ABSTRACT
Spin-orbit coupling (SOC) is the key to realizing time-reversal-invariant topological phases of matter1,2. SOC was predicted by Kane and Mele3 to stabilize a quantum spin Hall insulator; however, the weak intrinsic SOC in monolayer graphene4-7 has precluded experimental observation in this material. Here we exploit a layer-selective proximity effect-achieved via a van der Waals contact with a semiconducting transition-metal dichalcogenide8-21-to engineer Kane-Mele SOC in ultra clean bilayer graphene. Using high-resolution capacitance measurements to probe the bulk electronic compressibility, we find that SOC leads to the formation of a distinct, incompressible, gapped phase at charge neutrality. The experimental data agree quantitatively with a simple theoretical model in which the new phase results from SOC-driven band inversion. In contrast to Kane-Mele SOC in monolayer graphene, the inverted phase is not expected to be a time-reversal-invariant topological insulator, despite being separated from conventional band insulators by electric-field-tuned phase transitions where crystal symmetry mandates that the bulk gap must close22. Our electrical transport measurements reveal that the inverted phase has a conductivity of approximately e2/h (where e is the electron charge and h Planck's constant), which is suppressed by exceptionally small in-plane magnetic fields. The high conductivity and anomalous magnetoresistance are consistent with theoretical models that predict helical edge states within the inverted phase that are protected from backscattering by an emergent spin symmetry that remains robust even for large Rashba SOC. Our results pave the way for proximity engineering of strong topological insulators as well as correlated quantum phases in the strong spin-orbit regime in graphene heterostructures.
ABSTRACT
Non-Abelian anyons are a type of quasiparticle with the potential to encode quantum information in topological qubits protected from decoherence. Experimental systems that are predicted to harbour non-Abelian anyons include p-wave superfluids, superconducting systems with strong spin-orbit coupling, and paired states of interacting composite fermions that emerge at even denominators in the fractional quantum Hall (FQH) regime. Although even-denominator FQH states have been observed in several two-dimensional systems, small energy gaps and limited tunability have stymied definitive experimental probes of their non-Abelian nature. Here we report the observation of robust even-denominator FQH phases at half-integer Landau-level filling in van der Waals heterostructures consisting of dual-gated, hexagonal-boron-nitride-encapsulated bilayer graphene. The measured energy gap is three times larger than observed previously. We compare these FQH phases with numerical and theoretical models while simultaneously controlling the carrier density, layer polarization and magnetic field, and find evidence for the paired Pfaffian phase that is predicted to host non-Abelian anyons. Electric-field-controlled level crossings between states with different Landau-level indices reveal a cascade of FQH phase transitions, including a continuous phase transition between the even-denominator FQH state and a compressible composite fermion liquid. Our results establish graphene as a pristine and tunable experimental platform for studying the interplay between topology and quantum criticality, and for detecting non-Abelian qubits.
