Fulde-Ferrell state in heavy-fermion superconductors

Within the weak-coupling model we study the upper critical field of S-wave and D-wave superconductors in the clean limit close to the Chandrasekhar-Clogston limit. We find for parameters derived from ${\mathit{dH}}_{\mathit{c}2}$(T)/${\mathit{dT}}_{\mathit{T}=\mathit{T}\mathit{c}}$ of a single crystal of the recently discovered heavy-fermion superconductor ${\mathrm{UPd}}_2$ ${\mathrm{Al}}_3$ that the Fulde-Ferrell (FF) state is possible for the S-wave and one of the D-wave superconductors of ${\mathit{D}}_{6\mathit{h}}$ symmetry but not for the hybrid state. Indeed, choosing a g factor slightly less than 2, we can describe the temperature dependence of ${\mathit{H}}_{\mathit{c}2}$(T) for both H∥Rc and H∥a extremely well. On the other hand the D-wave model predicts the transition into the FF state at T/${\mathit{T}}_{\mathit{c}}$=0.29 in sharp contrast to the experimental observation T/${\mathit{T}}_{\mathit{c}0}$=0.8.