Bulk superconductivity at 36 K in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</mml:mi></mml:mrow><mml:mrow><mml:mn>1.8</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>0.2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We report the results of resistivity and magnetic susceptibility measurements in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Sr}}_{\mathrm{x}}$${\mathrm{CuO}}_{4}$ for x\ensuremath{\le}0.3. The x=0.2 sample shows a superconducting transition at 36.2 K with a width of 1.4 K. The associated dc diamagnetic susceptibility (Meissner effect) is a large fraction (60%--70%) of the ideal value. We estimate the density of states from critical-field and resistivity data and suggest, by analogy to ${\mathrm{BaPb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Bi}}_{\mathrm{x}}$${\mathrm{O}}_{3}$, that conventional phonon-mediated superconductivity can account for the high ${\mathrm{T}}_{\mathrm{c}}$ in this class of materials.

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