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We study the influence of Fermi surface topology on the quasiparticle densityof states in the vortex state of type II superconductors. We observe that thefield dependence and the shape of the momentum and spatially averaged densityof states is affected significantly by the topology of the Fermi surface. Weshow that this behavior can be understood in terms of characteristic Fermisurface functions and that an important role is played by the number of pointson the Fermi surface at which the Fermi velocity is directed parallel to themagnetic field. A critical comparison is made with a broadened BCS type densityof states, that has been used frequently in analysis of tunneling data. Wesuggest a new formula as a replacement for the broadened BCS model for thespecial case of a cylindrical Fermi surface. We apply our results to the twogap superconductor MgB$_2$ and show that in this particular case the fielddependence of the partial densities of states of the two gaps behaves verydifferently due to the different topologies of the corresponding Fermisurfaces, in qualitative agreement with recent tunneling experiments.Comment: 12 pages 12 figure

Influence of Fermi surface topology on the quasiparticle spectrum in the vortex state