Spatially resolved measurements of twisted bilayer graphene reveal more details of the strongly correlated electrons.
Over a decade after its discovery, it seemed as if graphene had already revealed its magic. Then last year, much to everyone’s surprise, experiments demonstrated that giving two layers of graphene just the right small twist will give rise to correlated electronic phases (an insulator1 or a superconductor2) that do not exist when the twist is not there. Writing in Nature Physics, Choi and colleagues utilize a local probe to provide more clues into the correlated states in twisted bilayer graphene close to the magic angle, as they tune the Fermi level of the system3.
Interlayer coupling between the atomically thin planes of layered van der Waals materials plays a fundamental role in determining their properties. In fact, it is an effective knob for tuning their electronic band structure. For example, charge carriers in a single layer of graphene are described by massless Dirac fermions. Add another layer on top with perfect alignment, and in this bilayer graphene system they will behave as massive Dirac fermions. If you now slightly misalign the two layers, the emerging moiré pattern imposes a spatial periodicity on the interlayer coupling. This way, you can create a new band structure that is unique for each angle.
The band structure’s sensitivity to rotational misalignment was realized both theoretically and experimentally a decade ago4,5, however, only with recent experimental advancements in fabricating samples with precise alignment can it now be fully exploited6. The primary manifestation of the twist is the appearance of Van Hove singularities in the density of states that originate from the hybridization of the Dirac cones belonging to each layer. These peaks in the density of states occur at angle-dependent energies and as the twist angle is reduced, their energy separation decreases4,7. At the smallest angles, things get interesting, as the band structure renormalization produces electronic bands with weak dispersion in momentum space — flat bands. For certain so-called ‘magic angles’, the flat bands become vanishingly narrow8 so that the kinetic energy of the charge carriers is minimized and can become smaller than Coulomb interactions. When the Fermi level is aligned with these flat bands, electron–electron interactions become the prevailing influence on the behaviour of the system, a condition rarely achieved in bulk materials and associated with new and interesting physics.
Thus far, the physics of electrons in these flat bands has only been addressed by electronic transport1,2,9. Those experiments established that when the number of electrons in graphene is tuned to specific fractions of filled states in the flat bands, correlated insulating phases appear; when the temperature is lowered further, superconducting states also appear. The challenge in fully interpreting such experiments comes from the fact that they average over an entire device, which typically has regions with slightly different twist angle or different amount of strain. Transport measurements also are restricted to addressing electrons at the Fermi level, with the rest of the band structure remaining inaccessible. Therefore, to gain insight at the microscopic level into the interplay of the key parameters (carrier density, twist angle, strain) as they give rise to the correlated states, local scanning probes are necessary. Scanning tunnelling techniques provide atomically resolved structural and electronic details and can visualize the symmetries of the electronic wave functions as they evolve through the phase diagram upon changing carrier densities or twist angle.
Choi and colleagues fabricated twisted bilayer graphene placed in proximity to a graphite gate, which is used to adjust the number of charge carriers. The twisted bilayer graphene is a highly tunable material system, allowing the authors to explore the evolution of its electronic states with the carrier density in the same sample, using the gate, without the complications that chemical doping would typically induce.
Spatial topographic maps are able to resolve both the atomic lattice of graphene as well as the moiré pattern formed by the twist. The rotation angle is deduced from the size of the pattern. Close to the largest magic angle, the moiré pattern can be as big as 13 nm, much greater than the bond length between the carbon atoms. Within a moiré pattern, one finds periodically varying stacking of the atoms from the two layers. The experiments can directly visualize that most of the electronic states of the flat bands are localized at places where the carbon atoms are in registry. Measurements of the microscopic details of the moiré superlattice also confirm the presence of strain, suggestive as a possible origin for the device-dependent fine features.
Measuring the differential tunnelling conductance probes the density of states. Consistent with previous reports, Choi and colleagues find the angle-dependent Van Hove singularities as peaks in their spectra. Taking advantage of the electronic gate, they then track the evolution of the peaks with carrier concentration. The important observation is that placing the Fermi level in one of the flat bands modifies the density of states, which is suggestive of the strong effect of correlations. This is in contrast with the regimes where flat bands are completely filled or empty. Interestingly, the changes in the density of states occur at certain moiré filling factors and could be an insight into the nature of the correlated effects. The size of the energy gaps measured in the tunnelling experiments differ from those found in transport experiments, underscoring the important role of strain and disorder. Through this local probe experiment, Choi and co-workers provide further insight by spatially mapping the density of states at the charge neutrality point. They suggest that the observed anisotropy is indicative of broken three-fold rotational symmetry. The results are supported by a theoretical framework based on a ten-band tight-binding model that captures the flat bands while preserving all symmetries10.
As the field of twisted two-dimensional materials rapidly evolves as a venue for exploring correlated electronic states, local scanning probes will be invaluable in deciphering the interplay of all relevant parameters.
Cao, Y. et al. Nature 556, 80–84 (2018).
Cao, Y. et al. Nature 556, 43–50 (2018).
Choi, Y. et al. Nat. Phys. https://doi.org/10.1038/s41567-019-0606-5 (2019).
Li, G. et al. Nat. Phys. 6, 109–113 (2010).
Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Phys. Rev. Lett. 99, 256802 (2007).
Kim, K. et al. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017).
Luican, A. et al. Phys. Rev. Lett. 106, 126802 (2011).
Bistritzer, R. & MacDonald, A. H. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Lu, X. et al. Preprint at https://arxiv.org/abs/1903.06513 (2019).
Po, H. C., Zou, L., Senthil, T. & Vishwanath, A. Phys. Rev. B 99, 195455 (2019).
About this article
Cite this article
Luican-Mayer, A. A needle in a moiré stack. Nat. Phys. 15, 1107–1108 (2019). https://doi.org/10.1038/s41567-019-0645-y