Supermoiré domains in helical trilayer graphene

Abstract

Helical trilayer graphene (HTG), stacked with equal twist angles in the same rotational sense, is predicted to reconstruct into triangular domains with uniform moiré wavelength, arranged on a supermoiré length scale. These domains exhibit local breaking of C2z symmetry and adjacent domains carry opposite Chern numbers, implying topological boundary modes. Hoke and colleagues directly imaged this supermoiré landscape using a scanning single-electron transistor (SET) probe, mapping local electronic compressibility variations. Their device, an HTG stack encapsulated in hexagonal boron nitride with a graphite back gate, revealed distinct domain types and provided direct evidence of lattice relaxation and topological domain walls, advancing the understanding of twisted multilayer graphene systems.

1. Introduction

The concept of semiconductor superlattices dates to 1969, when Leo Esaki and Ray Tsu proposed that stacking alternating thin layers of different materials could create artificial crystals with tailored electronic properties[1]. That insight underpins modern high-speed and optoelectronic devices, from quantum cascade lasers to high-electron-mobility transistors. Today, a new generation of superlattices has emerged not from layer-by-layer deposition, but from the moiré patterns that arise when two-dimensional crystals are twisted relative to one another or slightly mismatched. These moiré superlattices impose long-wavelength periodic potentials on the constituent layers, profoundly reshaping their electronic band structures[2]. In twisted bilayer graphene, this has led to the discovery of superconductivity, correlated insulators, and topological phases[3].

Yet the reality of these systems is more complex than the idealized rigid lattice. The weak van der Waals bonding between layers allows them to relax into lower-energy configurations, driven by competition between different stacking arrangements and the elastic cost of deformation. In bilayer graphene, such relaxation produces domains of distinct stacking order separated by narrow conducting channels[4]. When additional layers are introduced, as in trilayer graphene, the interference between multiple moiré patterns creates a secondary, longer-period modulation (a supermoiré) that introduces new length scales and new physics[5]. Among which, helical trilayer graphene (HTG) stacked with equal twist angles in the same rotational sense stands out as a particularly rich platform. The lattice is predicted to reconstruct into triangular domains[6], each characterized by a uniform moiré wavelength, where a is the graphene lattice constant and θ is the twist angle. The domains themselves are arranged on a supermoiré length scale, forming a mosaic of two inequivalent domain types that arise from the local breaking of C2z symmetry. Crucially, theory suggests that adjacent domains carry opposite Chern numbers, implying the existence of topological boundary modes along the domain walls[7]. These theoretical expectations strongly motivate the direct characterization of lattice relaxations in HTG and general twisted multilayers.