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Non-equilibrium transport and phonon branch-resolved size effects based on a multi-temperature kinetic model

Chuang Zhang, Houssem Rezgui, Meng Lian, Hong Liang

TL;DR

This work addresses non-equilibrium, branch-resolved heat transport in single-layer graphene by developing a multi-temperature kinetic framework that resolves electron and phonon-branch temperatures $T_e$ and $T_{p,k}$ with branch-specific electron-phonon couplings $G_{ep,k}$. Transport is treated via free-migration rather than diffusion, and the model is solved with the discrete unified gas kinetic scheme (DUGKS), enabling accurate capture of non-Fourier conduction and boundary slips. Key findings show that ZA phonons dominate heat conduction across system sizes, and branch-resolved effective conductivities can exceed the lattice conductivity in nanoscale regimes; in radial geometries with hotspots, a graded conductivity emerges from inside to outside. These results provide deeper insight into energy exchange mechanisms in graphene and offer routes to tailor heat flow by targeting specific phonon branches for excitation. The framework has broad implications for nanoscale thermal management and phonon-engineering in low-dimensional materials.

Abstract

Non-equilibrium transport and phonon branch-resolved size effects in single-layer graphene materials are studied under a multi-temperature kinetic model, which is developed for capturing the branch-dependent electron-phonon coupling. Compared with typical macroscopic multi-temperature models, the assumption of diffusive phonon transport is abandoned in this model and replaced by the free migration and scattering of particles. The phonon branch- and size-dependent effective thermal conductivity is predicted in nanosized graphene as well as the temperature slips near the boundaries. Compared with other phonon branches, the ZA branch contributes the most to thermal conduction regardless of system sizes. Furthermore, in nanosized homogeneous graphene with a hotspot at the center, the branch-dependent thermal conductivity increases from the inside to the outside even if the system size is fixed. The thermal conductivity of ZA branch is even higher than the lattice thermal conductivity when the system size is hundreds of nanometers.

Non-equilibrium transport and phonon branch-resolved size effects based on a multi-temperature kinetic model

TL;DR

This work addresses non-equilibrium, branch-resolved heat transport in single-layer graphene by developing a multi-temperature kinetic framework that resolves electron and phonon-branch temperatures and with branch-specific electron-phonon couplings . Transport is treated via free-migration rather than diffusion, and the model is solved with the discrete unified gas kinetic scheme (DUGKS), enabling accurate capture of non-Fourier conduction and boundary slips. Key findings show that ZA phonons dominate heat conduction across system sizes, and branch-resolved effective conductivities can exceed the lattice conductivity in nanoscale regimes; in radial geometries with hotspots, a graded conductivity emerges from inside to outside. These results provide deeper insight into energy exchange mechanisms in graphene and offer routes to tailor heat flow by targeting specific phonon branches for excitation. The framework has broad implications for nanoscale thermal management and phonon-engineering in low-dimensional materials.

Abstract

Non-equilibrium transport and phonon branch-resolved size effects in single-layer graphene materials are studied under a multi-temperature kinetic model, which is developed for capturing the branch-dependent electron-phonon coupling. Compared with typical macroscopic multi-temperature models, the assumption of diffusive phonon transport is abandoned in this model and replaced by the free migration and scattering of particles. The phonon branch- and size-dependent effective thermal conductivity is predicted in nanosized graphene as well as the temperature slips near the boundaries. Compared with other phonon branches, the ZA branch contributes the most to thermal conduction regardless of system sizes. Furthermore, in nanosized homogeneous graphene with a hotspot at the center, the branch-dependent thermal conductivity increases from the inside to the outside even if the system size is fixed. The thermal conductivity of ZA branch is even higher than the lattice thermal conductivity when the system size is hundreds of nanometers.
Paper Structure (5 sections, 16 equations, 3 figures, 1 table)

This paper contains 5 sections, 16 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Multi-temperature kinetic model
  3. Results and discussions
  4. Discrete unified gas kinetic scheme
  5. Dimensionless analysis

Figures (3)

  • Figure 1: (a) The two end sides of single-layer graphene materials are isothermal boundaries with fixed temperature $T_h=298$ K and $T_c=296$ K, respectively. (b) A Gaussian heating spot is added at the center and the four sides of single-layer graphene materials are isothermal boundaries with fixed environment temperature $297$ K.
  • Figure 2: Spatial distributions of (a,b) temperature and (c) branch-dependent effective thermal conductivity \ref{['eq:effectivekappa']}. (d) Size effects of single-layer suspended graphene at room temperature. Experimental data is obtained from Xu $et~al$xu_length-dependent_2014 when assuming thermal contact resistance contributes $0\%$, $5\%$, $11.5\%$ to the total measured thermal resistance in a $9~\mu$m-long sample with fixed width $1.5~\mu$m. BTE and nonequilibrium molecular dynamics (NEMD) results are obtained from Refs. PhysRevB.89.155426NEMD_park2013xu_length-dependent_2014, respectively. 'Present' is the total thermal conductivity of electron and phonon in this study.
  • Figure 3: Spatial distributions of (a-c) temperature and (d-f) thermal conductivity \ref{['eq:localkappa']} along the radial direction with different system sizes, where the horizontal axis is the distance from the center of geometry shown in \ref{['graphenesettings']}(b).