Moiréless correlations in ABCA graphene

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.

Two-dimensional (2D) van der Waals heterostructures with an interlayer twist have provided a new avenue for observing emergent tunable many-body electron phenomena. Recent experimental realizations include twisted bilayer graphene (tBG) near the so-called “magic angle” of 1.1° (1–3), twisted double-bilayer graphene (tDBG) (4–6), ABC trilayer graphene on near-perfectly aligned hexagonal boron nitride (hBN) (ABC-tLG/hBN) (7, 8) and transition-metal dichalcogenide heterostructures (9–12) [with predictions on a variety of other systems (13, 14)]. All of these systems host an interplay of two phenomena––the presence of one or more van Hove singularities (which we colloquially refer to as “flat bands” henceforth) at low energy where the density of states is sharply peaked, and the existence of a moiré pattern that creates a unit cell that is about a hundred times larger than the carbon–carbon nearest-neighbor distance in graphene. The large number of electrons with quenched kinetic energy make the flat bands conducive to interaction-driven phases (15). The enlarged moiré unit cell is thought to reduce both the flat-band bandwidth and the interaction energy scales, and also introduces easily accessible integer fillings that create Mott-like insulating states (1–12), the relation of which to nearby superconductivity is debated. A natural question that arises from all of these works is whether the moiré pattern is a necessary condition for the observation of correlated many-body phases, or whether it is simply sufficient to further reduce the flat-band bandwidth and hence the kinetic energy in the heterostructure.In this regard, multilayer rhombohedral (ABC) graphene offers a different perspective toward achieving a flat-band edge without the use of a moiré potential (16). Indeed, in a seminal work (17), it was theoretically shown that the low-energy band structure of multilayer rhombohedral graphene has a sharply peaked density of state (DOS), with the band structure E(k)∝kN (where N is the number of layers) at low energy in the nearest-neighbor hopping approximation. This implies a peak in the DOS at charge neutrality in this material for N>2, with an appreciable fraction of the entire band within this peak (18). Indeed, this physics is already at play in ABC-tLG/hBN (7, 8), where some of the flatness of the bands comes from the intrinsic band structure of ABC graphene, which is then further flattened and isolated by the moiré pattern from the hBN alignment. A facile alternative to flatten the bandwidth without introducing a moiré potential is to simply increase the number of layers of the rhombohedral stacked graphene. Unfortunately, isolating rhombohedral stacked graphene of any thickness is extremely difficult as it is less energetically favorable than the multilayer counterpart, Bernal stacked graphene. Since the difference between rhombohedral and Bernal graphene is simply a lattice shift, and the interlayer van der Waals forces are weak, it is well known that rhombohedral graphene reverts to the Bernal form when samples are processed with heat, pressure, or while performing lithography (19). In this work, we show that twisting two sheets of tDBG by a tiny (<0.1°) angle is a simple and robust method to create large area (up to micrometer-scale) rhombohedral graphene of four-layer thickness (ABCA graphene). We present gate-tunable scanning tunneling microscopy and spectroscopy (STM/STS) measurements at 5.7 K on these regions. We show that correlated phases can be achieved without the need for a moiré pattern and that rhombohedral graphene has unique topological properties.