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 WS2, CrI3, and WSe2/MoSe2.

Modulation of Phonons and Excitons Due to Moiré Potentials in Twisted Bilayer of WSe2/MoSe2

“…However, Rosenberger et al reported that the heterostructure of MoSe 2 and WSe 2 with a twist angle of 3° showed no reconstruction . On the other hand, there is a recent report of observation of torsional periodic lattice distortions, similar to that observed in MoS 2 /WSe 2 , in MoSe 2 /WSe 2 TBL with a twist angle of 5°. This suggests that such periodic lattice distortions can provide the in-plane restoring force necessary to sustain the LS modes.…”

An Atomistic Insight into Moiré Reconstruction in Twisted Bilayer Graphene beyond the Magic Angle

“…Though above θ m , the shape of the soliton walls is geometrically less regular in comparison as shown in Figure 4 b due to softening of the domain boundaries. 29 …”

“…Though above θ m , the shape of the soliton walls is geometrically less regular in comparison as shown in Figure 4b due to softening of the domain boundaries. 29 For small twist angle TBGs at or below θ m , the energetically unfavorable AA domains shrink drastically upon reconstruction, which translates to a large change in their area fraction. For example, the area fraction of AA regions in the θ m = 1.08°s tructure shows a dramatic reduction of 76% upon relaxation (Figure 4f).…”

“…As the size of MP decreases with an increasing twist, imaging for θ > 2° systems becomes unfeasible. , Therefore, the current understanding of reconstruction through experimental visualization is limited to low angle twists and is primarily based on image analysis techniques rather than physically measurable quantities. Aside from the scanning probe techniques, atomic reconstruction in twisted 2D heterostructures has been examined through angle-dependent scanning electron microscopy (SEM), dark-field transmission electron microscopy (DF-TEM), ,, electron diffraction, Bragg interferometry based on four-dimensional scanning transmission electron microscopy (4D-STEM), and annular dark-field (ADF) STEM. , Such techniques have examined twisted bilayers without strain that range from close to 0° to 4° twist angles between the 2D layers. Moreover, some of these works have also examined twisted bilayers with external heterostrain, where substantial atomic reconstruction has been observed regardless of their small moiré periodicities.…”

Superconductivity in Twisted Bilayer Graphene: Cooper-pairs distribution function analysis

“…The relative twisted angle between layers, in 2D materials such as TBLG 7,8 , has become an undeniable phenomenon and a new eld. In this way, magic angle value provided a novel knob for tuning superconducting properties 1 and many-body effects 2,9,10 .…”