Ab initio approaches to Resonant Raman Spectroscopy of Transition Metal Dichalcogenides

This thesis deals with the theory and simulation of resonant Raman spectroscopy in two-dimensional transition metal dichalcogenides. We present two different ab initio approaches. In the first, we calculate the Raman susceptibility tensor as a function of laser energy from the change of the dielectric susceptibility with atomic displacements. In the second, we formulate the Raman tensor in terms of time-dependent perturbation theory and calculate it using electron-light and electron-phonon coupling matrix elements obtained from density functional theory. We investigate the role of resonance, quantum interference and excitonic effects in the Raman spectra of single and triple-layer MoTe2. We compare our simulations with experimental results, explaining the dependence of the Raman intensities on the excitation energy. We demonstrate that the two approaches are formally and numerically equivalent in the adiabatic limit. In addition, the second approach allows to include the dynamical effects and captures a shift of the intensities with respect to the adiabatic case. This method is also more computationally efficient and is extended to include temperature effects using many-body perturbation theory. We have implemented both of these methods in a software package with interfaces to open source ab initio codes. Furthermore, we have developed web based tools to visualize excitonic states and phonon modes

Semi-empirical phonon calculations for graphene on different substrates

We investigate the graphene-substrate interaction via changes in the phonon dispersion of graphene. Ab-initio calculations on these systems are of high computational cost due to the non-commensurability of the unit cells of graphene and the substrate. This leads to the formation of Moiré patterns with accordingly large supercell sizes. We use a semi-empirical force constant model for the calculation of phonons of graphene on different metallic and insulating substrates. The interaction of graphene with the substrate is described via suitably chosen spring constants. The phonon dispersion in the primitive unit cell of graphene is obtained via an “unfolding procedure” similar to the ones used for the discussion of ARPES (angular resolved photo-emission spectroscopy) of graphene on incommensurate substrates

Phonon-limited carrier mobility and resistivity from carbon nanotubes to graphene

Under which conditions do the electrical transport properties of one-dimensional (1D) carbon nanotubes (CNTs) and 2D graphene become equivalent? We have performed atomistic calculations of the phonon-limited electrical mobility in graphene and in a wide range of CNTs of different types to address this issue. The theoretical study is based on a tight-binding method and a force-constant model from which all possible electron-phonon couplings are computed. The electrical resistivity of graphene is found in very good agreement with experiments performed at high carrier density. A common methodology is applied to study the transition from 1D to 2D by considering CNTs with diameter up to 16 nm. It is found that the mobility in CNTs of increasing diameter converges to the same value, the mobility in graphene. This convergence is much faster at high temperature and high carrier density. For small-diameter CNTs, the mobility strongly depends on chirality, diameter, and existence of a bandgap.Comment: 12 page

Phonon-limited electron mobility in Si, GaAs and GaP with exact treatment of dynamical quadrupoles

We describe a new approach to compute the electron-phonon self-energy and carrier mobilities in semiconductors. Our implementation does not require a localized basis set to interpolate the electron-phonon matrix elements, with the advantage that computations can be easily automated. Scattering potentials are interpolated on dense $\mathbf{q}$ meshes using Fourier transforms and ab initio models to describe the long-range potentials generated by dipoles and quadrupoles. To reduce significantly the computational cost, we take advantage of crystal symmetries and employ the linear tetrahedron method and double-grid integration schemes, in conjunction with filtering techniques in the Brillouin zone. We report results for the electron mobility in Si, GaAs, and GaP obtained with this new methodology

A force-constant model of graphene for conductivity calculations

Transport in graphene is strongly limited by the electron-phonon interaction. Accurate description of the phonon dispersion relations is essential for the study of this interaction. Using current state-of-the-art ab initio density-functional theory plane-wave codes, we are limited to systems with few atoms. For larger systems (e.g., nanotubes, nanoribbons), accurate semi-empircal models are needed. We have developed a force constant model for the phonon dispersion of graphene. Our implementation can include a large number of neighbours, which allows us to simulate accurately long-range interaction effects. As shown in previous publications it is possible to reproduce the phonon dispersion frequencies of graphene with a 4th nearest neighbours force constant model. However, some features can only be captured using long-range interactions (Kohn-anomalies, certain phonon eigenvectors). Using an ab initio phonon dispersion calculated with DFPT as reference, we show the nature of the long-range interactions and explore different ways to include them in our semi-empirical model. We also study the dependence of the force constants on charge and strain. Work in collaboration with Jing Li, Yann-Michel Niquet, Luigi Genovese, and Ivan Duchemin from L_Sim, SP2M, UMR-E CEA/UJF-Grenoble 1, INAC, Grenoble, France and Christophe Delerue from IEMN - Dept. ISEN, UMR CNRS 8520, Lille, Franc

Electronic and Vibrational proprieties of graphene on Ir(111) and SiC(100)

In the last years, graphene has become one of the most studied materials due to its peculiar electronic, optical, thermal, and mechanical properties. It is thus of major importance, for practical applications, to study how the electronic and vibrational proprieties of graphene change when deposited on a substrate. The non-commensurability of the unit cell of graphene with the substrate leads to the formation of Moiré patterns with accordingly large supercell sizes. Ab-initio calculations using standard plane-wave based codes on these large systems are of high computational cost even for the ground-state calculations. We show the effect that such Moiré patterns have on the band structure by projecting the resulting electronic structure and phonon dispersion onto the unit cell of free-standing graphene with an unfolding scheme. We compare our results with HREELS measurements of the phonon dispersion of graphene on Ir(111). The accurate knowledge of the interaction graphene-substrate will provide important information for future applications of graphene on electronic devices. Work performed in collaboration with the experimental groups of J. Kroeger (TU Ilmenau, Germany) and T. Seyller (TU Chemnitz, Germany)

Exciton-Phonon Coupling in the Ultraviolet Absorption and Emission Spectra of Bulk Hexagonal Boron Nitride

We present an ab initio method to calculate phonon-assisted absorption and emission spectra in the presence of strong excitonic effects. We apply the method to bulk hexagonal BN, which has an indirect band gap and is known for its strong luminescence in the UV range. We first analyze the excitons at the wave vector q¯ of the indirect gap. The coupling of these excitons with the various phonon modes at q¯ is expressed in terms of a product of the mean square displacement of the atoms and the second derivative of the optical response function with respect to atomic displacement along the phonon eigenvectors. The derivatives are calculated numerically with a finite difference scheme in a supercell commensurate with q¯. We use detailed balance arguments to obtain the intensity ratio between emission and absorption processes. Our results explain recent luminescence experiments and reveal the exciton-phonon coupling channels responsible for the emission lines

Quantum Interference Effects in Resonant Raman Spectroscopy of Single- and Triple-Layer MoTe2 from First-Principles

We present a combined experimental and theoretical study of resonant Raman spectroscopy in single- and triple-layer MoTe2. Raman intensities are computed entirely from first-principles by calculating finite differences of the dielectric susceptibility. In our analysis, we investigate the role of quantum interference effects and the electron−phonon coupling. With this method, we explain the experimentally observed intensity inversion of the A′1 vibrational modes in triple-layer MoTe2 with increasing laser photon energy. Finally, we show that a quantitative comparison with experimental data requires the proper inclusion of excitonic effects

First-principles investigation of CZTS Raman spectra

Cu2ZnSnS4 (CZTS) is an earth-abundant photovoltaic absorber material predicted to provide a sustainable solution for commercial solar applications. However, the efficiency of such solar cells is rather limited, cation disorder being often designated as the culprit. Raman spectroscopy has been widely used to characterize CZTS. Nonetheless, the interpretation of the spectra in terms of the atomic-scale disorder is precluded by the lack of consensus between theoretical and experimental results. In particular, there is a strong discrepancy in the relative intensities of the two prominent A phonon peaks of the spectra. In the present study, we demonstrate that the internal parameters characterizing the position of the S atoms strongly influence these intensities. We show that agreement with experiments can be completely recovered when adopting the geometry computed using a hybrid exchange-correlation functional. Finally, using special quasirandom structures, we demonstrate that the disorder only leads to a change of the shape of the Raman peaks (tailing or leading edges, shouldering and splitting). This could be exploited to assess the quality of the sample in terms of how ordered they are