Charge and energy transport in graphene with smooth finite-range disorder

We investigate charge and energy transport in monolayer graphene with smooth finite-range disorder, modeled by soft impurity potentials. Using a continuum Dirac model, we go beyond the Born approximation by computing the exact scattering matrix for individual impurities. This captures the full nonperturbative physics of smooth disorder. From the exact scattering data, we evaluate transport coefficients by solving the Boltzmann equation with energy-resolved phase shifts. We analyze electrical and electronic thermal conductivities versus carrier density and temperature, including deviations from the Wiedemann-Franz law. Our results reveal that finite-range disorder nontrivially modifies charge and heat currents, especially at low energies where perturbative methods fail. These findings provide a more accurate transport characterization for disordered Dirac materials and clarify how smooth disorder governs energy flow in graphene.