Controlling valley splitting and polarization of dark- And bi-excitons in monolayer WS₂ by a tilted magnetic field

We developed a comprehensive theoretical framework focusing on many-body effects of exciton species in monolayer WS₂, including bright and dark excitons, and intra- and inter-valley biexcitons, to investigate valley dynamics in monolayer WS₂ subjected to a tilted magnetic field . In particular, the evolution of the exciton population densities and the many-body particle scatterings are considered to calculate the valley polarization () as a function of the magnetic field. We found valley splittings for the dark exciton and biexciton energy levels that are larger than those of bright excitons, of -0.23 meV T^-1. For example, -0.46 meV T^-1 for dark excitons and -0.69 meV T^-1 for bright-dark intra-valley biexcitons. Furthermore, inter-valley bright-dark excitons have an opposite valley energy splittings of +0.23 meV T^-1. For the samples pumped by linearly polarized light, exhibits distinct magnetic field dependence for different types of many-body particle states. Among them, the of the intra-valley bright-dark biexcitons increases with increasing magnetic field and reaches nearly 50% at B = 65 T. The brightened dark exciton, on the other hand, exhibits vanishing , indicating long valley relaxation time. Remarkably, the inter-valley bright-dark biexciton shows unconventional behavior with an inverted . The opposite for intra- and inter-valley bright-dark biexcitons, coupled with their large valley splitting and long valley lifetime may facilitate their coherent manipulation for quantum computing.