The Heat Capacity of $^3$He-B in Silica Aerogel

TL;DR

This paper develops a theoretical model for the heat capacity of superfluid $^3$He-B in silica aerogel, extending Ginzburg-Landau theory to all temperatures and showing good agreement with experiments, indicating a gapless superfluid state.

Contribution

It introduces a quasiclassical functional for superfluid $^3$He-B in aerogel, extending thermodynamic predictions across all temperatures and supporting the gapless superfluid hypothesis.

Findings

The model agrees with experimental heat capacity data.

Superfluid $^3$He-B in aerogel is gapless at all pressures.

The functional extends Ginzburg-Landau theory to all temperatures.

Abstract

The thermodynamic potential for superfluid $^3$He-B embedded in a homogeneously distributed random potential is calculated from a quasiclassical reduction of the Luttinger-Ward functional to leading order in $k_{\mbox{$\tiny B$}} T_c/E_f$. The resulting functional provides an extension of the Ginzburg-Landau free energy functional to all temperatures $0<T\le T_c$. Theoretical predictions based on this functional for the heat capacity of superfluid $^3$He-B embedded in homogeneous, isotropic silica aerogel are in good agreement with experimental reports for superfluid $^3$He-B infused into 98.2% porous silica aerogel over the pressure range $p=11 - 29\,\mbox{bar}$. The analysis supports a conclusion that superfluid $^3$He-B infused into high-porosity silica aerogels is a gapless superfluid at all pressures.