Fig. 2: Energy landscape of twisted bilayer graphene (TBG) revealed by the interplay between double (DDW) and single (SDW) domain walls.

a Non-local nano-photocurrent map of moiré super-lattice of a TBG sample at the minimal twist limit (see “Methods” for more details). The technique reveals the formation of DDWs (marked by “DDW”) at strained domains, separating domains of identical stacking configurations (each configuration is indicated by dots of a given color [AB—orange, BA—cyan]). The green network overlaid on the data corresponds to the prediction by a single tuning parameter model with \(\bar \beta = 1.90\) (see text and Supplementary Information S6). b GSFE of TBG from ref. ³¹ (blue) and a moiré constrained version (magenta). The unit-less parameters ζ, τ, spanning the phase space of GSFE candidates for TBG, are illustrated (see Supplementary Information S6). Inset: path in configuration space for presented GSFE line-cuts. c Effective attraction between SDWs as reflected by DDW to SDW energy ratios for different SDW orientations (relative to armchair direction) for both models. E_DDW is the DDW line-energy for a DDW along the armchair direction and similarly E_SDW is for the average of the two SDWs comprising the DDW. d, e Stacking energy density from 2D relaxation calculation (see “Methods” and Supplementary Information S2) for the two discussed GSFE choices (d—literature, e—moiré constrained version with τ = 0.025, ζ = 0.3) of region marked by red dashed frame in (a), showing fundamental differences in formation of DDWs. Inset: extracted domain wall structures from relaxation calculations overlaid on experimental results.