Stripes and dimensional crossovers in high-T-c cuprates

The key problem in high T-c physics is whether the doping is inhomogeneous and holes are expelled into the 1D domains ("stripes"). Direct comparison o f the resistivity vs T curves of the 1D spin-ladder cuprates and underdoped cuprates below the pseudogap temperature T-o shows a remarkable similarity which implies that the main scattering mechanism is the same for these two classes of cuprates and therefore in the pseudogap regime the transport in underdoped cuprates is essentially 1D. All the resistivity curves in under doped cuprates (including high field transport data in fields up to 60 T) c an be fitted by the model of the 1D quantum transport with the inelastic le ngth in charge stripes being fully controlled by the magnetic spin correlat ion length in even-chain spin-ladders formed in the Cu-O plane as a result of inhomogeneous doping. Close to the insulator - metal transition disorder strongly influences the formation of stripes. Knight shift data are also s uccessfully interpreted by taking the same spin-gap value as the one found from resistivity data. The possible dimensional crossovers observed with de creasing temperature at T-o(x) (2D-1D) and T-c(x) (1D-2D) are discussed and the main unsolved problems of the evolution of the normal state properties with doping are outlined.