We report our investigation of the sample to sample fluctuation in transport
properties of phase coherent normal metal-superconductor hybrid systems.
Extensive numerical simulations were carried out for quasi-one dimensional and
two dimensional systems in both square lattice (Fermi electron) as well as
honeycomb lattice (Dirac electron). Our results show that when the Fermi energy
is within the superconducting energy gap Δ, the Andreev conductance
fluctuation exhibits a universal value (UCF) which is approximately two times
larger than that in the normal systems. According to the random matrix theory,
the electron-hole degeneracy (ehD) in the Andreev reflections (AR) plays an
important role in classifying UCF. Our results confirm this. We found that in
the diffusive regime there are two UCF plateaus, one corresponds to the
complete electron-hole symmetry (with ehD) class and the other to conventional
electron-hole conversion (ehD broken). In addition, we have studied the Andreev
conductance distribution and found that for the fixed average conductance ,G>
the Andreev conductance distribution is a universal function that depends only
on the ehD. In the localized regime, our results show that ehD continues to
serve as an indicator for different universal classes. Finally, if normal
transport is present, i.e., Fermi energy is beyond energy gap Δ, the AR
is suppressed drastically in the localized regime by the disorder and the ehD
becomes irrelevant. As a result, the conductance distribution is that same as
that of normal systems
