Identification of Superfluid Phases of ${}^3\mathrm{He}$ in Uniformly Isotropic 98.2% Aerogel

Superfluid ${}^3\mathrm{He}$ confined to high porosity silica aerogel is the paradigm system for understanding impurity effects in unconventional superconductors. However, a crucial first step has been elusive: exact identification of the microscopic states of the superfluid in the presence of quenched disorder. Using a new class of highly uniform aerogel materials, we report pulsed nuclear magnetic resonance experiments that demonstrate definitively that the two observed superfluid states in aerogel are impure versions of the isotropic and axial $p$-wave states. The theoretically predicted destruction of long-range orbital order (Larkin-Imry-Ma effect) in the impure axial state is not observed.

Figure 1

Liquid susceptibility (open green circles) and frequency shift (closed blue circles) versus reduced temperature at $P=26.1\mathrm{bar}$ and $H=196\mathrm{mT}$. The signal from the small amount of liquid outside the aerogel has been subtracted. The estimated systematic uncertainty in ${\chi }_{liq}$ is $\sim 15\%$ at the lowest temperature. Inset: Total ${}^3\mathrm{He}$ susceptibility versus temperature.

Figure 2

NMR spectra for ${}^3\mathrm{He}$ in aerogel in the normal state (black dashed), $A$-like (red solid line), and $B$-like (blue dashed-dot and green bold solid lines) phases. These spectra were obtained in $H=95.5\mathrm{mT}$ and at a $P=26.1\mathrm{bar}$ where the crossover between $\widehat{\ell }\perp$ and $\parallel \overrightarrow{H}$ in the $B$-like phase occurs at $T=1.2\mathrm{mK}$ and has a width of $\approx 100\mu \mathrm{K}$.

Figure 3

Frequency shift versus tip angle for the $B$-like phase at $P=26.1\mathrm{bar}$. The magnitude of the shifts presented have been scaled to a common field of $H=196\mathrm{mT}$. The solid (dashed) red curves are fits with the theory for the field mode (wall mode), Eqs. (1, 2, 3, 4), using a single fitting parameter ${\Omega }_B$ obtained from the data in Fig. 4 and with the addition of a small constant shift not contained in the theory and discussed in the text.

Figure 4

Temperature dependence of the longitudinal resonance frequency at $P=26.1\mathrm{bar}$ and $H=196\mathrm{mT}$ in the impurity suppressed isotropic (open red circles) and axial (blue circles, darkest color) states. The orange data (lightest color) were scaled from the axial state data using $5/2$. Inset: Leggett ratio versus temperature, Eq. (5).

Figure 5

Superfluid phase diagram for ${}^3\mathrm{He}$ in isotropic aerogel. The closed (open) purple symbols are $T_{ca}$ ($T_{BAa}$ for different fields at $P=26\mathrm{bar}$) and the solid (dashed) green curves correspond to $T_c$ ($T_{BA}$) for pure ${}^3\mathrm{He}$ at $H=196\mathrm{mT}$. The bold solid red curve is fit to $T_{ca}(P)$ using the HISM [3]. The phase diagram can also be fit well with a scattering model that includes particle-particle correlations in the aerogel [39] with a correlation length ${\xi }_a=0\mathrm{\text{−}}50\mathrm{nm}$ indicating that we are unable to precisely determine ${\xi }_a$.