Gap parameters and collective modes for 3He-B in the presence of a strong magnetic field

Abstract

First we determine the 4 × 4 matrix Green's function for a p-wave pairing superfluid in a magnetic field where the order parameter is given by a real 3 × 3 matrix. For the B phase we take an order parameter which is equal to δ1 times a 3 × 3 matrix, yielding a rotation of angle θ about the z-axis and a dilatation δ2/δ1 along the z-axis. Then the self-consistency equation for the 4 × 4 matrix self-energy reduces to three equations for δ1, δ2, and cos θ, and a fourth equation for the renormalized Larmor frequency. We find that, for increasing field, δ1 increases and δ2 decreases with respect to the zero-field gap δ00. Above a (temperature-dependent) critical field we find δ2 = 0 and α2 = 90° corresponding to the planar state of lowest dipole energy. The correlation functions for the order parameter collective modes are calculated with the help of a previous theory. The results can be expressed in terms of six universal functions describing internal magnetization and virtual excitations of pairs of quasiparticles with all spin orientations. The complete set of eigenfrequencies as functions of the field is calculated for T = 0 and q = 0. The longitudinal NMR frequency is found to be almost independent of the field. We find a splitting of the pair-vibration frequencies (8/5) 1/2δ00 and (12/5)1/2δ00 which is linear in the field. This splitting is caused by fluctuations involving the spin-singlet component of the anomalous propagator. The splitting of the pair-vibration frequency (12/5)1/2δ00 (of the order 6H MHz, H in kG) should be observable by sound absorption experiments in strong magnetic fields.