Mass Flux Characteristics in SolidHe4forT>100  mK: Evidence for Bosonic Luttinger-Liquid Behavior

Abstract

At pressure ∼ 25.7 bar the flux, F , carried by solid 4 He for T > 100 mK depends on the net chemical potential difference between two reservoirs in series with the solid, ∆µ, and obeys F ∼ (∆µ) b , where b ≈ 0.3 is independent of temperature. At fixed ∆µ the temperature dependence of the flux, F , can be adequately represented by F ∼ − ln(T /τ ), τ ≈ 0.6 K, for 0.1 ≤ T ≤ 0.5 K. A single function F = F0(∆µ) b ln(T /τ ) fits all of the available data sets in the range 25.6 -25.8 bar reasonably well. We suggest that the mass flux in solid 4 He for T > 100 mK may have a Luttinger liquid-like behavior in this bosonic system. [12,13] in the vicinity of 80 mK, where the major changes in torsional oscillator period or shear modulus [14] were seen.Here we seek to understand the behavior of F for T > 100 mK in more detail. We apply a temperature difference, ∆T , to create an initial chemical potential difference, ∆µ 0 , between two superfluid-filled reservoirs in series with a cell filled with solid 4 He. We then measure in some detail the behavior of the 4 He flux through the solid-filled cell for T >100 mK that results from the imposed ∆T as the pressure difference between the two reservoirs changes (the fountain effect) and the chemical potential difference between the two reservoirs, ∆µ, changes from ∆µ 0 to zero. For T > 100 mK modest period shifts have been seen in a number of torsional oscillator experiments, in some cases even above 400 mK [15].Since the apparatus [12,13] used for this work has been described in detail previously, our description here will be concise. A temperature gradient is present across the superfluid-filled Vycor [17][18][19] rods (Figure 1), V1 and V2, which ensures that the reservoirs R1 and R2 remain filled with superfluid, while the solid-filled cell (1.84 cm3 ) remains at a low temperature. For the present experiments a chemical potential difference can be imposed by the creation of a temperature difference, ∆T = T 1 − T 2, between the two reservoirs. The resulting change in the fountain pressure [20] between the two reservoirs results in a mass flux through the solid-filled cell to restore equilibrium. The experimental protocol is designed to minimize what has been described as the "syringe effect" [21,22] by which sequential net injections of atoms to the cell increase the density of the solid. By a reduction in the base temperatures of R1 and R2 we also eliminate the flow restriction that would be present for too high a Vycor temperature [13].To fill the cell initially, the helium gas (ultra high purity; assumed to contain ∼300 ppb 3 He) is condensed C1 and C2, the pressures in the superfluid-filled reservoirs, P 1, P 2, are measured at room temperature, and the sample cell temperature is measured by thermometer TC. [Not to scale; V1 and V2 are longer than shown here.]

Mass superflux in solid helium: The role ofHe3impurities

“…Similar behavior is seen for negative ∆T values. As was found earlier [12], a power law provides a good two-parameter characterization for data of this sort:…”

“…Within our errors, the parameter b is independent of temperature but depends on pressure. In the pressure range of our study b is less than 0.5 [12]. We will return to a discussion of the characteristics of A and b later.…”

“…Our experimental methods, have been described in substantial detail in Refs. [10][11][12]. We provide a brief discussion of our approach here.…”

“…In recent presentations [12,13], we have favored F = A − B exp(−E/T ), which is motivated by the thought that some thermally activated process may be relevant. Independent fits of this functional dependence to all of the data sets results in the characterization of the universal behavior of the temperature dependence.…”

“…We developed an apparatus, the so-called UMass Sandwich [9], to study the possible ability of solid helium to carry a helium mass flux [10][11][12]. Using porous media (here, Vycor rods) we are able to apply a chemical potential difference between two separated regions in a solid 4 He sample without mechanically squeezing the solid helium lattice itself.…”