  Diffusion currents are theoretically examined in two-dimensional Dirac
materials, such as those of the transition metal dichalcogenides (TMD) family.
The transversal effects are analogues of the valley Hall (VHE) and
photogalvanic (PGE) transport phenomena in case when the electron driving force
is not an electric field but a gradient of electron density distribution in the
sample. The latter can be created by a finite-sized laser spot or by the
injection of electrons from other materials. We develop the theory of diffusive
VHE effect assuming the anisotropic electron-short-range-impurity skew
scattering. The electron PGE-like transport caused by higher electron-density
derivatives is analyzed assuming the trigonal warping anisotropy of electron
valleys in a TMD monolayer. The nonlinear responses on electron-density
gradient are studied as well. The isotropic processes of electron scattering
off the short-range and Coulomb centers are taken into account in the PGE-like
transport theory.
