Recent conductivity measurements performed on the hole-doped two-leg ladder material ${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ reveal an approximately linear power law regime in the c-axis dc resistivity as a function of temperature for $x=11.\mathrm{}$ In this work, we employ a bosonic model to argue that Umklapp processes are responsible for this feature and for the high spectral weight in the optical conductivity which occurs beyond the finite frequency Drude-like peak. Including quenched disorder in our model allows us to reproduce experimental conductivity and resistivity curves over a wide range of energies.

• Received 22 April 2002

DOI:https://doi.org/10.1103/PhysRevB.66.165433