• conductivity
• Coulomb drag
• single layer graphene
• twisted bilayer graphene
• umklapp scattering

In this thesis we generalize the results obtained in the framework of linear response theory, for massless Dirac fermions and for 2D electron gas. We extend the treatment for Coulomb drag between two crystals including umklapp scattering contributions due to the interaction of charge carriers with the lattice. We calculate the drag conductivity by evaluating the longitudinal current-current correlator and using the finite temperature Green's function formalism. We show that in the direct current (D.C.) limit, the first non-zero term in the expansion of the drag conductivity is the second order in the interlayer interaction potential. We then express the drag conductivity at second order in the Coulomb-interaction potential, extending the formulation to account for drag between two periodic systems. The D.C. response is finally obtained by summing over the Matsubara frequencies and performing an analytical continuation. Starting from the drag conductivity, we show how the drag resistivity can be obtained, through inversion, incorporating crystal local field effects. Finally, in the long-wavelength limit, we recover the expression for the drag conductivity between two dimensional massless Dirac fermions and calculate the drag resistivity, between SLG and TBG in the low-temperature limit. Using a simplified model for TBG, where the bands are Dirac cones with a twist-angle dependent Fermi velocity, we show the results obtained in the weak and strong coupling regime.