Supertransport by Superclimbing Dislocations in ${}^4\mathrm{He}$: When All Dimensions Matter

The unique superflow-through-solid effect observed in solid ${}^4\mathrm{He}$ and attributed to the quasi-one-dimensional superfluidity along the dislocation cores exhibits two extraordinary features: (i) an exponentially strong suppression of the flow by a moderate increase in pressure and (ii) an unusual temperature dependence of the flow rate with no analogy to any known system and in contradiction with the standard Luttinger liquid paradigm. Based on ab initio and model simulations, we argue that the two features are closely related: Thermal fluctuations of the shape of a superclimbing edge dislocation induce large, correlated, and asymmetric stress fields acting on the superfluid core. The critical flux is most sensitive to strong rare fluctuations and hereby acquires a sharp temperature dependence observed in experiments.

Figure 1

Critical flux $F(T)$ [normalized by $F_0=F(T\approx 0)$] for differently grown ${}^4\mathrm{He}$ samples. All data points connected by thin lines as a guide to the eye are taken from Refs. [5, 6]. The dotted line represents the master curve, Ref. [1], fitting the data collected from multiple samples. In contrast to Refs. [5, 6], the data from Ref. [1] show no spread within $\sim 10\%$. All the data for $T<0.5\mathrm{K}$ are consistent with the stretched exponential law $\exp [-(T/T_{\alpha }{)}^{\alpha }]$, $\alpha =1–1.3$, predicted by our model: The thick solid lines are fits with $\alpha =5/4$ and $T_{5/4}\approx 0.20$, 0.45 K for the lowest and the highest datasets, respectively [5, 6].

Figure 2

Schematic visualization of shape fluctuations of the edge dislocation core in the climbing plane. The incomplete atomic plane is shown by the dark area with the core at its boundary. The superfluid density is confined to the core (between the dashed lines) and its local value strongly depends on the local pressure $P(\mathbf{r})$ (or stress).

Figure 3

Exponential sensitivity of the superfluid density in the dislocation core $n_s$ to small changes in the 3D number density of the ${}^4\mathrm{He}$ crystal $n$. Three different dislocations were simulated at $T=0.25\mathrm{K}$: a screw dislocation and two edge dislocation partials along the [1,0,0] and [0,1,0] directions labeled as $X$ and $Y$, respectively. Each data point corresponds to a different sample at the corresponding density. For more details see Ref. [15].

Figure 4

Superfluid density $n_s(N)$ as a function of the deviation $\delta N$ of the particle number $N$ from its equilibrium expectation value $⟨N⟩$ in the simulation cell for the superclimbing edge dislocation, at $T=0.5\mathrm{K}$, and the screw dislocation with a superfluid core, at $T=1\mathrm{K}$. The data are normalized by $⟨n_s⟩$, which is $n_s$ averaged over $N$.

Figure 5

Superfluid density $n_s$ (dashed lines are guides to the eye) for linear sizes $\tilde{L}$ specified next to each dataset. The solid line is the fit by $\exp [-(T/T_{\alpha }{)}^{\alpha }]$, with $\alpha =5/2$ and $T_{\alpha }=0.737\pm 0.005$. Inset: the critical current $J_c$ (normalized to unity at $T=0$) for $\tilde{L}=4,10,{10}^2,{10}^3,{10}^4,{10}^7$ increasing from the highest to the lowest dataset. The solid line is the fit of the $\tilde{L}={10}^4$ data by $J_c\propto \exp [-(T/T_{\alpha }{)}^{5/4}]$, with $T_{\alpha }=0.257\pm 0.01$. All data for $J_c$ are consistent with $\alpha \approx 5/4\pm 0.1$ for $0<T<0.6$ and the spread is due to $T_{\alpha }$ varying by a factor $\sim 2$ (cf. Fig. 1).