FIG. 10.1 Sketch of a twisted bilayer supercell with 3252 atoms, armchair edges, and at θ = 10°. The rotation axis is marked in dark gray in the inset and is centered on the A(B) sublattice of the upper (lower) layer. Reprinted with permission from Westerhout et al., 2D Mater. 9 , 014004 (2022). Copyright 2022 Author(s), licensed under a Creative Commons 4.0 Attribution License. More about this image found in Sketch of a twisted bilayer supercell with 3252 atoms, armchair edges, and ...

FIG. 10.5 Optical properties of twisted MoSe₂/WS₂ heterobilayers. (a) Room temperature PL spectra measured in CVD-grown MoSe₂ (black) and WS₂ (magenta) monolayers, as well as in a mechanically stacked MoSe₂/WS₂ heterostructure with rotation angle θ = 2° between the layers (blue). The two PL peaks appearing in the heterobilayer are labeled P1 and P2. (b) Normalized PL spectra showing peak P1 from (a) acquired in MoSe₂/WS₂ heterobilayers with interlayer twist angles θ ranging from 1 to 59°, indicated above each curve. A typical PL spectrum for a monolayer MoSe₂ is shown with a dashed black curve. The MoSe₂ A exciton PL peak is labeled XA, and its energy is marked with the vertical dashed line. (c) Variation in the P1 PL peak energy with twist angle measured on two substrates containing MoSe₂/WS₂ heterobilayers. Data for individual substrates are shown with light and dark red symbols. See the description of the fitting procedure in Methods. The blue curve shows the results of theoretical calculations as described in the text and Supplementary Note 1. The dashed horizontal line shows the spectral position of XA in an isolated MoSe₂ monolayer. Reprinted with permission from Alexeev et al., Nature 567 , 81–86 (2019). Copyright 2019 Springer Nature. More about this image found in Optical properties of twisted MoSe₂/WS₂ heterobilayer...

FIG. 3.12 Raman spectroscopic image for different twist angles representing moiré phonons in twisted-bilayer WSe₂. Reprinted with permission from H. Lin et al., Adv. Mater. 33 , 2008333 (2021). Copyright 2021 Authors, licensed under a Creative Commons 4.0 Attribution License. More about this image found in Raman spectroscopic image for different twist angles representing moiré pho...

FIG. 10.2 Raman spectra for TBG with different twist angles. (a) Raman spectra in the range of 1300 and 1700 cm⁻¹ for twist angles from 3.9° to 7.3° compared with AB stacked BLG as reference. (b) Raman spectra in the vicinity of the R′ band for 3.9° twisted BLG taken at different laser excitation energies. Reprinted with permission from Lu et al., ACS Nano 7 (3), 2587–2594 (2013). Copyright 2013 American Chemical Society. More about this image found in Raman spectra for TBG with different twist angles. (a) Raman spectra in the...

FIG. 10.4 HR-TEM images of TBG with different twist angles. The inset of each figure includes the fast Fourier transform for each image, indicating its twist angle. Reprinted with permission from Lu et al., ACS Nano 7 (3), 2587–2594 (2013). Copyright 2013 American Chemical Society. More about this image found in HR-TEM images of TBG with different twist angles. The inset of each figure ...

FIG. 10.3 STM characterizations taken in constant current mode. (a) Three typical 3D height images measured on TBG with twist angles of 0.6°, 1.1°, and 3.3°, respectively. (b) Four typical height profiles measured on TBG across two regions (one region with a twist angle of >12° and the other region with twist angles of 3.3°, 2.3°, 1.1°, and 0.6°, respectively). (c) High-resolution characterization of sub-moiré scale structure measured on TBG with a twist angle of 1.1°. Scale bar, 2 nm. Reprinted with permission from Zhang et al., Sci. Adv. 6 , eabc5555 (2020). Copyright 2020 Authors, licensed under a Creative Commons 4.0 Attribution License. More about this image found in STM characterizations taken in constant current mode. (a) Three typical 3D ...

FIG. 1.21 Examples of density shapes of twisted 3D solitons. (a) A toroidal hopfion produced by the Faddeev–Skyrme model [see Eq. ( 1.150 )]. (b) An example of a Q-ball in the twisted form ( Radu and Volkov, 2008 ). More about this image found in Examples of density shapes of twisted 3D solitons. (a) A toroidal hopfion p...

FIG. 5.1 (a) Typical STM topography of the TTG (tunnel current I = 320 pA, sample bias Vs = −0.6 V). The fast Fourier transforms the image of the two series of TTG moiré patterns, as shown in the top left inset [the scale bar is 0.16 (1/nm)]. A 2 × 2 nm² STM image of the TTG with a flawless honeycomb lattice can be seen in the upper right inset. (b) and (c) STM topographic pictures of the TTG in the same region measured at various sample biases, each 40 nm² in size. The simulated pictures of TBG with twist angles of 2.81 and 2.10, respectively, are displayed at the bottom of (b) and (c). The related FFT image is displayed in the insets; the scale bars in (b) and (c) are 0.17 and 0.15 nm, respectively. (d) The TTG simulation depicts the first layer (blue), the second layer (red), and the third layer (orange), as indicated by the legend [the TTG drawing is shown in the left bottom inset of (d)]. Figures (a)–(d) were reproduced with permission from Zuo et al., Phys. Rev. B 97 (3), 035440 (2018). Copyright 2018 American Physical Society. (e) An SLG/TMD junction is shown on the left, and a BLG/TMD junction is shown on the right, in schematics for the two configurations of the graphene/TMD heterojunction that we observed in our tests. For the sake of clarity, the SiC substrate is not displayed. This straightforward illustration demonstrates how the different work functions of SLG and BLG result in distinct band offsets for the TMD, or in other words, different Schottky barrier heights (SBH) for the graphene/TMD heterojunctions, in the absence of Fermi-level pinning. The vacuum level is evac, and the TMD's electronic affinity is χ. Figure (e) reproduced with permission from Quang et al., Phys. Rev. B 97 (3), 035440 (2018). Copyright 2017 IOP Science. More about this image found in (a) Typical STM topography of the TTG (tunnel current I = 320 pA, sample bi...

FIG. 3.6 Drilling delamination for a twist drill. Hocheng and Tsao, J. Mater. Process. Technol. 140 , 335–339 (2003). Copyright 2003 Elsevier. More about this image found in Drilling delamination for a twist drill. Hocheng and Tsao, J. Mater. Pro...