Atomic-scale structure and electronic properties of twisted double bilayer graphene: topological edge states and nematic order

Atomically thin van der Waals materials stacked with an interlayer twist are an excellent platform towards achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. We demonstrate the formation of emergent correlated phases in twisted double bilayer graphene (tDBG) in two regimes of twist angle: minimally twisted (<0.1°) and 1.1°. Minimally twisted tDBG hosts large regions of uniform rhombohedral four-layer (ABCA) graphene where scanning tunneling spectroscopy reveals unprecedentedly sharp flat band of 3-5 meV half-width. We demonstrate that, when this flat band straddles the Fermi level, a correlated many-body gap emerges. Moreover, under certain experimental conditions, topological helical edge states appear at the natural interface between rhombohedral and Bernal graphene domains. On the other hand, scanning tunneling microscopy on tDBG at a regime of twist angles (~1.1°) at which moiré physics play an important role, reveals the presence of van Hove singularities whose spatial distribution within the moiré unit cell is determined by the inequivalent stacking sites. Tuning the electron filling as well as the displacement field reveals broken C₃ symmetry that emerges when the Fermi level is brought in the flat band. This symmetry breaking is manifested as long-range commensurate stripes along a high-symmetry moiré crystallographic direction, distinctive of nematic correlations of electronic origin. Comparing our experimental data with a combination of microscopic and phenomenological modeling, we show that the nematic instability is not associated with the local scale of the graphene lattice, but is an emergent phenomenon at the scale of the moiré lattice, pointing to the universal character of this ordered state in flat band moiré materials.