Ab initio study of electron-phonon interaction in phosphorene

The monolayer of black phosphorus, or ``phosphorene,'' has recently emerged as a two-dimensional semiconductor with intriguing highly anisotropic transport properties. Existing calculations of its intrinsic phonon-limited electronic transport properties so far rely on the deformation potential approximation, which is in general not directly applicable to anisotropic materials since the deformation along one specific direction can scatter electrons traveling in all directions. We perform a first-principles calculation of the electron-phonon interaction in phosphorene based on density functional perturbation theory and Wannier interpolation. Our calculation reveals that (1) the high anisotropy provides extra phase space for electron-phonon scattering, and (2) optical phonons have appreciable contributions. Both effects cannot be captured by the deformation potential calculations. Our simulation predicts carrier mobilities $\ensuremath{\sim}170\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{V}\phantom{\rule{0.16em}{0ex}}\mathrm{s}$ for both electrons and holes at $300\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, and a thermoelectric figure of merit $zT$ of up to 0.14 in $p$-type impurity-free phosphorene at $500\phantom{\rule{0.16em}{0ex}}\mathrm{K}$.