Comment on the coupling of zero sound to theJ=1− modes of3He-B
Features in the zero sound attenuation near the pair-breaking edge in superfluid3He-B have been observed in large magnetic fields. Schopohl and Tewordt [J. Low Temp. Phys.57, 601 (1984)] claim that theJ=1−,M=±1 order-parameter collective modes couple to zero sound as a result of the distortion of the equilibrium order parameter by a magnetic field; they identify the new features with these modes. However, we show that, when the effect of gap distortion on the collective modes is properly taken into account, the collective modes equations of Schopohl and Tewordt yield no direct coupling of zero sound to theJ=1− modes. Thus, the identification of the absorption features reported by Ling, Saunders, and Dobbs [Phys. Rev. Lett.59, 461 (1987)] near the pair-breaking edge with theJ=1− modes is not clearly established.
Unable to display preview. Download preview PDF.
- 1.M. E. Daniels, E. R. Dobbs, J. Saunders, and P. L. Ward,Phys. Rev. B 27, 6988 (1983).Google Scholar
- 2.R. Ling, J. Saunders, and E. R. Dobbs,Phys. Rev. Lett. 59, 461 (1987).Google Scholar
- 3.J. Saunders, R. Ling, W. Wojtanowski, and E. R. Dobbs,J. Low Temp. Phys. 79, 75 (1990).Google Scholar
- 4.N. Schopohl and L. Tewordt,J. Low Temp. Phys. 57, 601 (1984).Google Scholar
- 5.J. W. Serene, inQuantum Fluids and Solids 1983, E. D. Adams and G. G. Ihas, eds. (American Institute of Physics, New York, 1983), p. 305.Google Scholar
- 6.See R. H. McKenzie and J. A. Sauls, inHelium Three, W. P. Halperin and L. P. Pitaevskii, eds. (Elsevier, Amsterdam, 1990), for the notation and a derivation of Eq. (3).Google Scholar
- 7.We note that for q ≠ 0 the collective modes which couple to zero sound are driven not just by the density and current oscillations on the right-hand side of Eq. (3), but also by the oscillations in the phase of the order parameter (theJ=0− mode). ST neglected the latter in both Refs. 4 and 8 because they incorrectly assumed that forq ≠ 0 modes with different total angular momentum do not couple. Consequently, the coupling contants which they obtained disagree with the results of other authors. Fort example, in Ref. 8, ST obtain a coupling constant for theJ=2 − modes, to first order inq 2, that is proportional to ∂λ(ω, η)/∂η2|η=0, whereas Wölfle [Phys. Rev. B 14, 89 (1976)] and Maki [J. Low Temp. Phys. 16, 465 (1974)] independently find the coupling to be proportional to λ(ω, 0) because they include the coupling to phase oscillations.Google Scholar
- 8.N. Schopohl and L. Tewordt,J. Low Temp. Phys. 45, 67 (1981).Google Scholar