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

Juan A. Cañas, Daniel A. Bonilla, J. C. Pérez-Pedraza, A. Martín-Ruiz

Abstract

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.

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

Abstract

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.
Paper Structure (14 sections, 33 equations, 7 figures)

This paper contains 14 sections, 33 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Basics of the model
  3. Scattering through Partial-waves
  4. Semiclassical transport analysis
  5. Electrical conductivity
  6. Electronic thermal conductivity.
  7. Lorenz coefficient.
  8. Seebeck coefficient.
  9. Figure of merit.
  10. Results and Discussion
  11. The transport relaxation time.
  12. Electrical and thermal conductivities.
  13. Thermoelectric analysis.
  14. Conclusions

Figures (7)

  • Figure 1: A schematic of the proposed model. Soft-sphere scatterer potentials are randomly distributed across a graphene sheet. The dilute impurity limit ensures statistically independent scattering centers with negligible overlap.
  • Figure 2: Transport relaxation time (in picoseconds) as a function of the Fermi energy, calculated using Eq. \ref{['eq:tautr_phases']} for a random distribution of 3 nm-radius soft spheres with a concentration of $n_{\mathrm{imp}} = 1 \times 10^{12}$ cm$^{-2}$, and for various potentials. The subfigure (a) corresponds to positive soft sphere potentials, whereas (b) corresponds to negative ones.
  • Figure 3: DC conductivity at zero temperature versus (a) the radii of the spheres and (b) the soft-sphere potential. In both cases, the Fermi energy is $\mathscr{E}_F = 200$ meV.
  • Figure 4: DC conductivity versus the Fermi energy at zero temperature for a distribution of: (a) 1.5 nm-radius spheres, (b) 3 nm-radius spheres and (c) 5 nm-radius spheres.
  • Figure 5: Temperature dependence of the DC conductivity. The conductivity was calculated at a Fermi energy of $\mathscr{E}_F = 200$ meV, for spheres distributed with density $n_{\mathrm{imp}} = 1 \times 10^{12}$ cm$^{-2}$ and with: (a) a $3$ nm-radius and (b) a $5$ nm-radius.
  • ...and 2 more figures