He, that anisotropic disorder, engineered from highly porous silica aerogel, stabilizes a chiral superfluid state that otherwise would not exist. Furthermore, we find that the chiral axis of this state can be uniquely oriented with the application of a magnetic field perpendicular to the aerogel anisotropy axis. At sufficiently low temperature we observe a sharp transition from a uniformly oriented chiral state to a disordered structure consistent with locally ordered domains, contrary to expectations for a superfluid glass phase 6 . Superconducting states with non-zero orbital angular momentum, L = 0, are characterized by a competitive, but essential, relationship with magnetism, strong normal-state anisotropy or both [1][2][3]5 . Moreover, these states are strongly suppressed by disorder, an important consideration for applications 7 and a signature of their unconventional behaviour 3,8,9 . Although liquid 3 He in its normal phase is perfectly isotropic, it becomes a p-wave superfluid at low temperatures with non-zero orbital and spin angular momenta, L = S = 1 (ref. 10). One of its two superfluid phases in zero magnetic field is anisotropic with chiral symmetry, where the handedness results from the orbital motion of the bound 3 He pairs about an axis . This chiral superfluid, called the A phase or axial state, is stable at high pressure near the normal-to-superfluid transition, Fig. 1a-c, whereas the majority of the phase diagram is the non-chiral B phase, with isotropic physical properties. The stability of the A phase is attributed to strong-coupling effects arising from collisions between 3 He quasiparticles 10 . However, in the presence of isotropic disorder these strong-coupling effects are reduced and the stable chiral phase disappears 11,12 , Fig. 1a. Here we show that anisotropic disorder can reverse this process and stabilize an anisotropic phase over the entire phase diagram, Fig. 1c.For many years it was thought to be impossible to introduce disorder into liquid 3 He because it is intrinsically chemically and isotopically pure at low temperatures. Then it was discovered 13,14 that 3 He imbibed in ∼ 98% porosity silica aerogel, Fig. 1d, is a superfluid with a transition temperature that is sharply defined 12 , but reduced from that of pure 3 He. To test predictions that isotropic disorder favours isotropic states and anisotropic disorder favours anisotropic states 15 , we have grown a 97.5% porosity anisotropic aerogel with growth-induced radial compression 16 , effectively stretching it along its cylinder axis by 14.3%. Experiments using uncharacterized stretched aerogels have been previously reported 17,18 and are in disagreement with the work presented here. Silica aerogels, as in Fig. 1d, are formed by silica particles ≈ 3 nm in diameter, precipitated from a tetramethylorthosilicate solution, and aggregated in a diffusion-limited process. After supercritical drying we obtain a Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA. *e-mail: w-halperin@northw...

Superfluid3 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.PACS numbers: 67.30. Hm, 67.30.Er, 67.30.Hj, 74.20.Rp The discovery of effects of quenched disorder on superfluid 3 He using high porosity silica aerogel [1, 2] has created an opportunity for systematic study of the role of impurities on unconventional pairing. Although the two observed superfluid phases in aerogel have characteristics similar to those of pure 3 He (where the A-phase is the axial state and the B-phase is the isotropic state), the identification of the states is lacking. Theory indicates that the presence of elastic quasiparticle scattering reduces strong coupling [3], which is known to be responsible for the axial state in pure 3 He. This should favor the isotropic state in aerogel, consistent with susceptibility and acoustic experiments [4][5][6]. However, a metastable phase is observed at high pressure on cooling, stabilized by magnetic field [6], and its identity is more in question. In this regard we note that without strong coupling, the planar and axial states are degenerate [7]. There are predictions that local or global anisotropy in the scattering rates favor various possible anisotropic states, e.g. axial [3], polar [8], or possibly a family of robust states [9]. Furthermore, random local disorder is predicted to lead to an orbitally disordered superfluid glass [10,11] or Larkin-Imry-Ma (LIM) state [12,13]. To resolve this problem, we have grown a new type of highly homogeneous aerogel and developed methods for its characterization [14]. In this Letter we present results on 3 He in a 98.2% porosity uniformly-isotropic aerogel sample in which we precisely determine the order parameter structure and identify the microscopic states of the superfluid phases to be the impurity suppressed axial and isotropic states. Additionally, we find no evidence for the existence of the predicted LIM superfluid glass.Pulsed NMR is a powerful technique for identifying the superfluid states of 3 He, where the frequency shifts of the spectrum are directly related to the amplitude of the order parameter, ∆, and the dependence of the shift on tip angle is a fingerprint of the microscopic state [7]. However, to date the interpretation of pulsed NMR experiments in aerogel has been complicated by distributions in the frequency shifts owing to spatially non-uniform directions of the angular momentum, called orbital textures, that can b...

It is established theoretically that an ordered state with continuous symmetry is inherently unstable to arbitrarily small amounts of disorder 1,2. This principle is of central importance in a wide variety of condensed systems including superconducting vortices 3,4 , Ising spin models 5 and their dynamics 6 , and liquid crystals in porous media 7,8 , where some degree of disorder is ubiquitous, although its experimental observation has been elusive. On the basis of these ideas, it was predicted 9 that 3 He in high-porosity aerogel would become a superfluid glass. We report here our nuclear magnetic resonance measurements on 3 He in aerogel demonstrating destruction of long-range orientational order of the intrinsic superfluid orbital angular momentum, confirming the existence of a superfluid glass. In contrast, 3 He-A generated by warming from superfluid 3 He-B has perfect long-range orientational order providing a mechanism for switching off this effect. Close to the absolute zero of temperature, liquid 3 He condenses into a p-wave superfluid of Cooper pairs resulting in two phases with fundamentally different symmetry: the isotropic B-phase and an anisotropic A-phase. In zero magnetic field, 3 He-A appears in a small corner of the pressure versus temperature phase diagram shown in Fig. 1d. Its anisotropy, a paradigm for more recently discovered unconventional superconductors 10 , is characterized by the orientation of its order parameter defined by orbital angular momentum and spin induced by magnetic field,l andŝ. The spin is necessarily aligned with an applied magnetic field, H; however, the orbital angular momentum has continuous rotational symmetry. That symmetry can be broken, for example, at a wall or interface to whichl must be perpendicular, thereby defining a preferred direction on a macroscopic scale. Volovik proposed 9 that this long-range orientational coherence of angular momentum would be destroyed by random microscopic disorder that can be realized if the 3 He is imbibed in highly porous silica aerogel as shown in our simulation Fig. 1a,b. This sensitivity to small amounts of disorder on a microscopic scale was discussed by Larkin 1 and Imry and Ma 2 for a broad range of physical phenomena 3-8 and we refer to this as the LIM effect. If this proposal is correct then in the LIM state the order parameter structure of the superfluid will be completely hidden, a behaviour of potential significance for understanding exotic superconductors such as URu 2 Si 2 (ref. 11). We use nuclear magnetic resonance (NMR) to look for the LIM state of superfluid 3 He-A, directly interrogating the orientation of l by measuring the Leggett shift 12 of the NMR spectrum, ω A. In pure 3 He this frequency shift is proportional to the nuclear dipole energy, F D ∝ −(l •d) 2 , whered is a spin-space vector constrained to be perpendicular toŝ while minimizing F D. This shift is strongly temperature dependent, but for an orbital glass it should be very small, or ideally zero (Supplementary Information) as we report here.

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In recent work, it was shown that new anisotropic p-wave states of superfluid (3)He can be stabilized within high-porosity silica aerogel under uniform positive strain. In contrast, the equilibrium phase in an unstrained aerogel is the isotropic superfluid B phase. Here we report that this phase stability depends on the sign of the strain. For a negative strain of ∼ 20% achieved by compression, the B phase can be made more stable than the anisotropic A phase, resulting in a tricritical point for A, B, and normal phases with a critical field of ∼ 100 mT. From pulsed NMR measurements, we identify these phases and the orientation of the angular momentum.