Strongly correlated systems can give rise to spectacular phenomenology, from high-temperature superconductivity to the emergence of states of matter characterized by long-range quantum entanglement. Low-density flat-band systems play a vital role because the energy range of the band is so narrow that the Coulomb interactions dominate over kinetic energy, putting these materials in the strongly-correlated regime. Experimentally, when a band is narrow in both energy and momentum, its filling may be tuned in situ across the whole range, from empty to full. Recently, one particular flat-band system—that of van der Waals heterostructures, such as twisted bilayer graphene—has exhibited strongly correlated states and superconductivity, but it is still not clear to what extent the two are linked. Here, we review the status and prospects for flat-band engineering in van der Waals heterostructures and explore how both phenomena emerge from the moire flat bands. The identification of superconductivity and strong interactions in twisted bilayer 2D materials prompted many questions about the interplay of these phenomena. This Perspective presents the status of the field and the urgent issues for future study.

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Superconductivity and strong correlations in moiré flat bands

Reducing the energy bandwidth of electrons in a lattice below the long-range Coulomb interaction energy promotes correlation effects. Moire superlattices—which are created by stacking van der Waals heterostructures with a controlled twist angle1–3—enable the engineering of electron band structure. Exotic quantum phases can emerge in an engineered moire flat band. The recent discovery of correlated insulator states, superconductivity and the quantum anomalous Hall effect in the flat band of magic-angle twisted bilayer graphene4–8 has sparked the exploration of correlated electron states in other moire systems9–11. The electronic properties of van der Waals moire superlattices can further be tuned by adjusting the interlayer coupling6 or the band structure of constituent layers9. Here, using van der Waals heterostructures of twisted double bilayer graphene (TDBG), we demonstrate a flat electron band that is tunable by perpendicular electric fields in a range of twist angles. Similarly to magic-angle twisted bilayer graphene, TDBG shows energy gaps at the half- and quarter-filled flat bands, indicating the emergence of correlated insulator states. We find that the gaps of these insulator states increase with in-plane magnetic field, suggesting a ferromagnetic order. On doping the half-filled insulator, a sudden drop in resistivity is observed with decreasing temperature. This critical behaviour is confined to a small area in the density–electric-field plane, and is attributed to a phase transition from a normal metal to a spin-polarized correlated state. The discovery of spin-polarized correlated states in electric-field-tunable TDBG provides a new route to engineering interaction-driven quantum phases. Twisted double bilayer graphene devices show tunable spin-polarized correlated states that are sensitive to electric and magnetic fields, providing further insights into correlated states in two-dimensional moire materials.

Tunable spin-polarized correlated states in twisted double bilayer graphene

Near a magic twist angle, bilayer graphene transforms from a weakly correlated Fermi liquid to a strongly correlated two-dimensional electron system with properties that are extraordinarily sensitive to carrier density and to controllable environmental factors such as the proximity of nearby gates and twist-angle variation. Among other phenomena, magic-angle twisted bilayer graphene hosts superconductivity, interaction-induced insulating states, magnetism, electronic nematicity, linear-in-temperature low-temperature resistivity and quantized anomalous Hall states. We highlight some key research results in this field, point to important questions that remain open and comment on the place of magic-angle twisted bilayer graphene in the strongly correlated quantum matter world.

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Graphene bilayers with a twist

Moire superlattices1,2 have recently emerged as a platform upon which correlated physics and superconductivity can be studied with unprecedented tunability3–6. Although correlated effects have been observed in several other moire systems7–17, magic-angle twisted bilayer graphene remains the only one in which robust superconductivity has been reproducibly measured4–6. Here we realize a moire superconductor in magic-angle twisted trilayer graphene (MATTG)18, which has better tunability of its electronic structure and superconducting properties than magic-angle twisted bilayer graphene. Measurements of the Hall effect and quantum oscillations as a function of density and electric field enable us to determine the tunable phase boundaries of the system in the normal metallic state. Zero-magnetic-field resistivity measurements reveal that the existence of superconductivity is intimately connected to the broken-symmetry phase that emerges from two carriers per moire unit cell. We find that the superconducting phase is suppressed and bounded at the Van Hove singularities that partially surround the broken-symmetry phase, which is difficult to reconcile with weak-coupling Bardeen–Cooper–Schrieffer theory. Moreover, the extensive in situ tunability of our system allows us to reach the ultrastrong-coupling regime, characterized by a Ginzburg–Landau coherence length that reaches the average inter-particle distance, and very large TBKT/TF values, in excess of 0.1 (where TBKT and TF are the Berezinskii–Kosterlitz–Thouless transition and Fermi temperatures, respectively). These observations suggest that MATTG can be electrically tuned close to the crossover to a two-dimensional Bose–Einstein condensate. Our results establish a family of tunable moire superconductors that have the potential to revolutionize our fundamental understanding of and the applications for strongly coupled superconductivity. Highly tunable moire superconductivity is observed in magic-angle twisted trilayer graphene, and observations suggest that this superconductor can be tuned close to the crossover to a two-dimensional Bose–Einstein condensate.

Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene

Quantum particles on a lattice with competing long-range interactions are ubiquitous in physics; transition metal oxides1,2, layered molecular crystals3 and trapped-ion arrays4 are a few examples. In the strongly interacting regime, these systems often show a rich variety of quantum many-body ground states that challenge theory2. The emergence of transition metal dichalcogenide moire superlattices provides a highly controllable platform in which to study long-range electronic correlations5-12. Here we report an observation of nearly two dozen correlated insulating states at fractional fillings of tungsten diselenide/tungsten disulfide moire superlattices. This finding is enabled by a new optical sensing technique that is based on the sensitivity to the dielectric environment of the exciton excited states in a single-layer semiconductor of tungsten diselenide. The cascade of insulating states shows an energy ordering that is nearly symmetric about a filling factor of half a particle per superlattice site. We propose a series of charge-ordered states at commensurate filling fractions that range from generalized Wigner crystals7 to charge density waves. Our study lays the groundwork for using moire superlattices to simulate a wealth of quantum many-body problems that are described by the two-dimensional extended Hubbard model3,13,14 or spin models with long-range charge-charge and exchange interactions15,16.

Correlated insulating states at fractional fillings of moiré superlattices.

Moire superlattices are emerging as a new route for engineering strongly correlated electronic states in two-dimensional van der Waals heterostructures, as recently demonstrated in the correlated insulating and superconducting states in magic-angle twisted bilayer graphene and ABC trilayer graphene/boron nitride moire superlattices. Transition metal dichalcogenide (TMDC) moire heterostructures provide another exciting model system to explore correlated quantum phenomena, with the addition of strong light-matter interactions and large spin-orbital coupling. Here we report the optical detection of strongly correlated phases in semiconducting WSe2/WS2 moire superlattices. Our sensitive optical detection technique reveals a Mott insulator state at one hole per superlattice site ({\nu} = 1), and surprising insulating phases at fractional filling factors {\nu} = 1/3 and 2/3, which we assign to generalized Wigner crystallization on an underlying lattice. Furthermore, the unique spin-valley optical selection rules of TMDC heterostructures allow us to optically create and investigate low-energy spin excited states in the Mott insulator. We reveal an especially slow spin relaxation lifetime of many microseconds in the Mott insulating state, orders-of-magnitude longer than that of charge excitations. Our studies highlight novel correlated physics that can emerge in moire superlattices beyond graphene.

Johan Carlstroem

Papers

Optical detection of Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices