  We develop a theory of Coulomb interaction-mediated contribution to valley
Hall effect (VHE) in two-dimensional non-centrosymmetric gapped Dirac
materials. We assume that the bare valley Hall current occurs in the system due
to the presence of disorder caused by impurities and is determined by the
valley-selective anisotropic skew scattering. Applying the Boltzmann transport
equation to describe the electron and hole transport in the material, we
calculate the renormalized VHE conductivity due to electron-electron and
electron-hole scattering processes, considering two regimes: (i) an $n$-doped
monolayer hosting a degenerate electron gas, and (ii) an intrinsic
semiconductor with the Boltzmann statistics of electron and hole gases. In both
regimes, the dominant mechanism of interparticle scattering is due to particles
residing in different valleys. Moreover, in case (ii), in addition to direct
scattering, electron-hole annihilation starts to play a role with the increase
in temperature. It might even become the dominant mechanism of the Coulomb
interaction-mediated VHE.
