A two-band spinful k.p Hamiltonian of monolayer MoS2 from a nine-band model based on group theory

We present a matrix representation of two-band low-energy spinful k.p Hamiltonian of mono layer MoS2 using group theory and Lowdin partitioning method. By considering the spin-orbit coupling and using nine bands, we have derived a two-band effective Hamiltonian for the last valance band (VB) and the first conduction band (CB) around the K and -K valleys. Our model clearly shows electronic properties such as electron-hole asymmetry, trigonal warping (TW), and spin-splitting of the conduction and valance bands. Using numerical values for material parameters, we have displayed these properties and transitions between the valence and conduction bands which lead to the formation of A and B excitons. Also, we have extracted the general method to determine the symmetry of each band. By calculating the matrix elements of Hamiltonian up to the third-order of perturbation and taking into account the second (VB-5) and third (VB-4) valance bands, we have been able to obtain a more accurate model for dispersion relations of CB and VB.