Contrary to empirical observations, lowest-order k . (p) over cap theory predicts that monolayer black phosphorus ("phosphorene") is completely immune to zigzag-polarized optical excitation at the band-gap energy. Using symmetry arguments, we derive a 2 x 2 Hamiltonian under the k . (p) over cap 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 . (p) over cap perturbation in the interband optical matrix element, whereas the effects of the spin-orbit interaction are negligible in this material, consistent with a trivial orbital diamagnetic contribution to the g-factors.
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机译：与经验观察相反，最低阶K. （P）通过帽理论预测，单层黑磷（“磷烯”）在带间隙能量下完全免受曲折极化光学激发。 使用对称性参数，我们在k下得出了2 x 2哈密顿人。 （p）在盖帽形式主义，包括高阶校正，其用于表明具有Z字形偏振的实验测量的带间隙转变由三阶k主导。 （p）在间带光学矩阵元件中覆盖扰动，而旋转轨道相互作用的效果在这种材料中可以忽略不计，与G伏因子的普通轨道磁磁贡献一致。
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