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The de Haas-van Alphen (dHvA) signal arising from orbits on the $\pi$ Fermisurface sheet of the two-gap superconductor MgB$_2$ has been observed in thevortex state below $H_{c2}$. An extra attenuation of the dHvA signal, beyondthose effects described in the conventional Lifshitz-Kosevich expression, isseen due to the opening of the superconducting gap. Our data show that the$\pi$ band gap is still present up to $H_{c2}$. The data are compared tocurrent theories of dHvA oscillations in the superconducting state which allowus to extract estimates for the evolution of the $\pi$ band gap with magneticfield. Contrary to results for other materials, we find that the most recenttheories dramatically underestimate the damping in MgB$_2$.

physical review. b, condensed matter and materials physics

Damping of the de Haas–van Alphen oscillations in the superconducting state of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Mg</mml:mi><mml:msub><mml:mi mathvariant="normal">B</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

Damping of the de Haas–van Alphen oscillations in the superconducting state ofMgB2