in Fig. \[figure2\](a), corresponding to an electric line current density $j_1 = (-e)n_1v_1 = 486$A/m, there is a small positive peak in $f(\omega)$. That means that part of the high-frequency modes can spontaneously emit external thermal radiation from bottom layer to top layer due to the drift velocity. Remarkably, with a higher drift velocity (black solid line), the height of the peak in the high-frequency region grows higher, and there is more heat transferred from bottom layer to the top layer. Qualitatively, the heat flux generated by a temperature difference can be suppressed or even reversed by the high drift velocity.

The above mentioned drift-induced effects in suspended layers can be further understood in Fig. \[figure2\](b): the distribution over the wavevector in the $\hat x$ (the driven) direction. In no drift case, $g(k_x)$ is negative and has the space inversion symmetry in $x$ direction. However, when we drift the electrons in $x$ direction, the $k_x$ symmetry is broken and the drift induced mode appears. In the $k_x < \omega/{v_1}$ and $\omega>0$ region, it is negative and the system locates at the normal Landau damping region. However, when $k_x > \omega/{v_1}$ and $\omega>0$, the drift induced modes carry positive value due 