Upper critical field of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ba</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi mathvariant="normal">−</mml:mi><mml:mi mathvariant="italic">x</mml:mi></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">K</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">x</mml:mi></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">BiO</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>single crystals

We report an extensive study on the temperature (T) dependence of the upper critical field ${\mathit{H}}_{\mathit{c}2}$ on ${\mathrm{Ba}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_{3}$ single crystals. The ${\mathit{H}}_{\mathit{c}2}$(T) curve shows a reproducible upward curvature at \ensuremath{\sim}22 K. This can be due to the presence of two superconducting phases, one with ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}30 K and low ${\mathit{H}}_{\mathit{c}2}$ ([${\mathit{dH}}_{\mathit{c}2}$/dT${]}_{\mathit{T}\mathit{c}}$\ensuremath{\sim}0.5 T/K) and another one with ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim} 25 K and higher ${\mathit{H}}_{\mathit{c}2}$ ([${\mathit{dH}}_{\mathit{c}2}$/dT${]}_{\mathit{T}\mathit{c}}$\ensuremath{\sim}1.1 T/K). However, we find that ${\mathit{H}}_{\mathit{c}2}$ may rise up to 32 T at 1.8 K. It turns out that the reduced critical field ${\mathit{h}}_{\mathit{c}2}$=${\mathit{H}}_{\mathit{c}2}$/[${\mathit{T}}_{\mathit{c}}$(${\mathit{dH}}_{\mathit{c}2}$/dT${)}_{\mathit{T}\mathit{c}}$] is \ensuremath{\ge}1 at low temperatures for both the 30- and 25-K phases, i.e., much higher than what is expected for a conventional superconductor. We compare the low-temperature ${\mathit{h}}_{\mathit{c}2}$ data with calculations recently performed by Marsiglio and Carbotte in the framework of an extended Werthamer-Helfand-Hohenberg theory.