Quantitative estimation of Andreev retroreflection contribution to Wigner solid mobility

Quantify the contribution of Andreev retroreflection to the mobility of the Wigner solid on the free surface of superfluid 3He-B when the parallel component of the order parameter Δ_parallel(z) is increased near the free surface, specifically for incident quasiparticles nearly parallel to the surface, as suggested by self-consistent order-parameter calculations.

Background

The paper analytically evaluates the effect of Andreev retroreflection on the mobility of a Wigner solid at the free surface of superfluid 3He-B using a model order parameter with Δ_parallel(z)=Δ and Δ_perp(z)=Δ tanh(z/ξ). Under this model, Andreev retroreflection is absent for quasiparticles with energy above the bulk gap, leading to no mobility enhancement from Andreev processes, in agreement with prior experiments.

However, self-consistent calculations in the literature indicate that the parallel component of the order parameter Δ_parallel(z) increases near the surface, which would enable Andreev retroreflection for quasiparticles incident nearly parallel to the surface. The authors note that, while this mechanism likely has limited impact due to angular weighting in the mobility integral, its quantitative contribution has not been established.