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. Here 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°. tDBG at a tiny twist angle, at which moiré physics do not play a role, host 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, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with Bernal graphene. 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 caracter of this ordered state in flat band moiré materials.