Upper critical field in a trigonal unconventional superconductor UPt_3

A theory of the upper critical field in a trigonal superconductor with a two-component order-parameter is developed. We demonstrate the existence of sixfold modulations of the upper critical field in the basal plane. The form of the angular dependence of H_c2 in the plane of the main symmetry axis is studied in the whole range of phenomenological rigidity coefficients. A qualitative dependence of these coefficients on the form of the Fermi surface is established. The results obtained are discussed in connection with the measurements of the direction dependence of H_c2 in the heavy fermion superconductor UPt_3 that has been recently found to possess trigonal crystalline structure. PACS numbers: 74.20.De, 74.70.Tx