Texture of Superfluid ${}^3\mathrm{He}$ Probed by a Wigner Solid

The resistivity of the Wigner solid floating on the free surface of superfluid ${}^3\mathrm{He}$ has been measured in both the $A$ and $B$ phases down to $200\mu \mathrm{K}$ in the magnetic field. The resistivity in the $A$ phase shows the asymptotic behavior to the temperature-square dependence at low temperatures. The temperature dependence is successfully explained by the uniform $\widehat{\mathit{l}}$ texture oriented normal to the surface and by the specular scattering of quasiparticles excited along $\widehat{\mathit{l}}$ vector. In the $B$ phase, the resistivity exhibits the exponential decrease at low temperatures. The steep increase of the resistivity observed at high magnetic field is attributable to the nonuniform texture of the field-distorted order parameter induced near the surface.

Figure 1

Schematic drawing of specular reflection of a QP by the dimple. The spacing between electrons is approximately $1\mu \mathrm{m}$, while the depth of the dimple is smaller than 0.1 nm.

Figure 2

(a) Schematic picture of the experimental cell and the profile of the magnetic field. (b) Lower electrode. The ac electric current ($\mathit{j}$) is induced in the direction perpendicular to the gap. The magnetic field is applied parallel to the electric current.

Figure 3

Resistivity at 0.363 Tesla, corresponding to the $A$ phase, as a function of $T/T_c$. The solid line is the theoretical curve when the $\widehat{\mathit{l}}$ vector uniformly aligns normal to the surface (see text). The dash-dotted line is that for the uniform $\widehat{\mathit{l}}$ texture aligning parallel to the field. The dashed line is the $T^2$ dependence.

Figure 4

Resistivity at several magnetic fields as a function of $T_c/T$. The vertical jumps correspond to the $AB$ transition. The blue and red lines are the theoretical curves of the ABM state and the isotropic BW state, respectively (see text). Inset: phase diagram of superfluid ${}^3\mathrm{He}$ at zero pressure obtained in this experiment.

Figure 5

(a) Isotherms of the resistivity at $T_c/T=3.0$ and 3.8 as a function of magnetic field. The blue and red solid lines are the theoretical curves for $\widehat{\mathit{t}}\parallel \widehat{\mathit{s}}$ at $T_c/T=3.0$ and 3.8, respectively. The dashed lines are those for $\widehat{\mathit{t}}\parallel \widehat{\mathit{B}}$. (b) Texture induced near the free surface. The black and red arrows indicate the $\widehat{\mathit{n}}$ and the $\widehat{\mathit{t}}$ vectors, respectively. In the bulk, the $\widehat{\mathit{t}}$ vector is oriented parallel to the field. As approaching to the surface, its direction gradually changes, and finally, it becomes normal to the surface.