We study the second-order Raman process of mono- and few-layer MoTe$_2$, by combining {em ab initio} density functional perturbation calculations with experimental Raman spectroscopy using 532, 633 and 785 nm excitation lasers. The calculated electro
nic band structure and the density of states show that the electron-photon resonance process occurs at the high-symmetry M point in the Brillouin zone, where a strong optical absorption occurs by a logarithmic Van-Hove singularity. Double resonance Raman scattering with inter-valley electron-phonon coupling connects two of the three inequivalent M points in the Brillouin zone, giving rise to second-order Raman peaks due to the M point phonons. The predicted frequencies of the second-order Raman peaks agree with the observed peak positions that cannot be assigned in terms of a first-order process. Our study attempts to supply a basic understanding of the second-order Raman process occurring in transition metal di-chalcogenides (TMDs) and may provide additional information both on the lattice dynamics and optical processes especially for TMDs with small energy band gaps such as MoTe$_2$ or at high laser excitation energy.
We have experimentally studied the optical refractive index of few-layer graphene through reflection spectroscopy at visible wavelengths. A laser scanning microscope (LSM) with a coherent supercontinuum laser source measured the reflectivity of an ex
foliated graphene flake on a Si/SiO2 substrate, containing monolayer, bilayer and trilayer areas, as the wavelength of the laser was varied from 545nm to 710nm. The complex refractive index of few-layer graphene, n-ik, was extracted from the reflectivity contrast to the bare substrate and the Fresnel reflection theory. Since the SiO2 thickness enters to the modeling as a parameter, it was precisely measured at the location of the sample. It was found that a common constant optical index cannot explain the wavelength-dependent reflectivity data for single-, double- and three-layer graphene simultaneously, but rather each individual few-layer graphene possesses a unique optical index whose complex values were precisely and accurately determined from the experimental data.
Strain engineering of graphene through interaction with a patterned substrate offers the possibility of tailoring its electronic properties, but will require detailed understanding of how graphenes morphology is determined by the underlying substrate
. However, previous experimental reports have drawn conflicting conclusions about the structure of graphene on SiO2. Here we show that high-resolution non-contact atomic force microscopy of SiO2 reveals roughness at the few-nm length scale unresolved in previous measurements, and scanning tunneling microscopy of graphene on SiO2 shows it to be slightly smoother than the supporting SiO2 substrate. Quantitative analysis of the competition between bending rigidity of the graphene and adhesion to the substrate explains the observed roughness of monolayer graphene on SiO2 as extrinsic, and provides a natural, intuitive description in terms of highly conformal adhesion. The analysis indicates that graphene adopts the conformation of the underlying substrate down to the smallest features with nearly 99% fidelity.
