Fig. 4: PLDs as a Fourier series in 2D Moiré materials.
From: Torsional periodic lattice distortions and diffraction of twisted 2D materials
a–c Evolution of periodic wave (Δ) as higher harmonic waves b N = 3, c N = 7) are included; Δ is normalized displacement magnitude over one period along one direction. Fourier coefficients (An) are tailored as exponential decay, which produces to a smooth “sawtooth”-like waveform. Including harmonic waves allows high-frequency (i.e., sharp) features in resultant waves. d–f Torsional PLD structure with higher harmonic PLD included. The color denotes the amount of local rotation (ΩN) due to the PLD displacement field (arrows). g–i Quantum mechanical electron diffraction simulations of TBG with single harmonic torsional PLD capture the distortions in high twist angles (i.e., near magic angle and higher) well. j–o Adding higher harmonics slightly modifies the diffraction patterns and shows qualitatively better matches with low twist angle systems.
