First-Principles Study of Structural and Electronic Properties of Monolayer PtX2 and Janus PtXY (X, Y = S, Se, and Te) via Strain Engineering

In this work, the structural parameters and electronic properties of PtX2 and Janus PtXY (X, Y = S, Se, and Te) are studied based on the density functional theory. The phonon spectra and the Born criteria of the elastic constant of these six monolayers confirm their stability. All PtX2 and Janus PtXY monolayers show an outstanding stretchability with Young's modulus ranging from 61.023 to 82.124 N/m, about one-fifth that of graphene and half that of MoS2, suggesting highly flexible materials. Our first-principles calculations reveal that the pristine PtX2 and their Janus counterparts are indirect semiconductors with their band gap ranging from 0.760 to 1.810 eV at the Perdew-Burke-Ernzerhof level (1.128-2.580 eV at the Heyd-Scuseria-Ernzerhof level). By applying biaxial compressive and tensile strain, the electronic properties of all PtX2 and Janus PtXY monolayers are widely tunable. Under small compressive strain, PtX2 and Janus PtXY structures remain indirect semiconductors. PtTe2, PtSeTe, and PtSTe monolayers undergo a semiconducting to metallic transition when the strain reaches -6, -8, and -10%, respectively. Interestingly, there is a transition from the indirect semiconductor to a quasi-direct one for all PtX2 and Janus PtXY monolayers when the tensile strain is applied.

Torsional and lateral eigenmode oscillations for atomic resolution imaging of HOPG in air under ambient conditions

Combined in-plane and out-of-plane multifrequency atomic force microscopy techniques have been demonstrated to be important tools to decipher spatial differences of sample surfaces at the atomic scale. The analysis of physical properties perpendicular to the sample surface is routinely achieved from flexural cantilever oscillations, whereas the interpretation of in-plane sample properties via force microscopy is still challenging. Besides the torsional oscillation, there is the additional option to exploit the lateral oscillation of the cantilever for in-plane surface analysis. In this study, we used different multifrequency force microscopy approaches to attain better understanding of the interactions between a super-sharp tip and an HOPG surface focusing on the discrimination between friction and shear forces. We found that the lateral eigenmode is suitable for the determination of the shear modulus whereas the torsional eigenmode provides information on local friction forces between tip and sample. Based on the results, we propose that the full set of elastic constants of graphite can be determined from combined in-plane and out-of-plane multifrequency atomic force microscopy if ultrasmall amplitudes and high force constants are used.