Anisotropic Kubo conductivity of electric field-induced monolayer β₁₂-borophene

In this paper, we used three monolayer β₁₂-borophene Hamiltonian models to calculate the band structure, intra-band, and inter-band optical conductivity (IOC). Linear response theory and the Kubo formula are employed to calculate optical conductivity. We have shown that the band gap proportional to the inversion non-symmetric model increases by applying an external electric field (EEF), and for homogeneous and inversion-symmetric models, gap opening occurs. We found an anisotropic behavior in the IOC of β₁₂-borophene for polarized light along x and y-directions. The peak of the real part of the IOC for polarized light along the x-direction (ℜσ ) locates at the energy equal to the band gap and by applying an EEF shifts to the higher energies and experiences a blue shift. Also, the electric field has little effect on the IOC along y-direction (σ ) and in contrast to σ , by applying an electric field, the peak of the IOC shifts towards lower energies and a redshift occurs. In addition, unlike inter-band transitions, the intra-band optical conductivity of β₁₂-borophene is isotropic in all three models, and an EEF can not shift plots to higher or lower energies and only reduces the height of both imaginary and real parts of the optical conductivity.