Coupling of Pair Fluctuations to Zero Sound: A Field Theoretical Approach*

In a seminal paper Paulson and Wheatley reported measurements of enhanced attenuation of zero sound in liquid He-3 at temperatures just above the onset of the superfluidity [1]. Here we report new results based on a field-theoretical formulation of the coupling of Cooper pair fluctuations and zero sound. Our theory is based on a functional integral formulation of interacting fermions. By introducing auxiliary bosonic fields to describe the zero sound and pair fluctuations, we obtain the collisionless Boltzmann-Landau equation for zero sound and the GL theory for the pair fluctuations. In addition we obtain the leading order interactions between these two bosonic excitations which give corrections to the Boltzmann-Landau equation, and thus the dispersion relation of zero sound. The corrections have a structure similar to those in the theory of paraconductivity which cause the increase of conductivity due to pair fluctuations at temperatures just above the superconducting phase transition. We discuss the implications of our theory, and comment on the report on attenuation of zero sound proposed by Samalam and Serene [2].

[1] D. N. Paulson and J. C. Wheatley, Phys. Rev. Lett., 41, 561, (1978).
[2] V. K. Samalam and J. W. Serene, Phys. Rev. Lett., 41, 497, (1978).