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Observation of a New Superfluid Phase for 3He Embedded in Nematically Ordered Aerogel

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Observation of a New Superfluid Phase for 3He Embedded in Nematically Ordered Aerogel ARTICLE Received 7 Jun 2016 | Accepted 23 Aug 2016 | Published 27 Sep 2016 DOI: 10.1038/ncomms12975 OPEN Observation of a new superfluid phase for 3He embedded in nematically ordered aerogel N. Zhelev1, M. Reichl1, T.S. Abhilash1, E.N. Smith1, K.X. Nguyen2, E.J. Mueller1 & J.M. Parpia1 In bulk superfluid 3He at zero magnetic field, two phases emerge with the B-phase stable everywhere except at high pressures and temperatures, where the A-phase is favoured. Aerogels with nanostructure smaller than the superfluid coherence length are the only means to introduce disorder into the superfluid. Here we use a torsion pendulum to study 3He confined in an extremely anisotropic, nematically ordered aerogel consisting of B10 nm-thick alumina strands, spaced by B100 nm, and aligned parallel to the pendulum axis. Kinks in the development of the superfluid fraction (at various pressures) as the temperature is varied correspond to phase transitions. Two such transitions are seen in the superfluid state, and we identify the superfluid phase closest to Tc at low pressure as the polar state, a phase that is not seen in bulk 3He. 1 Department of Physics and Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA. 2 School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA. Correspondence and requests for materials should be addressed to J.M.P. (email: [email protected]). NATURE COMMUNICATIONS | 7:12975 | DOI: 10.1038/ncomms12975 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12975 uperfluid 3He is our best example of a quantum system, estimate that the aerogel consists of B10 nm-thick strands, where the fermionic constituents form Cooper pairs spaced B100 nm apart. Swith finite angular momentum. Similar to unconventional superconductors, such as Sr2RuO4 and UPt3 (refs 1,2), the properties of this exotic superfluid can be engineered Ginzburg–Landau model. The order parameter for 3He is a 3,4 with disorder . Theory predicts that nanoscale confinement rank-2 tensor describing the spin and orbital angular momentum and anisotropic disorder profoundly change the stability of the of the pairs. In the bulk A-phase, the orbital angular momentum 5–8 pairing, and can lead to novel phases . points in a fixed direction, and there exist gapless excitations Two superfluid phases—the A and B phases are observed in whose momenta are parallel to this direction. In the B-phase, 3 bulk He when it is cooled to ultralow temperatures the superfluid gap is isotropic and nonzero in all directions 9 (below 0.902–2.444 mK depending on the pressure) . At these around the Fermi surface. The polar phase, which is not stable in 3 temperatures, bulk He is an extremely pure system free bulk 3He, has a nodal plane: for any momentum direction in of any disorder: anything besides helium is solid and condenses this plane, one can find gapless quasiparticles. Larger superfluid 4 on the surfaces, and He phase separates with practically densities are associated with having fewer low-energy excitations, 3 zero solubility in the He. To deliberately introduce disorder, allowing us to distinguish these phases. Figure 2a shows the bulk 10,11 3 one can embed the fluid in highly porous aerogels . For He in phase diagram, and Fig. 2b gives a visual representation of the aerogel, Tc is suppressed and the relative stability of the superfluid energy gaps in the various phases. A and B phases is markedly different compared with the bulk. Following convention, we represent the order parameter as a The phase diagram is further distorted when weak anisotropy is 3 Â 3 matrix A with components related to the coupling of the x, 3,12–14 introduced by compressing or stretching the aerogel . y and z components of the spin and orbital angular momentum. In the experiment described here, we embed the fluid All three phases that we see are captured by the ansatz 15–17 within a highly oriented nematic aerogel , which provides 0 1 extreme anisotropy. Nuclear magnetic resonance (NMR) A? 00 experiments15–17 identify the resulting phases as polar-distorted @ A A ¼ 0 A? 0 . A and B phases. Evidence for a novel polar phase was recently 0 iA A observed in a NMR measurement of a different high-density y k nematic aerogel18. In our experiments, the aerogel is mounted on The conventional bulk A-phase corresponds to A ¼ A and a torsion pendulum and the strands that comprise the aerogel are y || A> ¼ 0. Similarly, the isotropic B-phase has A> ¼ A and A ¼ 0. aligned parallel to the pendulum axis. This technique is very || y The polar phase has A> ¼ A ¼ 0. Guided by the form of the different from NMR and is specifically sensitive to the in-plane y Ginsburg–Landau (GL) free energy in refs 4,20, we write the free superfluid fraction. Spin diffusion measurements in an aerogel sample similar to the one we study reveal that the mean-free path for a particle travelling along the strands is nearly twice that of a one moving perpendicular19. From the period of this pendulum, 30 A we measure the fraction of the fluid that is decoupled from the container, which is related to the superfluid fraction. As we vary 20 B the temperature and pressure, we observe kinks when superfluid fraction is plotted versus temperature, corresponding to phase 10 Normal fluid transitions. We find a new superfluid phase just below the normal Pressure (bar) to superfluid transition that is not seen in bulk 3He. Drawing on 4,5,20,21 theoretical work , we argue that at low pressure this new 0 superfluid phase is the polar phase. 0.0 0.5 1.0 1.5 2.0 2.5 Temperature (mK) Results Microstructure of the nematic aerogel. Scanning electron b microscope images of the aerogel sample showing its highly oriented microstructure are shown in Fig. 1a,b. We B phase A phase Polar phase a b z zz Ay = 0 A⊥ = 0 A⊥,y = 0 ≠ ≠ ≠ A⊥,⎜⎜ 0 Ay,⎜⎜ 0 A ⎜⎜ 0 Figure 2 | Bulk fluid phase diagram and visual representation of the superfluid order parameter. (a) Superfluid phase diagram for bulk 3He at Figure 1 | Scanning electron microscope (SEM) micrographs showing the zero magnetic field. The anisotropic superfluid A phase is realized only in a microstructure of the aerogel sample used in this experiment. (a) SEM relatively small region at high pressures and at temperatures near the image in a plane parallel to the aerogel strands. Scale bar, 1 mm. (b) SEM superfluid transition temperature. (b) Visual representation of the image of the edge of the aerogel sample at the intersection of planes superfluid gap around the Fermi surface for various superfluid phases of parallel and perpendicular to the strands. Scale bar, 5 mm. Images are taken 3He. The direction of largest superfluid gap is aligned with the aerogel at Cornell, using Tescan Mira3 Field Emission SEM. strands along the z axis. 2 NATURE COMMUNICATIONS | 7:12975 | DOI: 10.1038/ncomms12975 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12975 ARTICLE energy for this system including the fourth-order terms scaled by degree of polar distortion. Experimental uncertainty in our data is the appropriate coefficients bi as follows: characterized by the relative spread of the data points. In ÀÁ addition, a small systematic error could arise due to the possible Tc À T 2 Tc À T 2 2 2 F ¼ D^2 A À þ d D^2 2jjA þ A þ b Tr AAT Tbulk k Tbulk ? y 1 thermal lag between our thermometer and the experimental cell. hic c hi 2 ÂÃÀÁ 2 Ã Differences between cooling and warming at 3.6 and 0.1 bar are b y b T T Ã b y b y y þ 2 Tr AA þ 3Tr AA AA þ 4Tr AA þ 5Tr AA AA attributed to this systematic error. ð1Þ At temperatures slightly above the hysteresis loop, on both cooling and warming, we observe a change in slope in the ^ bulk Here D is the value of the condensation energy, and Tc and Tc superfluid fraction versus T. The change in slope is especially the superfluid transition temperatures for the fluid within the pronounced at low pressures. We label the temperature of this aerogel and the bulk fluid, respectively. The anisotropy in the feature as Tkink. At 7.5 bar (Fig. 3b), data for cooling and warming system is parameterized by d. The nonzero value of d leads to two overlap at low temperatures and near Tc. A difference between the distinct transition temperatures, Tc> and Tc|| ¼ Tc, below cooling and warming traces larger than the experimental which the components of the order parameter perpendicular uncertainty is observed at intermediate temperatures. This and parallel to the aerogel anisotropy axis develop. The effect of difference is too large to be due to thermal lag. Instead, we the anisotropy of the system splitting the superfluid transition associate the difference with an A-to-B transition. In addition, we 22 has been observed for Sr2RuO4 under uniaxial strain . observe a very sharp and pronounced kink in the superfluid More precisely d can be defined as: fraction data. Thus, we conclude that there are three superfluid phases present. Near T a high-temperature phase is stable, which T À T b À b þ b À b À b c d ck c? 1 2 3 4 5 transitions on cooling to a distorted A phase. Cooling through the ¼ bulk 1 þ ð2Þ Tc b1 þ b2 þ b3 þ b4 þ b5 region of hysteresis the distorted A-phase transitions to a In the linear pair-breaking regime, d is given by ref.
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