A spatially indirect exciton is created when an electron and a hole, confined to separate layers of a double quantum well system, bind to form a composite boson 1,2 . Such excitons are long-lived, and in the limit of strong interactions are predicted to undergo a Bose-Einstein condensate-like phase transition into a superfluid ground state 1-3 . Here, we report evidence of an exciton condensate in the quantum Hall e ect regime of double-layer structures of bilayer graphene. Interlayer correlation is identified by quantized Hall drag at matched layer densities, and the dissipationless nature of the phase is confirmed in the counterflow geometry 4,5 . A selection rule for the condensate phase is observed involving both the orbital and valley indices of bilayer graphene. Our results establish double bilayer graphene as an ideal system for studying the rich phase diagram of strongly interacting bosonic particles in the solid state.In bulk semiconductors, an optically excited electron-hole pair interacts through Coulomb attraction to form a bound quasiparticle, referred to as a spatially direct exciton (Fig. 1a). Such excitons are easily generated but recombine on the nanosecond timescale. By confining the electrons and holes to separate, but closely spaced, two-dimensional (2D) quantum wells, strong attraction is maintained but recombination is blocked, leading to long-lived excitons. These so-called spatially indirect excitons are predicted to exhibit a rich phase diagram of correlated behaviours, including a type of superfluid BEC ground state, at temperatures much higher than for similar phenomena in atomic gases 1,2,6 .Realizing the exciton condensate (EC) phase in electron-hole quantum wells (QW) has proved difficult owing to the requirement of fabricating matched electron-and hole-doped layers that are strongly interacting but electrically isolated, while maintaining high mobility 7,8 . On the other hand, an equivalent condensate state is possible for identically doped (electron-electron or hole-hole) coupled quantum wells under application of a strong magnetic field. In the quantum Hall effect (QHE) regime, tuning both layers to half filling of the lowest Landau level can be viewed as populating the lowest band in each layer with an equal number of electrons and holes, which then couple across the layers, forming an equivalent system of indirect excitons 9 (Fig. 1a). Indeed, with this approach, several studies have revealed the existence of the EC in GaAs double layers 4,10-14 . The EC phase appears at total filling ν T = 1 for the balanced case (each layer tuned to ν = 1/2), and remains stabilized when the layer densities are imbalanced as long as ν T = 1, since this condition maintains an equal number of electron-and hole-like carriers across the barrier 15 .For spatially indirect excitons in a magnetic field B, the energy scale of the condensate is conveniently characterized by the effective interlayer separation, d/ B , where B = √ /eB is the magnetic length, which describes the carrier spacing within a l...

The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers.

The distinct Landau level spectrum of bilayer graphene (BLG) is predicted to support a non-abelian even-denominator fractional quantum Hall (FQH) state similar to the [Formula: see text] state first identified in GaAs. However, the nature of this state has remained difficult to characterize. Here, we report transport measurements of a robust sequence of even-denominator FQH in dual-gated BLG devices. Parallel field measurement confirms the spin-polarized nature of the ground state, which is consistent with the Pfaffian/anti-Pfaffian description. The sensitivity of the even-denominator states to both filling fraction and transverse displacement field provides new opportunities for tunability. Our results suggest that BLG is a platform in which topological ground states with possible non-abelian excitations can be manipulated and controlled.

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Controlling the strength of interactions is essential for studying quantum phenomena emerging in systems of correlated fermions. We introduce a device geometry whereby magic-angle twisted bilayer graphene is placed in close proximity to a Bernal bilayer graphene, separated by a 3-nanometer-thick barrier. By using charge screening from the Bernal bilayer, the strength of electron-electron Coulomb interaction within the twisted bilayer can be continuously tuned. Transport measurements show that tuning Coulomb screening has opposite effects on the insulating and superconducting states: As Coulomb interaction is weakened by screening, the insulating states become less robust, whereas the stability of superconductivity at the optimal doping is enhanced. The results provide important constraints on theoretical models for understanding the mechanism of superconductivity in magic-angle twisted bilayer graphene.