Transverse Zeeman magnetic field effects on the dynamical dielectric function of monolayer phosphorene: Beyond the continuum approximation

In this paper, we theoretically address the transverse Zeeman magnetic field effects on the frequency-dependent dynamical dielectric function of phosphorene including the refractive index and the absorption coefficient. An effective Hamiltonian model beyond the continuum approximation is employed to obtain the electronic dispersion energy. The linear response theory is applied to calculate the dynamical dielectric function at a certain temperature along both armchair and zigzag edges. Our numerical calculations show that, independent of the direction, the refraction (absorption) intensity decreases (increases) with the optical frequency at all magnetic field strengths. Moreover, we find out that the refraction and absorption processes along the armchair edge do not change after a critical magnetic field and this critical point increases with the optical frequency stemming from the spin-splitting effects. As for the zigzag edge, however, there is a little to no change for these processes with the magnetic field. Further, we observe that, on the average, the dominant contribution to the total magnetic field-dependent dynamical dielectric function comes from the armchair edge originating from the smaller (larger) carrier effective mass (velocity) than the zigzag edge. Tuning the optical responses of phosphorene with the transverse Zeeman magnetic field is useful for practical spintronic applications.