Charge Transport Modeling in Graphene Systems

Graphene’s single-atom thickness, hexagonal lattice and linear energy dispersion confer unique charge transport properties that bridge classical semiconductor physics and quantum electrodynamics. Models of charge transport in graphene systems span semiclassical approaches—based on the Boltzmann transport equation and drift-diffusion formalisms—to fully quantum kinetic descriptions employing Wigner functions and pseudospin formalisms. Semiclassical methods capture carrier drift, diffusion and scattering by phonons, impurities or substrate interactions, often via Monte Carlo or discontinuous Galerkin schemes. Quantum kinetic theories reveal ℏ-dependent corrections to current, pressure and plasmon dispersion, reflecting the quasi-relativistic nature of Dirac fermions. Hydrodynamic descriptions, derived by moment methods with maximum entropy closures, describe macroscopic fields such as carrier density, current density and energy flux, and account for viscous and non-local effects at nanometre scales. Recent advances integrate ab initio calculations with continuum theories, enabling predictive simulations for heterostructures, strain-engineered systems and high-frequency device architectures. Collectively, these multi-scale models underpin the design of graphene-based transistors, sensors, plasmonic components and quantum devices, leveraging the material’s extraordinary conductivity, tunability and compatibility with layered heterostructures.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Charge Transport Modeling in Graphene Systems publication trend

The graph below shows the total number of articles in charge transport modeling in graphene systems across all publications each year (not limited to Nature Index journals).

Technical terms

Boltzmann transport equation: A semiclassical equation describing the time evolution of carrier distribution under external forces and collisions.

Wigner function: A phase-space representation of quantum states, enabling a quantum kinetic description analogous to classical distribution functions.

Dirac fermion: A quasi-particle in graphene described by the Dirac equation, exhibiting linear energy–momentum relation and two-component pseudospin.

Hydrodynamic model: A continuum framework for charge and energy transport derived from moment equations, incorporating viscosity, pressure and non-local terms.

Maximum entropy principle: A closure method for moment hierarchies that selects distribution functions maximising entropy under given constraints, ensuring thermodynamic consistency.

References

1. Charge transport and mobility in monolayer graphene. Journal of Mathematics in Industry (2016).
2. Weyl–Wigner description of massless Dirac plasmas: ab initio quantum plasmonics for monolayer graphene. New Journal of Physics (2022).
3. Wigner Equations for Phonons Transport and Quantum Heat Flux. Journal of Nonlinear Science (2023).
4. Hydrodynamic equations for an electron gas in graphene. Journal of Mathematics in Industry (2016).
5. Quantum Navier–Stokes equations for electrons in graphene. ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (2024).