In computational studies using the Lennard-Jones (LJ) potential, the widely adopted 2.5<i>σ</i>cutoff radius effectively truncates pairwise interactions across diverse systems (Santra<i>et al</i>2008<i>J. Chem. Phys.</i><b>129</b>234704, Chen and Gao 2021<i>Friction</i><b>9</b>502-12, Bolintineanu<i>et al</i>2014<i>Part. Mech.</i><b>1</b>321-56, Takahiro and Kazuhiro 2010<i>J. Phys.: Conf. Ser.</i><b>215</b>012123, Zhou<i>et al</i>2016<i>Fuel</i><b>180</b>718-26, Toxvaerd and Dyre 2011<i>J. Chem. Phys.</i><b>134</b>081102, Toxvaerd and Dyre 2011<i>J. Chem. Phys.</i><b>134</b>081102). Here, we assess its adequacy in determining energy barriers encountered by a Si monoatomic tip sliding on various two-dimensional (2D) monolayers, which is crucial for understanding nanoscale friction. Our findings emphasize the necessity of a cutoff radius of at least 3.5<i>σ</i>to achieve energy barrier values exceeding 95% accuracy across all studied 2D monolayers. Specifically, 3.5<i>σ</i>corresponds to 12.70 Å in graphene, 12.99 Å in MoS₂and 13.25 Å in MoSe₂. The barrier values calculated using this cutoff support previous experiments comparing friction between different orientations of graphene and between graphene and MoS₂(Almeida<i>et al</i>2016<i>Sci. Rep.</i><b>6</b>31569, Zhang<i>et al</i>2014<i>Sci. China</i><b>57</b>663-7). Furthermore, we demonstrate the applicability of the 3.5<i>σ</i>cutoff for graphene on an Au substrate and bilayer graphene. Additionally, we investigate how the atomic configuration of the tip influences the energy barrier, finding a nearly threefold increase in the barrier along the zigzag direction of graphene when using a Si(001) tip composed of seven Si atoms compared to a monoatomic Si tip.

In computational studies using the Lennard-Jones (LJ) potential, the widely adopted 2.5<i>σ</i>cutoff radius effectively truncates pairwise interactions across diverse systems (Santra<i>et al</i>2008<i>J. Chem. Phys.</i><b>129</b>234704, Chen and Gao 2021<i>Friction</i><b>9</b>502-12, Bolintineanu<i>et al</i>2014<i>Part. Mech.</i><b>1</b>321-56, Takahiro and Kazuhiro 2010<i>J. Phys.: Conf. Ser.</i><b>215</b>012123, Zhou<i>et al</i>2016<i>Fuel</i><b>180</b>718-26, Toxvaerd and Dyre 2011<i>J. Chem. Phys.</i><b>134</b>081102, Toxvaerd and Dyre 2011<i>J. Chem. Phys.</i><b>134</b>081102). Here, we assess its adequacy in determining energy barriers encountered by a Si monoatomic tip sliding on various two-dimensional (2D) monolayers, which is crucial for understanding nanoscale friction. Our findings emphasize the necessity of a cutoff radius of at least 3.5<i>σ</i>to achieve energy barrier values exceeding 95% accuracy across all studied 2D monolayers. Specifically, 3.5<i>σ</i>corresponds to 12.70 Å in graphene, 12.99 Å in MoS₂and 13.25 Å in MoSe₂. The barrier values calculated using this cutoff support previous experiments comparing friction between different orientations of graphene and between graphene and MoS₂(Almeida<i>et al</i>2016<i>Sci. Rep.</i><b>6</b>31569, Zhang<i>et al</i>2014<i>Sci. China</i><b>57</b>663-7). Furthermore, we demonstrate the applicability of the 3.5<i>σ</i>cutoff for graphene on an Au substrate and bilayer graphene. Additionally, we investigate how the atomic configuration of the tip influences the energy barrier, finding a nearly threefold increase in the barrier along the zigzag direction of graphene when using a Si(001) tip composed of seven Si atoms compared to a monoatomic Si tip.

To facilitate the rapid development of van der Waals materials and heterostructures, scanning probe methods capable of nondestructively visualizing atomic lattices and moiré superlattices are highly desirable. Lateral force microscopy (LFM), which measures nanoscale friction based on the commonly available atomic force microscopy (AFM), can be used for imaging a wide range of two-dimensional (2D) materials, but imaging atomic lattices using this technique is difficult. Here, we examined a number of the common challenges encountered in LFM experiments and presented a universal protocol for obtaining reliable atomic-scale images of 2D materials under ambient environment. By studying a series of LFM images of graphene and transition metal dichalcogenides (TMDs), we have found that the accuracy and the contrast of atomic-scale images critically depended on several scanning parameters including the scan size and the scan rate. We applied this protocol to investigate the atomic structure of the ripped and self-folded edges of graphene and have found that these edges were mostly in the armchair direction. This finding is consistent with the results of several simulations results. Our study will guide the extensive effort on assembly and characterization of new 2D materials and heterostructures.

Moiré superlattices formed by vertically stacking van der Waals layers host a rich variety of correlated electronic phases and function as novel photonic materials. The moiré potential of the superlattice, however, is fixed by the interlayer coupling of the stacked functional layers (e.g. graphene) and dependent on carrier types (e.g. electrons or holes) and valleys (e.g. Γ vs. K). In contrast, twisted hexagonal boron nitride (hBN) layers are predicted to impose a periodic electrostatic potential that may be used to engineer the properties of an adjacent functional thin layer. Here, we show that this potential is described by a simple theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. We demonstrate that the potential depth and profile can be further controlled by assembling a double moiré structure. When the twist angles are similar at the two interfaces, the potential is deepened by adding the potential from the two twisted interfaces, reaching ~ 400 meV. When the twist angles are dissimilar at the two interfaces, multi-level polarization states are observed. As an example of controlling a functional layer, we demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in a semiconductor monolayer. These findings suggest exciting opportunities for engineering properties of an adjacent functional layer using the surface potential of a twisted hBN substrate.

Source data for paper "Electrostatic moiré potential from twisted-hexagonal boron nitride layers"

Null imaging ellipsometry was developed to show the net change in polarization state between two samples. This system has no moving parts for nulling and does not exhibit azimuthal dependence on the optical elements. Therefore, this system is fast in data acquisition and easy to operate. In addition, image uniformity can be improved through a normalization process. For a demonstration, this system was applied to annealing studies of indium oxide thin films. The results show that this system can visualize the temperature dependence of the annealing as well as the progress of the annealing over time.