Specific heat of single crystal MgB2: a two-band superconductor with two different anisotropies

Heat-capacity measurements of a 39 microg MgB2 single crystal in fields up to 14 T and below 3 K allow the determination of the low-temperature linear term of the specific heat, its field dependence, and its anisotropy. Our results are compatible with two-band superconductivity, the band carrying the smaller gap being isotropic, that carrying the larger gap having an anisotropy of approximately 5. Three different upper critical fields are thus needed to describe the superconducting state of MgB2.