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Magic-angle twisted trilayer graphene (TTG) has recently emerged as a platform to engineer strongly correlated flat bands. We reveal the normal-state structural and electronic properties of TTG using low-temperature scanning tunneling microscopy at twist angles for which superconductivity has been observed. Real trilayer samples undergo a strong reconstruction of the moiré lattice, which locks layers into near–magic-angle, mirror symmetric domains comparable in size with the superconducting coherence length. This relaxation introduces an array of localized twist-angle faults, termed twistons and moiré solitons, whose electronic structure deviates strongly from the background regions, leading to a doping-dependent, spatially granular electronic landscape. The Fermi-level density of states is maximally uniform at dopings for which superconductivity has been observed in transport measurements.

Graphene moiré superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron–electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report the existence of three-fold rotational (C3) symmetry breaking in twisted double bilayer graphene. Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C3 symmetry breaking, we find it to be prominent only at energies corresponding to the flat bands and nearly absent in the remote bands. We demonstrate that the magnitude of the rotational symmetry breaking does not depend on the degree of the heterostrain or the displacement field, being instead a manifestation of an interaction-driven electronic nematic phase. We show that the nematic phase is a primary order that arises from the normal metal state over a wide range of doping away from charge neutrality. Our modelling suggests 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., S.T. and A.N.P. acknowledge funding from Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443. STM equipment support (A.N.P.) and 2D sample synthesis (Y.S.) were provided by the Air Force Office of Scientific Research via grant no. FA9550-16-1-0601. C.R.-V. acknowledges funding from the European Union Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement no. 844271. A.R. acknowledges funding by the European Research Council (ERC-2015-AdG-694097), Grupos Consolidados (IT1249-19) and the Flatiron Institute, a division of the Simons Foundation. L.K., D.M.K. and A.R. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy-Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1-390534769 and Advanced Imaging of Matter (AIM) EXC 2056−390715994 and funding by the Deutsche Forschungsgemeinschaft (DFG) under RTG 1995, within the Priority Program SPP 2244 ‘2DMP’ and GRK 2247. A.R. acknowledges support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. H.O. is supported by the NSF MRSEC programme grant no. DMR-1420634. Tight-binding and fRG simulations were performed with computing resources granted by RWTH Aachen University under projects rwth0496 and rwth0589. R.S. and M.S.S. acknowledge support from the National Science Foundation under grant no. DMR-2002850. R.M.F. was supported by the DOE-BES under award no. DE-SC0020045. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant no. JPMXP0112101001), JSPS KAKENHI (grant no. JP20H00354) and the CREST (grant no. JPMJCR15F3) JST.

Significance Micrometer-sized uniform four-layer (ABCA) rhombohedral graphene is realized by introducing a small twist angle between two bilayers of Bernal graphene. By means of scanning tunneling spectroscopy we observe an extremely sharp van Hove singularity of 3–5-meV half-width and a correlated many-body gap of 9.5 meV at neutrality, thus making small twisted double-bilayer graphene a unique platform to realize electronic correlations in the absence of a moiré potential. Furthermore, ABCA graphene domain walls display tunable topological edge states, of great interest in Floquet engineering., Atomically thin van der Waals materials stacked with an interlayer twist have proven to be an excellent platform toward achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. In this work we demonstrate the formation of emergent correlated phases in multilayer rhombohedral graphene––a simple material that also exhibits a flat electronic band edge but without the need of having a moiré superlattice induced by twisted van der Waals layers. We show that two layers of bilayer graphene that are twisted by an arbitrary tiny angle host large (micrometer-scale) regions of uniform rhombohedral four-layer (ABCA) graphene that can be independently studied. Scanning tunneling spectroscopy reveals that ABCA graphene hosts an unprecedentedly sharp van Hove singularity of 3–5-meV half-width. We demonstrate that when this van Hove singularity straddles the Fermi level, a correlated many-body gap emerges with peak-to-peak value of 9.5 meV at charge neutrality. Mean-field theoretical calculations for model with short-ranged interactions indicate that two primary candidates for the appearance of this broken symmetry state are a charge-transfer excitonic insulator and a ferrimagnet. Finally, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with ABAB graphene which can be turned on and off with gate voltage, implying that small-angle twisted double-bilayer graphene is an ideal programmable topological quantum material.

Graphene-based moir\'{e} systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moir\'{e} unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moir\'{e} superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the nematic phase of tDBG and its experimental manifestations. First, we perform a detailed comparison between the theoretically calculated local density of states and recent scanning tunneling microscopy data [arXiv:2009.11645] to resolve the internal structure of the nematic order parameter in terms of the layer, sublattice, spin, and valley degrees of freedom. We find strong evidence that the dominant contribution to the nematic order parameter comes from states at the moir\'{e} scale rather than at the microscopic scale of the individual graphene layers, which demonstrates the key role played by the moir\'e degrees of freedom and confirms the correlated nature of the nematic phase in tDBG. Secondly, our analysis reveals an unprecedented tunability of the orientation of the nematic director in tDBG by an externally applied electric field, allowing the director to rotate away from high-symmetry crystalline directions. We compute the expected fingerprints of this rotation in both STM and transport experiments, providing feasible ways to probe it. Rooted in the strong sensitivity of the flat bands of tDBG to the displacement field, this effect opens an interesting route to the electrostatic control of electronic nematicity in moir\'{e} systems., Comment: 21 pages, 10 figures