Large power dissipation of hot Dirac fermions in twisted bilayer graphene
We have carried out a theoretical investigation of hot electron power loss $P$, involving electron-acoustic phonon interaction, as a function of twist angle $\theta$, electron temperature $T_e$ and electron density $n_s$ in twisted bilayer graphene (tBLG). It is found that as $\theta$ decreases closer to magic angle $\theta_m$, $P$ enhances strongly and $\theta$ acts as an important tunable parameter, apart from $T_e$ and $n_s$. In the range of $T_e$ =1-50 K, this enhancement is $\sim$ 250-450 times the $P$ in monolayer graphene (MLG), which is manifestation of the great suppression of Fermi velocity ${v_F}^*$ of electrons in moir\'e flat band. As $\theta$ increases away from $\theta_m$, the impact of $\theta$ on $P$ decreases, tending to that of MLG at $\theta$ $\sim$ 3$^{\circ}$. In the Bloch-Gr\"uneisen (BG) regime, $P$ $\sim$ ${T_e}^4$, ${n_s}^{-1/2}$ and ${v_F}^{*-2}$. In the higher temperature region ($\sim$10- 50 K), $P$ $\sim$ ${T_e}^{\delta}$, with $\delta \sim$ 2.0, and the behavior is still super linear in $T_e$, unlike the phonon limited linear-in- $T$ ( lattice temperature) resistivity $\rho_p$. $P$ is weakly, decreasing (increasing) with increasing $n_s$ at lower (higher) $T_e$, as found in MLG. The energy relaxation time $\tau_e$ is also discussed as a function of $\theta$ and $T_e$. Expressing the power loss $P = F_e(T_e)- F_e(T)$, in the BG regime, we have obtained a simple and useful relation $F_e(T) \mu_p (T) = (e{v_s}^2$/2) i.e. $Fe(T) = (n_se^2 {v_s}^2/2)\rho_p$, where $\mu_p$ is the acoustic phonon limited mobility and $v_s$ is the acoustic phonon velocity. The $\rho_p$ estimated from this relation using our calculated $F_e(T)$ is nearly agreeing with the $\rho_p$ of Wu et al (Phys. Rev. B 99, 165112 (2019)).