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The stacking dependent electronic structure and optical properties of bilayer black phosphorus.

By employing density-functional theory, the G0W0 method and Bethe-Salpter equation, we explore quasi-particle energy bands, optical responses and excitons of bilayer black phosphorus (BBP) with four different stacking patterns. All the structures are direct band gap semiconductors and the band gap is highly dependent on the stacking pattern, with a maximum of 1.31 eV for AB-stacking and a minimum of 0.92 eV for AD-stacking. Such dependence can be well understood by the tight-binding model in terms of the interlayer hopping. More interestingly, stacking sensitive optical absorption and exciton binding energy are observed in BBPs. For x-polarized light, more red-shift of optical adsorption appears in AA-stacking and the strong exciton binding energy in the AA-stacking bilayer can be as large as 0.82 eV, that is ∼1.7 times larger than that of AD-stacking bilayer.