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Excitons and optical spectra of phosphorene nanoribbons

On the basis of many-body {\it ab-initio} calculations, using single-shot G$_0$W$_0$ method and Bethe-Salpeter equation, we study phosphorene nanoribbons (PNRs) in the two typical zigzag and armchair directions. The electronic structure, optical absorption, electron-hole (exciton) binding energy, exciton exchange splitting, and exciton wave functions are calculated for different size of PNRs. The typically strong splitting between singlet and triplet excitonic states make PNRs favorable systems for application in optoelectronic. Quantum confinement occurs in both kinds of PNRs, and it is stronger in the zPNRs, as behave like quasi-zero-dimensional systems. Scaling laws are investigated for the size-dependent behaviors of PNRs. The first bright excitonic state in PNRs is explored in detail.