fixed drift velocity $v_1=9.0\times 10^5$m/s. As seen in Fig. \[figure3\], the heat current density is almost linearly decreasing as the temperature $T_2$ increases. When $T_2$ equals 331K, there is no heat current between the layers and the “off temperature” for RHT is reached.

Nonequilibrium Green’s function calculation
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The above calculation is based on FE for the infinite suspended double-layer graphene. To extend drift induced effect in the nanoscale system, we consider a small graphene nano-ribbon of 72 atoms in each layer (see Fig. 1), connected to two baths, in each layer. The chemical potential difference ($\mu_{1R}-\mu_{1L}$) between bath 1L and bath 1R produces the drift electrons in layer 1. In such a nanoscale system, the Coulomb interaction (virtual photon or scalar photon) will be the dominant mechanism for RHT.

The calculation is based on a tight-binding model with a nearest neighbor hopping parameter $t=2.8$eV and Coulomb interactions between the electrons [@zhang2018energy; @wang2018coulomb; @peng2017scalar]. The energy transfer out of layer 1 to layer 2 of a nanoscale double-layer graphene due to the Coulomb interaction can be calculated through the Meir-Wingreen formula [@lu2016; @lu-AIP-2015; @MeirWingreen] under a lowest order expansion of the Coulomb interaction (see Appendix \[app-e\] for a derivation): $$\begin{aligned}
