Engineering moiré superlattices by twisting layers in van der Waals (vdW) heterostructures has uncovered a wide array of quantum phenomena. Here, we construct a vdW heterostructure consisting of three graphene layers stacked with alternating twist angles ±θ. At the average twist angle θ ~ 1.56°, a theoretically predicted magic angle for the formation of flat electron bands, we observed displacement field tunable superconductivity with a maximum critical temperature of 2.1 K. By tuning the doping level and displacement field, we find that superconducting regimes occur in conjunction with flavor polarization of moiré bands and are bounded by a van Hove singularity (vHS) at high displacement fields. Our findings display inconsistencies with a weak coupling description, suggesting that the observed moiré superconductivity has an unconventional nature.

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.

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