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Multiband model for penetration depth in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">MgB</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
The results of first-principles calculations of the electronic structure and the electron-phonon interaction in ${\mathrm{MgB}}_{2}$ are used to study theoretically the temperature dependence and anisotropy of the magnetic-field penetration depth. The effects of impurity scattering are essential for a proper description of the experimental results. We compare our results with …