Large power dissipation of hot Dirac fermions in twisted bilayer graphene

Abstract

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 ${v_F}^{\ast }$ of electrons in moiré 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-Grüneisen (BG) regime, $P$ $\sim$ ${T_e}^4$, ${n_s}^{-1/2}$ and ${v_F}^{\ast -2}$. 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. $Fe(T)=(n_s{e}^2{v_s}^2/2){\rho }_p$, 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)).