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 θ, electron temperature T_e and electron density n_s in twisted bilayer graphene (tBLG). It is found that as θ decreases closer to magic angle θ_m, P enhances strongly and θ 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 ~ 250-450 times the P in monolayer graphene (MLG), which is manifestation of the great suppression of Fermi velocity v_F^* of electrons in moire flat band. As θ increases away from θ_m, the impact of θ on P decreases, tending to that of MLG at θ ~ 3^o. In the Bloch- Gruneisen (BG) regime, P ~ T_e^ 4, n_s^ - ½ and v_F^*^ -2. In the higher temperature region (~10- 50 K), P ~ T_e^ δ, with δ ~2.0, and the behavior is still super linear in T_e, unlike the phonon limited linear-in- T ( lattice temperature) resistivity ρ_p. P is weakly, decreasing (increasing) with increasing n_s at lower (higher) T_e, as found in MLG. The energy relaxation time τ_e is also discussed as a function of θ 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) μ_p (T) = (ev_s^2/2) i.e. F_e (T) = (n_s e^2 v_s^2/2) ρ_p , where μ_p is the acoustic phonon limited mobility and v_s is the acoustic phonon velocity. The ρ_p estimated from this relation using our calculated F_e (T) nearly agreeing with the ρ_p of Wu et al (Phys. Rev. B 99, 165112 (2019)).