Anomalous Attenuation of Transverse Sound in ${}^3\mathrm{He}$

We present the first measurements of the attenuation of transverse sound in superfluid ${}^3\mathrm{He}\mathrm{\text{−}}B$. We use fixed path length interferometry combined with the magnetoacoustic Faraday effect to vary the effective path length by a factor of 2, resulting in absolute values of the attenuation. We find that attenuation is significantly larger than expected from the theoretical dispersion relation, in contrast with the phase velocity of transverse sound. We suggest that the anomalous attenuation can be explained by surface Andreev bound states.

Figure 1

The energy of pair-breaking (green or gray curve) and the ISQ mode (blue or dark gray curve) as a function of temperature normalized to $T_c$. TS propagates only in the shaded blue region. The low temperature pressure sweep technique follows a path represented by the red (or black) arrow.

Figure 2

Attenuation of transverse sound as a function of energy normalized to the energy gap at constant temperature, $\approx 550\mu \mathrm{K}$ from a pressure sweep. Blue (or dark gray) circles and gold (or gray) squares are for 88 and 111.5 MHz, respectively. In the insets (88 MHz) we show examples of the acoustic interference oscillations in $V_Z$ over small energy ranges for comparison, both on the same energy and amplitude scales.

Figure 3

Phase velocity of transverse sound (upper panel) and attenuation (lower panel) at 88 MHz at $\approx 550\mu \mathrm{K}$ in zero magnetic field. In the upper panel, the red (or black) circles are the data, the dashed gray curve is calculated from Eq. (1), and the black curve is the dispersion that accounts for the $2\Delta$-mode [15]. In the lower panel, the attenuation data (blue or dark gray circles) have been deconvolved by subtracting the contribution from coupling to the ISQ mode (gray curve) calculated from Eq. (1) leaving an anomalous attenuation given by the green (or gray) squares.

Figure 4

The temperature dependence of the TS attenuation. The pressures are chosen for the acoustic frequencies such that $\hslash \omega /\Delta$ is within the shaded region of Fig. 1 and never crosses the ISQ mode. The data have been minimally smoothed and are shown as a line for clarity. Quasiparticle-quasiparticle scattering, seen as an increasing attenuation at high $T/T_c$, is expected to decrease to zero at zero temperature. Instead, there is a crossover from the quasiparticle dominated region at high $T/T_c$ to a temperature independent anomalous region at low $T/T_c$. The low temperature endpoints of the data correspond to $\hslash \omega /\Delta \approx 1.64$.

Figure 5

The anomalous attenuation, for 88 MHz (blue or dark gray circles) and 111.5 MHz (gold or gray squares). A smooth crossover in the attenuation appears at $\hslash \omega =\Delta +{\Delta }^{\star }\approx 1.7\Delta$. The inset shows the local density of states, as a function energy normalized to $\Delta$, at the transducer surface (red or black) and in the bulk ${}^3\mathrm{He}$ (light blue or light gray) at $T/T_c=0.5$ for diffusive boundary conditions.