Quantum melting of the hole crystal in the spin ladder of Sr14-xCaxCu24O41

We have used resonant soft x-ray scattering to study the effects of discommensuration on the hole Wigner crystal (HC) in the spin ladder Sr14-xCaxCu24O41 (SCCO). As the hole density is varied the HC forms only with the commensurate wave vectors L-L=1/5 and L-L=1/3; for incommensurate values it ``melts.{''} A simple scaling between L-L and temperature is observed, tau(1/3)/tau(1/5)=5/3, indicating an inverse relationship between the interaction strength and wavelength. Our results suggest that SCCO contains hole pairs that are crystallized through an interplay between lattice commensuration and Coulomb repulsion, reminiscent of the ``pair density wave{''} scenario.