Indirect-direct band gap transition of two-dimensional arsenic layered semiconductors cousins of black phosphorus

The monolayer arsenic in the puckered honeycomb structure was recently predicted to be a stable two-dimensional layered semiconductor and therefore named arsenene. Unfortunately, it has an indirect band gap, which limits its practical application. Using first-principles calculations, we show that the band gaps of few-layer arsenic have an indirect-direct transition as the number of arsenic layers （n） increases from n=1 to n=2. As n increases from n=2 to infinity, the stacking of the puckered hon- eycomb arsenic layers forms the orthorhombic arsenic crystal （ε-As, arsenolamprite）, which has a similar structure to the black phosphorus and also has a direct band gap. This indirect-direct transition stems from the distinct quantum-confinement effect on the indirect and direct band-edge states with different wavefunction distribution. The strain effect on these electronic states is also studied, showing that the in-plane strains can induce very different shift of the indirect and direct band edges, and thus inducing an indirect-direct band gap transition too. The band gap dependence on strain is non-monotonic, with both positive and negative deformation potentials. Although the gap of arsenene opens between As p-p bands, the spin-orbit interaction de- creases the gap by only 0.02 eV, which is much smaller than the decrease in GaAs with an s-p band gap. The calculated band gaps of arsenene and ε-As using the hybrid functional are 1.4 and 0.4 eV respectively, which are comparable to those of phos- phorene and black phosphorus.