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Recent measurements of the anisotropy of the upper critical field Bc2 on MgB2single crystals have shown a puzzling strong temperature dependence. Here, wepresent a calculation of the upper critical field based on a detailed modelingof bandstructure calculations that takes into account both the unusual Fermisurface topology and the two gap nature of the superconducting order parameter.Our results show that the strong temperature dependence of the Bc2 anisotropycan be understood as an interplay of the dominating gap on the sigma-band,which possesses a small c-axis component of the Fermi velocity, with theinduced superconductivity on the pi-band possessing a large c-axis component ofthe Fermi velocity. We provide analytic formulas for the anisotropy ratio atT=0 and T=Tc and quantitatively predict the distortion of the vortex latticebased on our calculations.Comment: 4 pages, 4 figures, typos removed, minor changes, to appear in Phys.  Rev. Let

physical review letters

Fermi Surface Topology and the Upper Critical Field in Two-Band Superconductors: Application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow><mml:mi mathvariant="normal">M</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mi mathvariant="normal">B</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:math>

Fermi Surface Topology and the Upper Critical Field in Two-Band Superconductors: Application toMgB2