Gate induced monolayer behavior in twisted bilayer black phosphorus

Abstract

Optical and electronic properties of black phosphorus strongly depend on the number of layers and type of stacking. Using first-principles calculations within the framework of density functional theory, we investigate the electronic properties of bilayer black phosphorus with an interlayer twist angle of 90${}^{\circ }$. These calculations are complemented with a simple $\vec{k}\cdot \vec{p}$ model which is able to capture most of the low energy features and is valid for arbitrary twist angles. The electronic spectrum of 90${}^{\circ }$ twisted bilayer black phosphorus is found to be x-y isotropic in contrast to the monolayer. However x-y anisotropy, and a partial return to monolayer-like behavior, particularly in the valence band, can be induced by an external out-of-plane electric field. Moreover, the preferred hole effective mass can be rotated by 90${}^{\circ }$ simply by changing the direction of the applied electric field. In particular, a +0.4 (-0.4) V/Å out-of-plane electric field results in a $\sim$60\% increase in the hole effective mass along the y (x) axis and enhances the $m_y^{\ast }/m_x^{\ast }$ ($m_x^{\ast }/m_y^{\ast }$) ratio as much as by a factor of 40. Our DFT and $\vec{k}\cdot \vec{p}$ simulations clearly indicate that the twist angle in combination with an appropriate gate voltage is a novel way to tune the electronic and optical properties of bilayer phosphorus and it gives us a new degree of freedom to engineer the properties of black phosphorus based devices.

8 pages, 8 figures

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