Invariant Expansion of Monolayer MoS$_2$ electron states at the $K$ point

Using group theory, we derive the invariant expansion for the Hamiltonian of the electron states at the $K$ points of monolayer Molybdenum Disulfide (MoS$_2$), a transition metal dichalcogenide (TMDC). Unlike monolayers of graphite known as graphene, TMDCs provide a wider variety of physical phenomena due to the strong spin-orbit coupling attributed to the higher atomic number of the metal atoms. Our results also include the effects of external electric and magnetic fields. The low-order terms in the derived Hamiltonian are consistent with previous studies on the same material.