Contrary to empirical observations, lowest-order $k\cdot\hat{ p}$ theory predicts that monolayer black phosphorus ("phosphorene") is completely immune to zigzag-polarized optical excitation at the bandgap energy. Using symmetry arguments, we derive a $2\times2$ Hamiltonian under the $k\cdot\hat{ p}$ formalism including higher-order corrections, which is used to show that the experimentally-measured band-gap transition with zigzag polarization is dominated by the third order $k\cdot\hat{ p}$ perturbation in the interband optical matrix element, whereas the effects of spin-orbit interaction are negligible in this material, consistent with a trivial orbital diamagnetic contribution to the $\textit{ g}$-factor.
Categories: cond-mat.mtrl-sci