Magic Doping Fractions for High-Temperature Superconductors

We report hole-doping dependence of the in-plane resistivity \rho_{ab} in acuprate superconductor La_{2-x}Sr_{x}CuO_{4}, carefully examined using a seriesof high-quality single crystals. Our detailed measurements find a tendencytowards 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 ofcharge order and is most consistent with the recent theoretical prediction ofthe checkerboard-type ordering of the Cooper pairs at rational doping fractionsx = (2m+1)/2^n, with integers m and n.Comment: 5 pages, 3 figure, resubmitted to Phys. Rev. Lett. The Tc vs. x diagram has been added and the discussions have been modified to focus more on the experimental result