Role of hydrodynamic viscosity on phonon transport in suspended graphene
Role of hydrodynamic viscosity on phonon transport in suspended graphene
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DOI：
10.1103/physrevb.97.094309
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发表时间：
2018-03
影响因子：
3.7
通讯作者：
Xun Li;Sangyeop Lee
中科院分区：
文献类型：
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作者：
Xun Li;Sangyeop Lee
当声子输运处于流体动力学区域时，热导率对温度（$T$）和样品宽度（$W$）呈现出特殊的依赖关系。过去，这些特性被用于通过实验证实三维块状材料中的流体动力学声子输运。最近预测悬浮石墨烯在比三维块状材料高得多的温度下，在热输运中会表现出强烈的流体动力学特征，但其实验验证需要理论和模拟的定量指导。在此，我们使用带有从头算全三声子散射矩阵的佩尔斯 - 玻尔兹曼方程的蒙特卡罗解法，对这些特殊的依赖关系进行定量预测。发现在低温下，热导率随${T}^{\alpha}$增加，其中$\alpha$根据样品宽度在1.89到2.49之间变化，远大于弹道情况的1.68。在100 K时，热导率具有${W}^{1.17}$的宽度依赖性，这与弹道 - 扩散区域的次线性依赖性明显不同。这些特殊特征可以用流体动力学区域的声子粘性阻尼效应来解释。我们从佩尔斯 - 玻尔兹曼方程推导出了声子流体动力学粘度的表达式，并讨论了声子粘性阻尼很好地解释了100 K时热导率的这些特殊依赖关系这一事实。当温度为300 K且样品宽度约为1μm时，即使在这种条件下流体动力学区域并不比其他区域占优势，声子粘性阻尼仍然会产生显著的热阻。
When phonon transport is in the hydrodynamic regime, the thermal conductivity exhibits peculiar dependences on temperatures ($T$) and sample widths ($W$). These features were used in the past to experimentally confirm the hydrodynamic phonon transport in three-dimensional bulk materials. Suspended graphene was recently predicted to exhibit strong hydrodynamic features in thermal transport at much higher temperature than the three-dimensional bulk materials, but its experimental confirmation requires quantitative guidance by theory and simulation. Here we quantitatively predict those peculiar dependences using the Monte Carlo solution of the Peierls-Boltzmann equation with an ab initio full three-phonon scattering matrix. Thermal conductivity is found to increase as ${T}^{\ensuremath{\alpha}}$ where $\ensuremath{\alpha}$ ranges from 1.89 to 2.49 depending on a sample width at low temperatures, much larger than 1.68 of the ballistic case. The thermal conductivity has a width dependence of ${W}^{1.17}$ at 100 K, clearly distinguished from the sublinear dependence of the ballistic-diffusive regime. These peculiar features are explained with a phonon viscous damping effect of the hydrodynamic regime. We derive an expression for the phonon hydrodynamic viscosity from the Peierls-Boltzmann equation, and discuss the fact that the phonon viscous damping explains well those peculiar dependences of thermal conductivity at 100 K. The phonon viscous damping still causes significant thermal resistance when a temperature is 300 K and a sample width is around 1 \textmu{}m, even though the hydrodynamic regime is not dominant over other regimes at this condition.