The Stochastic Variational Method (SVM) is used to show that the effective mass model correctly estimates the binding energies of excitons and trions but fails to predict the experimental binding energy of the biexciton. Using high-accuracy variational calculations, it is demonstrated that the biexciton binding energy in transition metal dichalcogenides is smaller than the trion binding energy, contradicting experimental findings. It is also shown that the biexciton has bound excited states and that the binding energy of the L = 0 excited state is in very good agreement with experimental data. This excited state corresponds to a hole attached to a negative trion and may be a possible resolution of the discrepancy between theory and experiment.

The stochastic variational method is applied to excitonic formations within semiconducting transition metal dichalcogenides using a correlated Gaussian basis. The energy and structure of two-to six-particle systems are investigated along with their dependence on the effective screening length of the two-dimensional Keldysh potential and the electron-hole effective mass ratio. Excited state biexcitons are shown to be bound, with binding energies of the L = 0 state showing good agreement with experimental measurements of biexciton binding energies. Ground and newly discussed excited state exciton-trions are predicted to be bound and their structures are investigated.

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

We report a combined theoretical/experimental study of dynamic screening of excitons in media with frequency-dependent dielectric functions. We develop an analytical model showing that interparticle interactions in an exciton are screened in the range of frequencies from zero to the characteristic binding energy depending on the symmetries and transition energies of that exciton. The problem of the dynamic screening is then reduced to simply solving the Schrodinger equation with an effectively frequency-independent potential. Quantitative predictions of the model are experimentally verified using a test system: neutral, charged and defect-bound excitons in two-dimensional monolayer WS2, screened by metallic, liquid, and semiconducting environments. The screening-induced shifts of the excitonic peaks in photoluminescence spectra are in good agreement with our model.

An efficient and accurate basis comprised of Volkov states is implemented and tested for timedependent simulations of interactions between strong laser pulses and crystalline solids. The Volkov states are eigenstates of the free electron Hamiltonian in an electromagnetic field and analytically represent the rapidly oscillating time-dependence of the orbitals, allowing significantly faster time propagation than conventional approaches. The Volkov approach can be readily implemented in plane wave codes by multiplying the potential energy matrix elements with a simple time-dependent phase factor.