Spreads in Critical Current and Normal Conductance of High-$T_{\rm c}$ dc SQUID

The statistical behaviors of the critical current (
I

_c
) and the normal conductance (
G

_n
) of high-
T

_c
dc SQUIDs were investigated theoretically and experimentally. The voltage-current and voltage-flux characteristics of 38 SQUIDs fabricated on a chip were measured by using a switching-channel cryostat, which can characterize up to 43 elements individually in a series array. It was found that the spatial correlation in
I

_c
between the neighboring SQUIDs is low, which implies that the critical current can be taken as a spatially independent random variable. The
I

_c
and
G

_n
histograms follow the gamma distributions. In addition, the statistical linear correlation between ln
I

_c
and ln
G

_n
is 0.6, which suggests that the
I

_c
spread is partly originated from the variation in local oxygen content of bicrystal junctions.