Stacking-dependent excitonic properties of bilayer blue phosphorene

Ab initio calculations in the framework of many-body perturbation theory (MBPT) are performed to calculate the electronic and optical properties of monolayer and bilayer blue phosphorene with different stacking configurations. It is found that the stacking configuration of bilayer blue phosphorene strongly affects the electronic band gap of the material. By solving the Bethe-Salpeter equation (BSE) on top of the $G_0{W}_0$ calculation, the binding energies, spectral positions, and band decomposition of excitons of monolayer and bilayer configurations are investigated. The most prominent two excitonic peaks of bilayers are examined in detail. Our calculations show that different stacking configurations lead to distinct interlayer interaction characteristics which lead to substantial change in the optical spectrum of bilayer blue phosphorene. Mostly intralayer and mixed interlayer excitons with quite high binding energies are obtained in bilayer blue phosphorene. Our results show that excitonic properties of ultrathin materials play an important role in tuning and improving the optoelectronic performance of two-dimensional materials.

Figure 1

(a) Top and side views of optimized geometric structures and (b) the orbital-projected electronic band dispersions of monolayer blue phosphorene. The rhombus represents a unit cell of the structure. Light and dark blue atoms show the upper and lower P atoms in the layer, respectively.

Figure 2

Top and side views of optimized geometric structures and the orbital projected electronic band dispersions of (a) ${\mathrm{AA}}_L$, (b) ${\mathrm{AA}}_H$, (c) ${\mathrm{AB}}_L$, and (d) ${\mathrm{AB}}_H$ stacked bilayer blue phosphorene. Light and dark blue atoms show the upper and lower P atoms in each layer, respectively.

Figure 3

(a) Electronic band structures within $G_0{W}_0$ and (b) optical absorption spectrum and oscillator strengths of monolayer blue phosphorene. The insets show the real space exciton wave functions.

Figure 4

Electronic band dispersions within $G_0{W}_0$ (the upper panels); optical absorption spectra, oscillator strengths, and top views of the real space exciton wave functions (the middle panels); and the percentage of the excitonic wave function on each layer (the bottom panels), of (a) ${\mathrm{AA}}_L$, (b) ${\mathrm{AA}}_H$, (c) ${\mathrm{AB}}_L$, and (d) ${\mathrm{AB}}_H$ stacked bilayer blue phosphorene. In all cases, the hole position is indicated by the black arrow.