  We propose an effective lattice Hamiltonian for monolayer MoS$_2$ in order to
describe the low-energy band structure and investigate the effect of
perpendicular electric and magnetic fields on its electronic structure. We
derive a tight-binding model based on the hybridization of the $d$ orbitals of
molybdenum and $p$ orbitals of sulfur atoms and then introduce a modified
two-band continuum model of monolayer MoS$_2$ by exploiting the
quasi-degenerate partitioning method. Our theory proves that the low-energy
excitations of the system are no longer massive Dirac fermions. It reveals a
difference between electron and hole masses and provides trigonal warping
effects. Furthermore, we predict a valley degeneracy breaking effect in the
Landau levels. Besides, we also show that applying a gate voltage perpendicular
to the monolayer modifies the electronic structure including the band gap and
effective masses.
