Hopping-Mediated Charge Transport in Graphene Beyond the Ballistic Regime

Abstract

We present a trajectory-resolved framework for charge transport in graphene and related two-dimensional carbon systems beyond the ideal ballistic and fully coherent limits. Transport is described by kinetic Monte Carlo hopping on a predefined atomic lattice, allowing the combined treatment of disorder, thermal activation, and external fields. Current and effective transmittance are extracted directly from stochastic carrier trajectories, without phenomenological transport coefficients. We apply the method to graphene under bias voltage (0-0.10 V), temperature (300-900 K), magnetic field (0-10 T), in-plane strain (2-10%, uniaxial and biaxial), and vacancy concentration (0-10%). Pristine graphene shows an almost ohmic response, with currents of about 7-8 uA, effective transmittance near 0.98-1.00, and conductance of about (5.8-7.8) x 10^-5 S at 0.10 V, depending on direction. Vacancies strongly suppress transport, reducing transmittance to about 0.45-0.75 at 10% vacancy. Higher temperature accelerates hopping and partly restores transport, but cannot overcome severe connectivity loss. Magnetic fields further reduce transport, especially in disordered networks. The framework provides a unified computational scheme for realistic two-dimensional carbon materials and also yields diffusion coefficients and effective mobilities from carrier displacements and transit times.