Many-body quantum Monte Carlo study of single-layer phosphorene: cohesion and band gap

Phosphorene is perhaps the most promising member of the family of two-dimensional (2D) materials with unique and tunable electronic and photonic properties combined with high carrier mobility. The direct band gap is tunable over the visible to near infrared range by changing the number of layers, straining, or alloying to cover the technologically important applications. However, due to experimental limitations such as presence of substrates, capping layers, defects, etc. and available accuracy of the mainstream modeling techniques, the a la carte property tuning for device applications is hampered by absence of accurate and unbiased data on even the simplest systems, such as the free-standing unstrained single-layer phosphorene. By determining the benchmark value of the fundamental gap in single-layer phosphorene to be 2.40+/-0.17 from cluster calculations and 2.68+/-0.10 eV from periodic supercell model using explicitly correlated quantum Monte Carlo (QMC) methods we provide one of the key missing links. We also predict the cohesion of the phosphorene layer as 3.194+/-0.025 eV/atom.