Effects of spin-orbit interaction and crystal fields on superconductingp-wave pair states and their collective excitations in cubic systems

Abstract

Superconducting pair states for systems with strong spin-orbit interaction and crystallographic anisotropy are usually assumed to transform as the basis functions of the irreducible representations Γ n of the appropriate point group. Transitions to pair states belonging to different irreducible representations are supposed to occur at different transition temperaturesT c (Γ n ). Here it is shown forp-wave states that, as soon as nonlinear terms in the gap equation or quartic terms in the Ginzburg-Landau free energy are taken into account, linear combinations of pair states belonging to different irreducible representations can result. This applies to all those states that are not solutions of the gap equation when the pairing interaction is of the isotropic form V0 $$\hat k \cdot \hat k'$$ used in the theory of superfluid3He. The spectrum of collective excitations of those states, which are actually solutions of the gap equation, becomes much more complex when spin-orbit interaction and crystal field effects are taken into account by assuming different transition temperaturesT c (Γ n ). In particular, a number of additional modes are found whose frequencies scale as ω2 ∝ ln[T c (Γ n )/T c (Γ m )]. If the deviation from the isotropic interaction is not very large, these modes will have very low frequencies. They couple to density fluctuations toO(q2) due to particle-hole asymmetry. This can be a large effect in heavy fermion compounds because of the sharp peak in the density of states. These modes could, therefore, be very well responsible for the peaks in the acoustic attenuation observed just belowT c .