Fig. 1: TDBG, LDOS maps, and nematicity.
From: Machine learning the microscopic form of nematic order in twisted double-bilayer graphene
a Representation in real space of the TDBG heterostructure. Green highlighted domains emphasize the emerging moiré pattern due to the combination of two AB-stacks of graphene bilayers with a relative twist angle, which in this case is given by θ = 7.24∘. C3 and C2x describe threefold and twofold rotations along the z- and x-axes, as illustrated in the small coordinate system. b Band structure for θ = 1.05∘ along highly symmetrical points from the moiré Brillouin zone (inset). Solid lines represent conduction and valence flat bands (CFB/VFB) as well as remote bands (R). The chemical potential corresponds to roughly a half-filling fraction (ν = 0.475) of the CFB. c LDOS for three fixed energies (black dotted horizontal lines in b) as a function of position, and for varying energy at fixed high-symmetry positions in the moiré unit cell (black rhombus). The \({{{{{{{{\mathcal{D}}}}}}}}}_{{\omega }_{0}}({{{{{{{\bf{r}}}}}}}})\) map intensities are always normalized accordingly to the corresponding colorbar. The \({{{{{{{{\mathcal{D}}}}}}}}}_{{{{{{{{{\bf{r}}}}}}}}}_{0}}(\omega )\) map is vertically shifted for better visual comparison. The solid lines are taken from the r0 = (BAAC, ABAB, ABCA) stacking positions in \({{{{{{{{\mathcal{D}}}}}}}}}_{{{{{{{{{\bf{r}}}}}}}}}_{0}}(\omega )\) maps. d Schematic real-space illustration of two limiting cases of graphene and moiré nematicity, along with two samples of LDOS plots for fixed energy in the VFB; both show clear C3 symmetry breaking.
