Magic doping fractions for high-temperature superconductors.

We report hole-doping dependence of the in-plane resistivity rho(ab) in a cuprate superconductor La(2-x)Sr(x)CuO4, carefully examined using a series of high-quality single crystals. Our detailed measurements find a tendency towards charge ordering at particular rational hole-doping fractions of 1/16, 3/32, 1/8, and 3/16. This observation appears to suggest a specific form of charge order and is most consistent with the recent theoretical prediction of the checkerboard-type ordering of the Cooper pairs at rational doping fractions x = (2m+1)/2n, with integers m and n.