Three-band k.p Hamiltonian of monolayer MoS2 based on the group theory and infinitesimal basis transformations approach

In this work, we present the matrix representation of three-band low-energy k.p Hamiltonian of monolayer MoS2 (ML-MDS) based on the group theory and infinitesimal basis transformations approach. We have derived the matrix representation of k.p Hamiltonian up to the second-order of perturbation at the Gamma point of the Brillouin zone. Due to the symmetries of doubly degenerate conduction band (CB), namely the CB+1 and (CB+1)', the optical transitions from these bands to valance band (VB) are allowed. Therefore, we have chosen three bands to describe the dynamics of ML-MDS around the G point. We have obtained three main 3 x 3 matrices including a zero-order matrix describing the edge band energies, a first-order matrix describing the coupling of VB, CB + 1, and (CB + 1)' away from the G point, and a second-order matrix which is itself consisted of three matrices as a free-electron energy matrix, an isotropic diagonal matrix and a anisotropic matrix. The whole matrix definitely show the isotropic and parabolic properties of VB and the anisotropy property of two degenerate CB + 1 and (CB + 1)'.