Giant thermopower and power factor in magic angle twisted bilayer graphene at low temperature

The in-plane phonon-drag thermopower $S^g$, diffusion thermopower $S^d$ and the power factor $PF$ are theoretically investigated in twisted bilayer graphene (tBLG) as a function of twist angle $\theta$, temperature $T$ and electron density $n_s$ in the region of low $T$ (1-20 K). As $\theta$ approaches magic angle $\theta_m$, the $S^g$ and $S^d$ are found to be strongly enhanced, which is manifestation of great suppression of Fermi velocity ${\nu_F}^*$ of electrons in moire flat band near $\theta_m$. This enhancement decreases with increasing $\theta$ and $T$. In the Bloch- Gruneisen (BG) regime, it is found that $S^g \sim {\nu_F}^{* -2}$, $T^3$ and ${n_s}^{-1/2}$. As $T$ increases, the exponent $\delta$ in $S^g \sim T^\delta$, changes from 3 to nearly zero and a maximum $S^g$ value of $\sim$ 10 mV/K at $\sim$ 20 K is estimated. $S^g$ is larger (smaller) for smaller $n_s$ in low (high) temperature region. On the other hand, $S^d$, taken to be governed by Mott formula, $\sim {\nu_F}^{* -1}$, $T$ and ${n_s}^{-1/2}$ and $S^d<<S^g$ for $T > \sim$ 2 K. The power factor $PF$ is also found to be strongly $\theta$ dependent and very much enhanced. Consequently, possibility of a giant figure of merit is discussed.In tBLG, $\theta$ acts as a strong tuning parameter of both $S^g$ and $S^d$ and $PF$ in addition to $T$ and $n_s$. Our results are qualitatively compared with the measured out-of-plane thermopower in tBLG.