Imaging inter-valley coherent order in magic-angle twisted trilayer graphene

Magic-angle twisted trilayer graphene (MATTG) exhibits a range of strongly correlated electronic phases that spontaneously break its underlying symmetries1,2. Here we investigate the correlated phases of MATTG using scanning tunnelling microscopy and identify marked signatures of interaction-driven spatial symmetry breaking. In low-strain samples, over a filling range of about two to three electrons or holes per moire unit cell, we observe atomic-scale reconstruction of the graphene lattice that accompanies a correlated gap in the tunnelling spectrum. This short-scale restructuring appears as a Kekule supercell-implying spontaneous inter-valley coherence between electrons-and persists in a wide range of magnetic fields and temperatures that coincide with the development of the gap. Large-scale maps covering several moire unit cells further reveal a slow evolution of the Kekule pattern, indicating that atomic-scale reconstruction coexists with translation symmetry breaking at a much longer moire scale. We use auto-correlation and Fourier analyses to extract the intrinsic periodicity of these phases and find that they are consistent with the theoretically proposed incommensurate Kekule spiral order3,4. Moreover, we find that the wavelength characterizing moire-scale modulations monotonically decreases with hole doping away from half-filling of the bands and depends weakly on the magnetic field. Our results provide essential insights into the nature of the correlated phases of MATTG in the presence of strain and indicate that superconductivity can emerge from an inter-valley coherent parent state.