Conductivity of Doped Two-Leg Ladders

Recently, conductivity measurements were performed on the hole-doped two-leg ladder material ${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. In this work, we calculate the conductivity for doped two-leg ladders using a model of hole pairs forming a strongly correlated liquid. Quantum interference effects are handled using renormalization group methods. We find that our model can account for the low-energy features of the experiments. However, at higher energies there are deviations from the predictions of this model. Using the results of our calculations as well as results on the ground state of doped two-leg ladders, we suggest a scenario to explain the experimental results.