Large power dissipation of hot Dirac fermions in twisted bilayer graphene

TL;DR

This paper theoretically investigates hot electron power loss in twisted bilayer graphene, revealing significant enhancement near the magic angle due to suppressed Fermi velocity, with detailed temperature and density dependence.

Contribution

It provides a comprehensive analysis of electron-phonon interactions and power loss in tBLG, highlighting the tunability of power dissipation via twist angle and deriving a simple relation in the Bloch-Grüneisen regime.

Findings

Power loss is 250-450 times higher near the magic angle compared to monolayer graphene.

Power loss scales as T_e^4 in the Bloch-Grüneisen regime and as T_e^2 at higher temperatures.

The derived relation between energy relaxation and phonon-limited resistivity agrees with previous experimental data.

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 ${v_F}^*$ 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)).