  Spin-ladder compounds make interesting analogs of the high-temperature
superconductors, because they contain layers of nearly one-dimensional
"ladders" consisting of a square array of copper and oxygen atoms. Increasing
the number of legs in the ladders provides a step-wise approach toward the
two-dimensional copper-oxygen plane, that structure believed to be a key to
high temperature superconductivity. Short-range spin correlations in ladders
have been predicted to lead to formation of hole pairs favorable for
superconductivity, once enough holes are introduced onto the ladders by doping.
Indeed, superconductivity has been discovered in the two-leg ladder compound
(Sr,Ca)$_{14}$Cu$_{24}$O$_{41}$ under high pressure. Here we show that charge
transport in the non-superconducting state of (Sr,Ca)$_{14}$Cu$_{24}$O$_{41}$
shares three distinct regimes in common with high-temperature superconductors,
including an unexplained insulating behavior at low temperatures in which the
resistivity increases as the logarithm of the temperature. These observations
suggest that the logarithmic divergence arises from a new localization
mechanism common to the ladder compounds and the high-temperature
superconductors, which may arise from nearly one-dimensional charge transport
in the presence of a spin gap.
