Specific Heat of Disordered Superfluid $^{3}$He

TL;DR

This study investigates how silica aerogel-induced disorder affects the specific heat and superfluid transition of $^{3}$He, revealing suppressed discontinuity and linear low-temperature behavior consistent with gapless excitations.

Contribution

It demonstrates the impact of disorder on superfluid $^{3}$He, showing suppressed specific heat discontinuity and confirming gapless excitations through experimental data and Ginzburg-Landau theory.

Findings

Sharp discontinuity in specific heat at transition is reduced by disorder.

Low-temperature specific heat becomes linear, indicating gapless excitations.

Disorder suppresses both transition temperature and order parameter amplitude.

Abstract

The specific heat of superfluid $^{3}$He, disordered by a silica aerogel, is found to have a sharp discontinuity marking the thermodynamic transition to superfluidity at a temperature reduced from that of bulk $^{3}$He. The magnitude of the discontinuity is also suppressed. This disorder effect can be understood from the Ginzburg-Landau theory which takes into account elastic quasiparticle scattering suppressing both the transition temperature and the amplitude of the order parameter. We infer that the limiting temperature dependence of the specific heat is linear at low temperatures in the disordered superfluid state, consistent with predictions of gapless excitations everywhere on the Fermi surface.