Robust intrinsic superconducting phases in underdoped LSCO single crystals

We have measured the superconducting critical temperature (TC) and the diamagnetic susceptibility of La2−xSrxCuO4 single crystals in various magnetic fields. We observed a field-induced evolution from an apparent TC phase to an intrinsic TC1=15K or TC2=30K phase characterized by “magic” hole concentration which is commensurate with that of a two-dimensional electronic lattice. The onset TC of the intrinsic superconducting phases remains robust up to H=5T. We suggest that the intrinsic superconducting phases at “magic” doping concentrations are the pristine electronic phases of high temperature superconductors.