PerspectiveSolid-State Physics

Squeezing strong correlations from graphene

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Science  08 Mar 2019:
Vol. 363, Issue 6431, pp. 1035-1036
DOI: 10.1126/science.aaw4642

The arrangement of atoms in solids and molecules, together with the resulting distribution of electrons within them, dictates many of their physical properties. However, emergent phenomena may arise when solids or molecules are combined to form superstructures. A prime example is the ability to stack atomically thin two-dimensional (2D) crystals into heterostructures (1). Such van der Waals (vdW) heterostructures enable tailoring of electronic properties through control over the twist angle between layers. On page 1059 of this issue, Yankowitz et al. (2) show that applying pressure to modify the interlayer separation of a twisted bilayer graphene device provides a second control parameter to tune between regimes with strong and weak electronic interactions in a single sample.

Collective effects that result from interacting electrons underlie many exotic physical phenomena across multiple materials systems, ranging from strongly correlated materials such as high-temperature superconductors to the fractional quantum Hall effect in 2D electron systems subjected to a strong magnetic field. The common thread that connects these phenomena is that Coulomb repulsion dominates over the kinetic energy of individual electrons because the electronic bands are flat, which allows many electronic states to pile up over a narrow range of energies.

The two seemingly disparate fields of strongly correlated and vdW materials were recently thrust together. When neighboring 2D layers have similar lattice constants and are only slightly misaligned, the resulting device exhibits a periodic moiré pattern whose wavelength can be large compared to atomic spacing (see the figure, left). Electronic bands associated with the large moiré unit cell can substantially modify the low-energy electronic states of the system. Theoretical predictions (3, 4) showed that at certain “magic” twist angles in bilayer graphene, the interlayer coupling is precisely tuned to produce exceptionally flat electronic bands near charge neutrality (see the figure, top). Recent experiments of twisted bilayer graphene samples near the predicted magic angle indeed showed evidence of correlated insulating states (5) and proximate superconductivity (6), which are similar to the phenomenology observed in high-temperature superconductors.

The measurements reported by Yankowitz et al. confirm key aspects of the earlier results on magic-angle twisted bilayer graphene samples under ambient conditions, and the cleanliness of their devices adds further insight. The data reveal a panoply of correlated insulating states that emerge at half-filling and multiples of quarter-filling of the flat bands. In contrast to earlier reports, the authors observe that superconducting domes are present at half-band filling on both the electron and the hole sides of charge neutrality, but that superconductivity is only pronounced when carrier density is increased above half-filling.

Dual routes to flat-band conditions

Twisting two layers of graphene creates an interference (moiré) pattern. Coupling between layers causes hybridization of the moiré bands (shown as a function of momentum k) and creates “flat bands” (highlighted in yellow)—dense regions of electronic states at low energy E that are susceptible to electronic interactions. Yankowitz et al. show that higher twist angles can also support a flat-band region if applied pressure is used to increase the interlayer electronic coupling, leading to a rich phase diagram of correlated electronic states.

GRAPHIC: N. CARY/SCIENCE

Even more exciting, Yankowitz et al. demonstrate that hydrostatic pressure (7) applied to the heterostructure can be used as an additional tuning knob to control the importance of electronic correlations. The flat bands of magic-angle vdW heterostructures arise when the interlayer hybridization is precisely matched to the momentum-space separation of the low-energy electronic states in each layer. As the twist angle rises, pressure must also be applied to increase the interlayer coupling and recover the flat band (see the figure, bottom). Yankowitz et al. demonstrate this more general criterion by using a pressure cell to squeeze the two graphene layers together. In a device with moderate twist angle that shows relatively weak correlation at ambient pressure, applying additional hydrostatic pressure leads to the development of robust insulating states and superconductivity that persists to higher temperatures than in magic-angle devices under ambient conditions (see the figure, right). Thus, pressure and twist angle allow for dual control and validate our current theoretical understanding of why strongly correlated states emerge.

Several aspects of the twisted bilayer graphene platform distinguish it from other strongly correlated superconductors. For example, the entire range of flat-band filling can be explored within a single device using a nearby electrostatic gate, rather than preparing many samples with different doping levels to fully map out the phase diagram of traditional strongly correlated materials. In addition, the hexagonal moiré pattern of twisted bilayer graphene distinguishes it from the square lattice of the Mott phase in cuprates, and may have important consequences for the ground-state order. More generally, electrons in graphene possess an approximate fourfold degeneracy arising from the spin and valley degrees of freedom, providing additional complexity. Yankowitz et al. observe an unusual pattern of degeneracies present in the Landau-level fans emanating from various partial band fillings and interpret the results as signs of symmetry breaking within the parent Fermi surfaces (see the figure, right). Intriguingly, there is also a shift in the sequence of quantum Hall states between quarter- and half-band filling.

These unexpected observations signal a richness reminiscent of the distinctive set of tunable symmetry-broken phases previously observed in monolayer and standard Bernal-stacked bilayer graphene. Even with the additional guidance provided by the measurements of Yankowitz et al., the detailed nature of the correlated insulating states and the mechanism that drives superconductivity in twisted bilayer graphene samples remains an open question (and a frenzied area of research at the moment) (811). Demonstrating that pressure serves as a tuning knob, relaxes the precise angular alignment necessary to study these intriguing phenomena, and opens up new regions of parameter space to explore. More importantly, the formation of flat bands in twisted vdW heterostructures is predicted to be a general phenomenon—it was recently discovered in trilayer graphene on boron nitride (12, 13). The full complement of 2D materials now awaits exploration.

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