Abstract

We introduce a trajectory-resolved framework for charge transport in graphene and similar two-dimensional carbon systems, functioning beyond the idealized ballistic and fully coherent regimes. Transport is modeled using kinetic Monte Carlo hopping dynamics on a predefined atomic lattice, enabling concurrent analysis of disorder, thermal activation, and external fields. We can obtain the current and the effective transmittance directly from random carrier paths, without recourse to phenomenological transport coefficients. We use this method to measure how 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%) change the paths that electrons take through graphene networks. For pristine graphene, the response is almost ohmic over the bias window we examined. At 0.10 V, the current is about 7–8 µA, the effective transmittance goes up to about 0.98–1.00, and the conductance is about (5.8–7.8) ×10⁻⁵ S, depending on the direction. Vacancies progressively suppress transport: at 10% vacancy, the transmittance can drop to 0.45–0.75 (depending on bias and direction), and the current is significantly reduced compared to the pristine case. Increasing the temperature (from 300 K to 900 K) speeds up hopping kinetics and partially restores transport, but it can’t fully compensate for the loss of connectivity that occurs when many defects are present. External magnetic fields cause additional suppression, with the largest drops occurring in more disordered networks and at high fields (up to 10 T). In general, the framework brings together current, transmittance, and field- and defect-dependent transport regimes into one clear computational scheme for realistic two-dimensional carbon materials. It also allows the determination of diffusion coefficients and effective mobilities from carrier displacements and transit times.

Abstract

We introduce a trajectory-resolved framework for charge transport in graphene and similar two-dimensional carbon systems, functioning beyond the idealized ballistic and fully coherent regimes. Transport is modeled using kinetic Monte Carlo hopping dynamics on a predefined atomic lattice, enabling concurrent analysis of disorder, thermal activation, and external fields. We can obtain the current and the effective transmittance directly from random carrier paths, without recourse to phenomenological transport coefficients. We use this method to measure how 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%) change the paths that electrons take through graphene networks. For pristine graphene, the response is almost ohmic over the bias window we examined. At 0.10 V, the current is about 7–8 µA, the effective transmittance goes up to about 0.98–1.00, and the conductance is about (5.8–7.8) ×10⁻⁵ S, depending on the direction. Vacancies progressively suppress transport: at 10% vacancy, the transmittance can drop to 0.45–0.75 (depending on bias and direction), and the current is significantly reduced compared to the pristine case. Increasing the temperature (from 300 K to 900 K) speeds up hopping kinetics and partially restores transport, but it can’t fully compensate for the loss of connectivity that occurs when many defects are present. External magnetic fields cause additional suppression, with the largest drops occurring in more disordered networks and at high fields (up to 10 T). In general, the framework brings together current, transmittance, and field- and defect-dependent transport regimes into one clear computational scheme for realistic two-dimensional carbon materials. It also allows the determination of diffusion coefficients and effective mobilities from carrier displacements and transit times.

Abstract

We introduce a trajectory-resolved framework for charge transport in graphene and similar two-dimensional carbon systems, functioning beyond the idealized ballistic and fully coherent regimes. Transport is modeled using kinetic Monte Carlo hopping dynamics on a predefined atomic lattice, enabling concurrent analysis of disorder, thermal activation, and external fields. We can obtain the current and the effective transmittance directly from random carrier paths, without recourse to phenomenological transport coefficients. We use this method to measure how 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%) change the paths that electrons take through graphene networks. For pristine graphene, the response is almost ohmic over the bias window we examined. At 0.10 V, the current is about 7–8 µA, the effective transmittance goes up to about 0.98–1.00, and the conductance is about (5.8–7.8) ×10⁻⁵ S, depending on the direction. Vacancies progressively suppress transport: at 10% vacancy, the transmittance can drop to 0.45–0.75 (depending on bias and direction), and the current is significantly reduced compared to the pristine case. Increasing the temperature (from 300 K to 900 K) speeds up hopping kinetics and partially restores transport, but it can’t fully compensate for the loss of connectivity that occurs when many defects are present. External magnetic fields cause additional suppression, with the largest drops occurring in more disordered networks and at high fields (up to 10 T). In general, the framework brings together current, transmittance, and field- and defect-dependent transport regimes into one clear computational scheme for realistic two-dimensional carbon materials. It also allows the determination of diffusion coefficients and effective mobilities from carrier displacements and transit times.

Abstract

We introduce a trajectory-resolved framework for charge transport in graphene and similar two-dimensional carbon systems, functioning beyond the idealized ballistic and fully coherent regimes. Transport is modeled using kinetic Monte Carlo hopping dynamics on a predefined atomic lattice, enabling concurrent analysis of disorder, thermal activation, and external fields. We can obtain the current and the effective transmittance directly from random carrier paths, without recourse to phenomenological transport coefficients. We use this method to measure how 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%) change the paths that electrons take through graphene networks. For pristine graphene, the response is almost ohmic over the bias window we examined. At 0.10 V, the current is about 7–8 µA, the effective transmittance goes up to about 0.98–1.00, and the conductance is about (5.8–7.8) ×10⁻⁵ S, depending on the direction. Vacancies progressively suppress transport: at 10% vacancy, the transmittance can drop to 0.45–0.75 (depending on bias and direction), and the current is significantly reduced compared to the pristine case. Increasing the temperature (from 300 K to 900 K) speeds up hopping kinetics and partially restores transport, but it can’t fully compensate for the loss of connectivity that occurs when many defects are present. External magnetic fields cause additional suppression, with the largest drops occurring in more disordered networks and at high fields (up to 10 T). In general, the framework brings together current, transmittance, and field- and defect-dependent transport regimes into one clear computational scheme for realistic two-dimensional carbon materials. It also allows the determination of diffusion coefficients and effective mobilities from carrier displacements and transit times.