Exciton Dynamics Studies from First-Principles Calculations: Radiative Recombination, Exciton-Phonon Interactions, and Ultrafast Exciton Relaxation

Citation

Chen, Hsiao-Yi (2021) Exciton Dynamics Studies from First-Principles Calculations: Radiative Recombination, Exciton-Phonon Interactions, and Ultrafast Exciton Relaxation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4edg-jw48. https://resolver.caltech.edu/CaltechTHESIS:05312021-191637587

Abstract

Excitons are bound electron-hole pairs that dominate the optical response of semi-conductors and insulators, especially in nanoscale and wide bandgap materials where the Coulomb interaction is weakly screened. Excitons can enhance light-matter coupling at certain wavelengths, thus making their host materials candidates for optoelectronic, photovoltaic, and quantum technology devices. For instance, two-dimensional transition metal dichalcogenides have a large and tunable optical response and hold promise for next-generation ultrathin light-emitting diodes. It is remarkable that exciton properties such as the binding energy and radiative lifetime can vary by orders of magnitude in different materials and can be further tuned by material properties like defects and lattice vibrations. Therefore, quantitative studies of exciton interactions and dynamics can advance understanding of the optical response of complex materials and play a role in the design of future devices. Among theoretical studies, numerical approaches based on density functional theory (DFT) can quantitatively address the electronic structure in real materials and their response to external perturbations, enabling accurate calculations of the conductivity and dielectric properties. These first-principle methods, which employ numerical quantum mechanics and use only the atomic structure of the material as input (making no use of empirical parameters) have revolutionized studies of materials and condensed matter physics. Over the last few years, first-principles methods for studies of excitons have focused on the GW-Bathe-Salpeter equation (GW-BSE) method to compute exciton energies and optical absorption spectra. However, going beyond calculations of exciton energetics to address the exciton dynamical processes remains challenging and is an exciting new frontier of first-principles studies.

This thesis develops theory and novel numerical approaches to study exciton radiative and nonradiative interactions from first-principles. For the radiative processes, we demonstrate a systematic derivation of exciton radiative lifetimes in materials ranging from bulk to nanostructures and molecules. The results correctly reproduce the observed power-law temperature dependence of the radiative lifetimes. To benchmark our calculations, we study exciton radiative lifetimes in gas-phase molecules, obtaining excellent agreement between theory and experiment. Our framework is then applied in three different studies. First, we extend the radiative lifetime formula to account for the dependence on light polarization and valley occupation and investigate exciton recombination in two-dimensional transition metal dichalcogenides (2D-TMDs). We show that excitons emit light anisotropically upon recombination when they are in any quantum superposition state of the K and K' inequivalent valleys. When averaged over the emission angle and exciton momentum, our new treatment recovers the temperature-dependent radiative lifetimes derived in early literature. Second, we use the exciton energy and radiative lifetimes to identify the atomic structure of the defects in monolayer hexagonal boron nitride (h-BN). In the study, we narrow down the potential structures to nine candidates and identify the highest-likelihood structure as the V_NN_B defect, consisting of a nitrogen vacancy plus a carbon replacing boron in h-BN. Finally, we generalize the discussion of isotropic bulk system to accurately compute the exciton radiative lifetimes in bulk uniaxial crystals, focusing on wurtzite GaN. Our computed radiative lifetimes are in very good agreement with experiments at low temperature. We show that taking into account excitonic effect and spin-orbit coupling (to include the exciton fine structure) is essential for computing accurate radiative lifetimes. A model for exciton dissociation into free carriers allows us to compute the radiative lifetimes up to room temperature.

In the study of exciton non-radiative process, we focus on the exciton-phonon (ex-ph)interaction, which plays an important role to understand the dynamics of excitons in materials. We establish and implement a first-principle formalism to compute the ex-ph coupling constants by combining the electron-phonon couplings and the exciton wavefunctions from the GW-BSE approach. Using the computed ex-ph coupling matrix elements, we calculate the ex-ph relaxation times as a function of exciton energy, momentum, temperature, and phonon mode in bulk h-BN. Our calculations reveal the dominant ex-ph coupling with the longitudinal optical (LO) mode and identify the threshold for LO phonon emission with an associated ∼15 fs LO emission characteristic time. In addition, we derive the phonon-assisted photoluminescence(PL) from the ex-ph interaction and correctly reproduce the PL spectrum observed in h-BN at both 8 K and 100 K. Based on our successful study of ex-ph interactions in bulk h-BN, we extend the discussion to materials with strong spin-orbit coupling. We investigate the bright exciton linewidth broadening and PL in monolayer WSe₂. The numerical results show an increase of linewidth by 20 meV from 0 K to 250 K as observed in early experiments and identify the main PL peak as a consequence of LA phonon emission while the side band is due to optical phonons. Lastly, we present results from a joint theory-experiment study of the ultrafast exciton dynamics in WSe₂. We develop a Boltzmann equation for excitons and employ it to model ultrafast exciton relaxation due to ex-ph processes. The simulation and experiment both show a ~70 fs time delay for the electron intervalley scattering from the K- to the Q-valley due to exciton dynamical effects. We also develop accurate simulations of time-domain angle-resolved photoemission (ARPES) experiments, which are becoming a powerful experimental probe of exciton dynamics in condensed matter. In summary, this thesis work paves the way to quantitative studies of exciton radiative and non-radiative processes, as well as exciton ultrafast dynamics, and quantitative modeling of pump-probe experiments in materials with strongly bound excitons.

Thesis Files