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Defects in materials significantly influence their properties and enhance functionality. Hybrid functionals like HSE06, though effective for describing defects, face challenges in geometry optimization for large supercells. The r2SCAN+rVV10+U+Ud method provides a computationally efficient alternative. By selecting appropriate U and Ud values for the d orbitals of host and defect atoms, this method accurately describes defects in materials. Our study on small polaron defects in layered transition-metal oxides demonstrates this. Using literature values for U and Ud, we investigated birnessite (KnMnO2, n = 0.03) and KnNiO2, n = 0.03. With one K atom intercalated in a supercell, both materials show a localized eg polaronic state on the transition metal ion reduced by the K atom, when the geometry is calculated using published U values. The expected Jahn-Teller distortion is not observed when U=Ud=0. In layered cobalt oxide with additional potassium ions (KnCoO2, n = 1.03), a single extra K atom in the supercell leads to four localized electrons in the band gap, using standard U values, and even for U=Ud=0. Monolayer MoS2 exhibits intriguing properties and potential technological applications when subjected to strain. A recent experimental study reported that the bandgap of monolayer MoS2 on a mildly curved graphite surface decreases by 400 meV/% strain under biaxial strain with a Poisson’s ratio of 0.44. We conducted density functional theory (DFT) calculations on a free-standing MoS2 monolayer using the generalized gradient approximation (GGA) PBE, the hybrid functional HSE06, and many-body perturbation theory with the GW approximation using PBE wavefunctions (G0W0@PBE). Our findings indicate that under biaxial strain with the experimental Poisson’s ratio, the bandgap decreases at rates of 63 meV/% strain (PBE), 73 meV/% strain (HSE06), and 43 meV/% strain (G0W0@PBE), which are significantly lower than the experimental rate. Additionally, PBE predicts a reduction rate of 90 meV/% strain for a Poisson’s ratio of 0.25. Spin-orbit correction (SOC) has minimal impact on the bandgap or its strain dependence. We also observed a semiconductor-to-metal transition at 10% tensile biaxial strain and a shift from a direct to an indirect bandgap, aligning with previous theoretical studies. / Physics

Nanomaterials are playing an increasing role in novel technologies, and it is important to develop optical methods to characterize them in situ.  To that end, backside absorbing layer microscopy (BALM) has emerged as a powerful tool, being capable to resolve sub-nanometer height profiles, with video-rate acquisition speeds and a suitable geometry to couple live experiments.  In the internship, several techniques involving BALM were developed, and applied to study optical and electrical properties of the transition metal dichalcogenide (TMD) monolayer MoS2, a type of 2-dimensional (2D) crystalline semiconductor.  A simulations toolkit was created in MATLAB to model BALM, a workflow to reliably extract linear intensities from the CMOS detector was realized, and 2D MoS2 was synthesized by chemical vapor deposition followed by transfer to appropriate substrates.  BALM data of the 2D MoS2 was acquired and combined with simulations, giving a preliminary result for its complex refractive index at 5 optical wavelengths.  In addition, the first steps towards coupling BALM with a gate biased 2D MoS2 field-effect transistor were explored.  To complement BALM measurements, the grown samples were also characterized by conventional optical microscopy, scanning electron microscopy, atomic force microscopy, photoluminescence spectroscopy, and Raman spectroscopy.  This work provides new additions to an existing platform of BALM techniques, enabling novel BALM experiments with nanomaterial systems.  In particular, it introduces a new alternative for local extraction of optical parameters and for probing of electrical charging effects, both of which are vital in the research and development of nano-optoelectronics.