Torsional Periodic Lattice Distortions and Diffraction of Twisted 2D Materials

Abstract

Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89°and the amplitude reaches 8 pm around the magic angle of 1.1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS 2 , CrI 3 , and WS 2 / MoSe 2 .

Hyperspectral imaging of exciton confinement within a moiré unit cell with a subnanometer electron probe

“…oiré superlattices formed by stacking monolayers of van der Waals crystals are a burgeoning platform for discovery of fundamental physical phenomena (1). For example, the moiré superlattice of semiconducting transitionmetal dichalcogenides (TMDCs) have been predicted to form a topologically protected lattice of bound electron-hole pairs or excitons that can act as a model system for quantum simulations and technologies (2)(3)(4). Recent optical spectroscopy studies have found signatures of interlayer and intralayer moiré excitons in TMDC heterostructures (5)(6)(7)(8)(9), investigated exciton diffusion in a superlattice potential (10), and found evidence for the cooperative nature of moiré excitons (11).…”

“…A clear understanding of the degree of confinement of intralayer excitons as well as a measurement of the stacking at which the localization occurs has remained out of reach because of the diffraction limit of optical probes or the loss of phase information in ARPES. Such real-space visualization of the exciton localization is necessary to address the fundamental question of whether a moiré superlattice can support a periodic array of well-localized quantum excitations (2)(3)(4).…”