Recently, the rich phase diagrams found in few-layer materials have attracted much attention from the scientific community; competition of correlated states, including Mottness, superconductivity, and magnetic and charge order were observed in these systems [1-4]. One characteristic these distinct materials share is the Moiré structure originated by layer misalignment or intentional twist between them. However, a central point of the Moiré superlattice is the increase in the unit cell in real space, meaning smaller momentum space Brillouin Zones. This scenario can favor scattering between small-momentum electronic states, meaning that long-range real-space interactions might play a relevant role. Therefore, in this ongoing project, under the Random Phase Approximation (RPA), we investigate the influence of these longe-range interactions on the magnetic fluctuations of twisted bilayer graphene as a model system, in order to trigger the possible collective states resulting from the Moiré superlattice scenario. Finally, we find that long-range interactions might favor superconductivity up to a certain interaction strength, and then suppress it thereon depending on the doping of the sample. Also, in qualitative agreement with experiments, we also show both charge and magnetic order might be present, where the first one is closely related to the long-range interactions.

References: 

[1] - Science, 6539, 264-271 (2021). https://doi.org/10.1126/science.abc283

[2] - Wong et al., Nature 582, 198–202 (2020). https://doi.org/10.1038/s41586-020-2339-0

[3] - Devakul et al., Nat Commun 12, 6730 (2021). https://doi.org/10.1038/s41467-021-27042-9

[4] - Jiang et al., Nature 573, 91–95 (2019). https://doi.org/10.1038/s41586-019-1460-4