Effective lattice Hamiltonian for monolayer MoS<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>: Tailoring electronic structure with perpendicular electric and magnetic fields

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 quasidegenerate 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. In addition, we also show that applying a gate voltage perpendicular to the monolayer modifies the electronic structure, including the band gap and effective masses.