Understanding the physical mechanism of heat dissipation is a matter of increasing concern from the perspective of waste heat management in nanostructure-based devices. The impurity-driven electron–phonon scattering is a significant channel for energy relaxation in graphene and its bilayer. The recently developed Keldysh formalism for single-layer graphene (SLG) is extended to investigate the transport phenomena due to phonon interaction via the deformation potential in disordered bilayer graphene (BLG) at low temperatures within the impure limit, $ql\ll 1$. It is observed that in the BLG system also, the temperature dependence of the relaxation rate and the cooling power are affected by the occurrence of disorder and screening, with the temperature exponent of pure BLG $T^4$ modified to $T^3$ in impure BLG. A comparison with the temperature and mean free path exponents of SLG reveals that the exponents in BLG turn out to be the same, but they both differ from the conventional 2DEG. However, the magnitude of the scattering rate and cooling power is more pronounced in BLG in a low-temperature regime. As the magnitude of the relaxation rate and the cooling rate varies with impurity, the impurity-assisted electron–phonon scattering has rich implications on hot carrier transport in BLG devices.

中文翻译：

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低温下不纯双层石墨烯的能量弛豫和冷却

从基于纳米结构的设备中废热管理的角度来看，了解散热的物理机制是一个越来越受到关注的问题。杂质驱动的电子-声子散射是石墨烯及其双层中能量弛豫的重要通道。最近开发的用于单层石墨烯 (SLG) 的 Keldysh 形式主义被扩展到在不纯极限内的低温下通过无序双层石墨烯 (BLG) 中的变形势研究声子相互作用引起的传输现象，$q升\ll \mathrm{1个}$. 据观察，在 BLG 系统中，弛豫率和冷却功率的温度依赖性也受到无序和筛选的影响，纯 BLG 的温度指数${吨}^{\mathrm{4个}}$修改为${吨}^{\mathrm{3个}}$在不纯的BLG中。与 SLG 的温度和平均自由程指数的比较表明，BLG 中的指数是相同的，但它们都不同于传统的 2DEG。然而，在低温状态下，BLG 的散射率和冷却功率的大小更为明显。由于弛豫速率和冷却速率的大小随杂质而变化，杂质辅助的电子-声子散射对 BLG 器件中的热载流子传输具有丰富的影响。