We report the observation of superconductivity in rhombohedral trilayer graphene electrostatically doped with holes. Superconductivity occurs in two distinct regions within the space of gate-tuned charge carrier density and applied electric displacem
ent field, which we denote SC1 and SC2. The high sample quality allows for detailed mapping of the normal state Fermi surfaces by quantum oscillations, which reveal that in both cases superconductivity arises from a normal state described by an annular Fermi sea that is proximal to an isospin symmetry breaking transition where the Fermi surface degeneracy changes. The upper out-of-plane critical field $B_{Cperp}approx 10 mathrm{mT}$ for SC1 and $1mathrm{mT}$ for SC2, implying coherence lengths $xi$ of 200nm and 600nm, respectively. The simultaneous observation of transverse magnetic electron focusing implies a mean free path $ellgtrsim3.5mathrm{mu m}$. Superconductivity is thus deep in the clean limit, with the disorder parameter $d=xi/ell<0.1$. SC1 emerge from a paramagnetic normal state and is suppressed with in-plane magnetic fields in agreement with the Pauli paramagnetic limit. In contrast, SC2 emerges from a spin-polarized, valley-unpolarized half-metal. Measurements of the in-plane critical field show that this superconductor exceeds the Pauli limit by at least one order of magnitude. We discuss our results in light of several mechanisms including conventional phonon-mediated pairing, pairing due to fluctuations of the proximal isospin order, and intrinsic instabilities of the annular Fermi liquid. Our observation of superconductivity in a clean and structurally simple two-dimensional metal hosting a variety of gate tuned magnetic states may enable a new class of field-effect controlled mesoscopic electronic devices combining correlated electron phenomena.
At high magnetic fields, monolayer graphene hosts competing phases distinguished by their breaking of the approximate SU(4) isospin symmetry. Recent experiments have observed an even denominator fractional quantum Hall state thought to be associated
with a transition in the underlying isospin order from a spin-singlet charge density wave at low magnetic fields to an antiferromagnet at high magnetic fields, implying that a similar transition must occur at charge neutrality. However, this transition does not generate contrast in typical electrical transport or thermodynamic measurements and no direct evidence for it has been reported, despite theoretical interest arising from its potentially unconventional nature. Here, we measure the transmission of ferromagnetic magnons through the two dimensional bulk of clean monolayer graphene. Using spin polarized fractional quantum Hall states as a benchmark, we find that magnon transmission is controlled by the detailed properties of the low-momentum spin waves in the intervening Hall fluid, which is highly density dependent. Remarkably, as the system is driven into the antiferromagnetic regime, robust magnon transmission is restored across a wide range of filling factors consistent with Pauli blocking of fractional quantum hall spin-wave excitations and their replacement by conventional ferromagnetic magnons confined to the minority graphene sublattice. Finally, using devices in which spin waves are launched directly into the insulating charge-neutral bulk, we directly detect the hidden phase transition between bulk insulating charge density wave and a canted antiferromagnetic phases at charge neutrality, completing the experimental map of broken-symmetry phases in monolayer graphene.
Nonabelian anyons offer the prospect of storing quantum information in a topological qubit protected from decoherence, with the degree of protection determined by the energy gap separating the topological vacuum from its low lying excitations. Origin
ally proposed to occur in quantum wells in high magnetic fields, experimental systems thought to harbor nonabelian anyons range from p-wave superfluids to superconducting systems with strong spin orbit coupling. However, all of these systems are characterized by small energy gaps, and despite several decades of experimental work, definitive evidence for nonabelian anyons remains elusive. Here, we report the observation of arobust, incompressible even-denominator fractional quantum Hall phase in a new generation of dual-gated, hexagonal boron nitride encapsulated bilayer graphene samples. Numerical simulations suggest that this state is in the Pfaffian phase and hosts nonabelian anyons, and the measured energy gaps are several times larger than those observed in other systems. Moreover, the unique electronic structure of bilayer graphene endows the electron system with two new control parameters. Magnetic field continuously tunes the effective electron interactions, changing the even-denominator gap non-monotonically and consistent with predictions that a transition between the Pfaffian phase and the composite Fermi liquid (CFL) occurs just beyond the experimentally explored magnetic field range. Electric field, meanwhile, tunes crossings between levels from different valleys. By directly measuring the valley polarization, we observe a continuous transition from an incompressible to a compressible phase at half-filling mediated by an unexpected incompressible, yet polarizable, intermediate phase. Valley conservation implies this phase is an electrical insulator with gapless neutral excitations.
