heterostructures*

Proximity effects in graphene/transition-metal dichalcogenides heterostructures are expected to play a major role in the fields of spintronics and valleytronics. We investigate the electronic dispersion of such heterostructures in the presence of a proximity induced spin-orbit interaction (SOI) using a tight-binding (TB) model. The competition between different perturbation terms leads to inverted bands, when graphene is on WSe₂, and to topologically trivial band structures when it is placed on MoS₂, MoSe₂, and WS₂. In addition, we study the effect of symmetry breaking terms on ac and dc transport by evaluating the corresponding conductivities within linear response theory. The scattering-dependent diffusive conductivity increases linearly with electron density but weakens as the screening gets stronger. Further, we evaluate the power spectrum and assess its dependence on the spin and valley degrees of freedom and on the scattering which is essential at low frequencies.