Microscopic Theory of Exciton Dynamics in Two-Dimensional Materials

Transition Metal Dichalcogenides (TMDs) present a giant leap forward towards the realization of nanometer-sized quantum devices. As a direct consequence of their truly two-dimensional character, TMDs exhibit a strong Coulomb-interaction, leading to the formation of stable electron-hole pairs, so-called excitons. These quasi-particles have a large impact on optical properties as well as charge-transport characteristics in TMDs. Therefore, a microscopic understanding of excitonic degrees of freedom and their interactions with other particles becomes crucial for a technological application of TMDs in a new class of optoelectronic devices. The aim of this thesis is to investigate the many-particle processes governing the ultrafast dynamics of excitons in TMD mono- and bilayers. Based on the density matrix formalism we develop equations describing an interacting system of electrons, phonons and photons, and numerically simulate the dynamics of excitons in TMDs. First, we provide a detailed picture of exciton-light and exciton-phonon interactions with special focus on the impact of momentum-dark exciton states. In particular, we develop and apply quantitative models for the i) broadening of excitonic resonances in linear absorption spectra, ii) formation of side peaks in photoluminescence spectra resulting from phonon-assisted recombination of momentum-dark excitons and iii) dynamical simulations of the formation of bound excitons out of a free electron-hole gas. Then, we investigate how the exciton-light interaction is modified when two TMD monolayers are vertically stacked into homo- and hetero-bilayers. Here we focus on the modification of optical spectra in bilayer systems by controlling the stacking angle. In particular, we iv) show how the interlayer hybridization of momentum-dark excitons can be controlled through the stacking angle and v) investigate how the localization phase of moir\\u27e excitons can be tuned. Our theoretical models have allowed us to predict experimentally accessible excitonic characteristics, which have been demonstrated in several joint experiment-theory collaborations including linear absorption, photoluminescence and ultrafast pump-probe experiments

Exciton Relaxation Cascade in Two-dimensional Transition-metal dichalcogenides

Monolayers of transition-metal dichalcogenides (TMDs) are characterized by an extraordinarily strong Coulomb interaction giving rise to tightly bound excitons with binding energies of hundreds of meV. Excitons dominate the optical response as well as the ultrafast dynamics in TMDs. As a result, a microscopic understanding of exciton dynamics is the key for technological application of these materials. In spite of this immense importance, elementary processes guiding the formation and relaxation of excitons after optical excitation of an electron-hole plasma has remained unexplored to a large extent. Here, we provide a fully quantum mechanical description of momentum- and energy-resolved exciton dynamics in monolayer molybdenum diselenide (MoSe$_2$) including optical excitation, formation of excitons, radiative recombination as well as phonon-induced cascade-like relaxation down to the excitonic ground state. Based on the gained insights, we reveal experimentally measurable features in pump-probe spectra providing evidence for the exciton relaxation cascade

Spatio-temporal dynamics in graphene

Temporally and spectrally resolved dynamics of optically excited carriers in graphene has been intensively studied theoretically and experimentally, whereas carrier diffusion in space has attracted much less attention. Understanding the spatio-temporal carrier dynamics is of key importance for optoelectronic applications, where carrier transport phenomena play an important role. In this work, we provide a microscopic access to the time-, momentum-, and space-resolved dynamics of carriers in graphene. We determine the diffusion coefficient to be $D \approx 360$cm$^{2}$/s and reveal the impact of carrier-phonon and carrier-carrier scattering on the diffusion process. In particular, we show that phonon-induced scattering across the Dirac cone gives rise to back-diffusion counteracting the spatial broadening of the carrier distribution

Bosonic Delocalization of Dipolar Moir\'e Excitons

In superlattices of twisted semiconductor monolayers, tunable moir\'e potentials emerge, trapping excitons into periodic arrays. In particular, spatially separated interlayer excitons are subject to a deep potential landscape and they exhibit a permanent dipole providing a unique opportunity to study interacting bosonic lattices. Recent experiments have demonstrated density-dependent transport properties of moir\'e excitons, which could play a key role for technological applications. However, the intriguing interplay between exciton-exciton interactions and moir\'e trapping has not been well understood yet. In this work, we develop a microscopic theory of interacting excitons in external potentials allowing us to tackle this highly challenging problem. We find that interactions between moir\'e excitons lead to a delocalization at intermediate densities and we show how this transition can be tuned via twist angle and temperature. The delocalization is accompanied by a modification of optical moir\'e resonances, which gradually merge into a single free exciton peak. The predicted density-tunability of the supercell hopping can be utilized to control the energy transport in moir\'e materials

Terahertz Fingerprint of Monolayer Wigner Crystals

The strong Coulomb interaction in monolayer semiconductors represents a unique opportunity for the realization of Wigner crystals without external magnetic fields. In this work, we predict that the formation of monolayer Wigner crystals can be detected by their terahertz response spectrum, which exhibits a characteristic sequence of internal optical transitions. We apply the density matrix formalism to derive the internal quantum structure and the optical conductivity of the Wigner crystal and to microscopically analyze the multipeak shape of the obtained terahertz spectrum. Moreover, we predict a characteristic shift of the peak position as a function of charge density for different atomically thin materials and show how our results can be generalized to an arbitrary two-dimensional system

Exciton-exciton interaction in transition metal dichalcogenide monolayers and van der Waals heterostructures

Due to a strong Coulomb interaction, excitons dominate the excitation kinetics in 2D materials. While Coulomb-scattering between electrons has been well studied, the interaction of excitons is more challenging and remains to be explored. As neutral composite bosons consisting of electrons and holes, excitons show a non-trivial scattering dynamics. Here, we study on microscopic footing exciton-exciton interaction in transition-metal dichalcogenides and related van der Waals heterostructures. We demonstrate that the crucial criterion for efficient scattering is a large electron/hole mass asymmetry giving rise to internal charge inhomogeneities of excitons and emphasizing their cobosonic substructure. Furthermore, both exchange and direct exciton-exciton interactions are boosted by enhanced exciton Bohr radii. We also predict an unexpected temperature dependence that is usually associated to phonon-driven scattering and we reveal an orders of magnitude stronger interaction of interlayer excitons due to their permanent dipole moment. The developed approach can be generalized to arbitrary material systems and will help to study strongly correlated exciton systems, such as moire super lattices.Comment: 13 pages, 6 figure

Optical fingerprint of bright and dark localized excitonic states in atomically thin 2D materials

Point defects, local strain or impurities can crucially impact the optical response of atomically thin two-dimensional materials as they offer trapping potentials for excitons. These trapped excitons appear in photoluminescence spectra as new resonances below the bright exciton that can even be exploited for single photon emission. While large progress has been made in deterministically introducing defects, only little is known about their impact on the optical fingerprint of 2D materials. Here, based on a microscopic approach we reveal direct signatures of localized bright excitonic states as well as indirect phonon-assisted side bands of localized momentum-dark excitons. The visibility of localized excitons strongly depends on temperature and disorder potential width. This results in different regimes, where either the bright or dark localized states are dominant in optical spectra. We trace back this behavior to an interplay between disorder-induced exciton capture and intervalley exciton-phonon scattering processes

Microscopic Mechanisms of the Formation, Relaxation and Recombination of Excitons in Two-Dimensional Semiconductors

Monolayers of Transition Metal Dichalcogenides (TMDs) present a giant leap forward towards the realization of semiconductor devices with atomic scale thickness. As a natural consequence of their two-dimensional character TMDs exhibit a reduced dielectric screening, leading to the formation of unusually stable excitons, i.e. Coulomb-bound electron-hole pairs. Excitons dominate the optical response as well as the ultrafast dynamics in TMDs. As a result, a microscopic understanding of excitons, their formation, relaxation and decay dynamics becomes crucial for a technological application of TMDs. A detailed theoretical picture of the internal structure of excitons and their scattering channels allows for a controlled manipulation of TMD properties enabling an entire new class of light emitters and detectors. The aim of this thesis is to investigate the many-particle processes governing the ultrafast dynamics of excitons. The focus is to provide a sophisticated picture of exciton-phonon and exciton-photon interaction mechanisms and the impact of dark exciton states starting from the formation of bound excitons out of a free electron-hole gas up to the eventual radiative decay of bright and dark exciton populations. Based on an equations-of-motion approach for the density matrix of an interacting electron, phonon and photon system, we simulate the dynamics of excitons in TMDs across the full Rydberg-like series of bright and dark states. Our theoretical model allows us to predict fundamental relaxation time scales as well as spectral features accessible in multiple spectroscopic experiments, such as absorption, photoluminescence and ultrafast pump-probe. In particular we predict intriguing features appearing in the terahertz absorption spectrum during the formation of excitons as well as distinct -so far unexplained- low temperature luminescence features stemming from phonon-assisted recombinations of dark excitons

Impact of strain on the excitonic linewidth in transition metal dichalcogenides

Monolayer transition metal dichalcogenides (TMDs) are known to be highly sensitive to externally applied tensile or compressive strain. In particular, strain can be exploited as a tool to control the optical response of TMDs. However, the role of excitonic effects under strain has not been fully understood yet. Utilizing the strain-induced modification of electron and phonon dispersion obtained by first principle calculations, we present in this work microscopic insights into the strain-dependent optical response of various TMD materials. In particular, we explain recent experiments on the change of excitonic linewidths in strained TMDs and predict their behavior for tensile and compressive strain at low temperatures.Comment: 7 pages, 7 figure

Microscopic Modeling of Pump-Probe Spectroscopy and Population Inversion in Transition Metal Dichalcogenides

Optical properties of transition metal dichalcogenide (TMD) monolayers are dominated by excitonic effects. These are significantly altered at high carrier densities, leading to energy renormalization, absorption bleaching, and even optical gain. Such effects are experimentally accessible in ultra-fast pump-probe measurements. Herein, the semiconductor Bloch equations are combined with the generalized Wannier equation to investigate the effect that excited carriers have on the excitonic properties of TMD monolayers. In particular, the dynamics of carrier occupation, energy renormalization, and absorption bleaching as well as population inversion and optical gain are investigated