Contribution of Andreev reflection to the mobility of surface state electrons on superfluid $^3$He-B

TL;DR

This paper analytically investigates how Andreev retroreflection affects the mobility of surface state electrons on superfluid $^3$He-B, finding it negligible for quasiparticles above the energy gap and consistent with experimental data.

Contribution

The study provides a detailed analytical calculation of Andreev retroreflection's role in electron mobility on superfluid $^3$He-B, incorporating realistic and self-consistent order parameters.

Findings

Andreev retroreflection does not increase mobility for quasiparticles above the energy gap.

The model's predictions align well with experimental observations.

Andreev retroreflection's contribution is negligible under the studied conditions.

Abstract

The mobility of the Wigner solid on the superfluid $^3$He is determined by the momentum transfer from the scattered $^3$He quasiparticles at the free surface. The scattering process of the quasiparticles is classified into the normal reflection and the Andreev retroreflection. Since the quasiparticles nearly conserve the momentum in the process of the Andreev retroreflection at the free surface, the Andreev reflected quasiparticles do not produce a resistive force to the Wigner solid. In this report, we have analytically calculated the contribution of the Andreev retroreflection to the mobility of the Wigner solid on superfluid $^3$He-B by employing a realistic model order parameter with the free surface. The Andreev retroreflection is lacked for quasiparticles with energy above the bulk energy gap under the model order parameter. Then, the Andreev retroreflection does not contribute to a rise in the mobility of the Wigner solid on the superfluid $^3$He-B. The present model calculation is in good agreement with the previous experimental observation. We have also discussed the Andreev retroreflection under a self-consistently calculated order parameter.