Signature of excitonic insulators in phosphorene nanoribbons

Phosphorene is a recently developed two-dimensional (2D) material that has attracted tremendous attention because of its unique anisotropic optical properties and quasi-one-dimensional (1D) excitons. We use first-principles calculations combined with the maximally localized Wannier function tight binding Hamiltonian and Bethe-Salpeter equation (BSE) formalism to investigate quasiparticle effects of 2D and quasi-1D blue and black phosphorene nanoribbons. Our electronic structure calculations shows that both blue and black monolayered phases are semiconductors. On the other hand black phosphorene zigzag nanoribbons are metallic. Similar behavior is found for very thin blue phosphorene zig-zag and armchair nanoribbon. As a general behavior, the exciton binding energy decreases as the ribbon width increases, which highlights the importance of quantum confinement effects. The solution of the BSE shows that the blue phosphorene monolayer has an exciton binding energy four times higher than that of the black phosphorene counterpart. Furthermore, both monolayers show a different linear optical response with respect to light polarization, as black phosphorene is highly anisotropic. We find a similar, but less pronounced, optical anisotropy for blue phosphorene monolayer, caused exclusively by the quasi-particle effects. Finally, we show that some of the investigated nanoribbons show a spin-triplet excitonic insulator behavior, thus revealing exciting features of these nanoribbons and therefore provides important advances in the understanding of quasi-one dimensional phosphorus-based materials.