Surface Specific Heat of ${}^3\mathrm{He}$ and Andreev Bound States

High resolution measurements of the specific heat of liquid ${}^3\mathrm{He}$ in the presence of a silver surface have been performed at temperatures near the superfluid transition in the pressure range of 1–29 bar. The surface contribution to the heat capacity is identified with Andreev bound states of ${}^3\mathrm{He}$ quasiparticles that have a range of half a coherence length.

Figure 1

Heat capacity of both bulk and confined ${}^3\mathrm{He}$ obtained from a slow warm-up trace at 11.31 bar. The solid trace is the heat capacity expected for bulk ${}^3\mathrm{He}$ determined from Greywall’s measurements [20]. The data points are our measurements.

Figure 2

$\delta C=(C-C_s)$ is the difference between the measured heat capacity $C$ and that of the bulk superfluid $C_s$ as a function of temperature at 11.31 bar. The inset is a sketch of the volume distribution in the calorimeter. $V_1$ is the fluid inside the silver heat exchanger and $V_2$ the volume outside. In our model, Andreev bound states reside within a distance $\alpha \xi (T,P)$ from the surface in the volume $V_1$; the rest of the ${}^3\mathrm{He}$ in $V_1$ and all of that in $V_2$ is taken to be bulk superfluid. The model calculation, given by the smooth curve with a constant scale factor $\alpha =0.48\pm 0.08$, agrees well with the data.

Figure 3

Measurements of the heat capacity discontinuity at $T_c$ interpreted as the volume in the heat exchanger, $V_1$ for various pressures.

Figure 4

The scale factor $\alpha$ for the surface heat capacity as a function of pressure. The present measurements are shown as open circles and are pressure independent with an average of $\alpha =0.51$. There is good agreement with earlier work from Greywall [20] (diamond) and Kishishita et al. [22] (solid circle) interpreted in terms of our model.