Evidence for a charge-density wave or spin-density wave in the Cu-O chains in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{x}}$

The Doppler-broadened positron annihilation spectra of polycrystalline samples of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{x}}$ have been measured and analyzed. By studying the difference between the normal-state (room-temperature) and superconducting-state (liquid-nitrogen temperature) spectra, we have deduced that the valence electrons undergo a significant redistribution in momentum states when the material becomes superconducting. We present evidence to demonstrate that this redistribution is consistent with the formation of a static charge-density wave or spin-density wave in the Cu-O chains either concurrent or very closely associated with the superconducting transition.