We have measured and calculated the electron-positron momentum distribution of ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ samples for Sr concentrations of 0, 0.1, 0.13, and 0.2. Measured distributions were obtained at room temperature with high statistical precision, greater than 4\ifmmode\times\else\texttimes\fi{}${10}^{8}$ events, in the Lawrence Livermore National Laboratory positron-annihilation angular correlation spectrometer on single-crystal samples fabricated using the traveling solvent floating zone technique. Corresponding theoretical momentum-density calculations were performed using the linear muffin-tin-orbital method. The momentum distribution of all samples contained features derived from the overlap of the positron distribution with the valence electrons. In addition, discontinuities typical of a Fermi surface are seen in the doped samples. The form and position of these features are in general agreement with the Fermi surface and overall momentum distributions as predicted by band theory. However, the evolution of the Fermi surface with doping differed significantly from expectations based on single electron band theories.
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