Charge compressibility and quantum magnetic phase transition in MoS2

We investigate the ground-state properties of monolayer MoS2 incorporating the Coulomb interaction together with a short-range intervalley interaction between charged particles between two valleys within the Hartree-Fock approximation. We consider four variables as independent parameters, namely, homogeneous charge (electron or hole) density, averaged dielectric constant, spin degree of freedom, and, finally, the Hubbard repulsion coefficient, which originates mostly from 4d orbits of Mo atoms. We find the electronic charge compressibility within the mean-field approximation and show that nonmonotonic behavior of the compressibility as a function of carrier density which is rather different from those of the two-dimensional electron gas. We also explore a paramagnetic-to-ferromagnetic quantum phase transition for the wide range of the electron density in the parameter space.