论文标题
扭曲的双层石墨烯中热dirac费米的大量耗散
Large power dissipation of hot Dirac fermions in twisted bilayer graphene
论文作者
论文摘要
我们已经对热电子功率损失$ p $进行了理论研究，涉及电子声音声子相互作用，这是扭曲角$θ$，电子温度$ t_e $和电子密度$ n_s $ n_s $ n_s $ in Twisted Bileyer石墨烯（TBLG）的函数。据发现，随着$θ$的降低，更接近魔术角$θ_m$，$ p $强烈增强，$θ$充当重要的可调参数，除了$ t_e $和$ n_s $。在$ t_e $ = 1-50 K的范围内，这种增强是$ \ sim $ 250-450倍单层石墨烯（MLG）的$ 250-450倍，这表明了Moiré平面乐队中电子速度$ {v_f}^*$的Fermi Velocity $ {v_f}^*$。随着$θ$从$θ_m$增加，$θ$对$ p $的影响会减少，趋向于MLG $θ$ $ \ sim $ 3 $ 3 $^{\ circ} $。在Bloch-Grüneisen（BG）制度中，$ P $ \ sim $ $ {t_e}^4 $，$ {n_s}^{ - 1/2} $和$ {v_f}^{* - 2} $。在较高的温度区域（$ \ sim $ 10-50 K），$ p $ \ sim $ $ {t_e}^δ$，带有$δ\ sim $ 2.0，并且该行为仍然是$ t_e $的超级线性，与Phonon Limited LimitareArimear-limitarearearimear-limitarear-$ t $ t $（lattice）电阻性温度$ρ_p$ρ_p$。 $ p $弱，随着MLG中发现的$ n_s $的增加（较高）$ t_e $的$ n_s $减少（增加）。还讨论了$θ$和$ t_e $的函数的能量放松时间$τ_e$。表示电源损失$ p = f_e（t_e） - f_e（t）$，在BG制度中，我们获得了简单而有用的关系$ f_e（t）μ_p（t）=（e {e {v_s}^2 $/2）声子有限的移动性和$ v_s $是声音声子速度。使用我们计算出的$ f_e（t）$从此关系中估算的$ρ_p$几乎与Wu等人的$ρ_p$一致（Phys。Rev.B 99，165112（2019））。
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 $\sim$ 250-450 times the $P$ in monolayer graphene (MLG), which is manifestation of the great suppression of Fermi velocity ${v_F}^*$ of electrons in moiré flat band. As $θ$ increases away from $θ_m$, the impact of $θ$ on $P$ decreases, tending to that of MLG at $θ$ $\sim$ 3$^{\circ}$. In the Bloch-Grüneisen (BG) regime, $P$ $\sim$ ${T_e}^4$, ${n_s}^{-1/2}$ and ${v_F}^{*-2}$. In the higher temperature region ($\sim$10- 50 K), $P$ $\sim$ ${T_e}^δ$, with $δ\sim$ 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 $F_e(T) μ_p (T) = (e{v_s}^2$/2) i.e. $Fe(T) = (n_se^2 {v_s}^2/2)ρ_p$, 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 $F_e(T)$ is nearly agreeing with the $ρ_p$ of Wu et al (Phys. Rev. B 99, 165112 (2019)).
