Electronic States of doped spin ladders (Sr,Ca)14Cu24O41

We examine the electronic states of Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ by the ionic and cluster model approach. It is found that self-doped holes are likely to stay on the chain at $x=0$ and the Ca substitution drives the holes to move to the ladder. This feature is caused by the change of the positions of (Sr,Ca) layers, which enhances the electrostatic potentials in the chain. The optical conductivity is calculated applying the exact diagonalization method to small Cu-O clusters. It is shown that the excitations below 2 eV are governed by the ladder, giving rise to the spectral weight transfer from the charge-transfer excitation around 2 eV to low energy Drude excitation, while the contribution from the chain mainly emerges in higher energy region showing large weight around 3 eV. These provide consistent explanation to recent experiment.