energy region suppressed by the enhancement of superconducting order parameters. Since the localization lengths of quasiparticles are proportion to the the inverse of the square root of the above intercept.

Some enhancement still persists even in the presence of moderate phase fluctuations crudely modelled by increasing the percolation threshold. Here the energies are unit of. Trivedi, Physical Review B, Vol. To our surprise, we also find that disorder can strongly enhance the superconducting order in some small local regions.