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

The 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 $n_s$. As $\theta$ approaches magic angle $\theta_m$, the $S^g$ and $S^d$ are found to be highly enhanced, which is manifestation of great suppression of Fermi velocity ${\nu_F}^*$ of electrons in moire flat band near $\theta_m$. In the Bloch- Gruneisen (BG) regime, it is found that $S^g \sim {\nu_F}^{* -2}$, $T^3$ and ${n_s}^{-1/2}$. The $T^3$ and ${n_s}^{-1/2}$ dependencies are, respectively, signatures of 2D phonons and the Dirac fermions. An enhancement of $S^g$ up to $\sim$ 500 times that of monolayer graphene (MLG) is predicted at $\sim$ 1 K. This enhancement decreases with increasing $\theta$ and $T$. As $T$ increases, the power $\delta$ in $S^g \sim T^\delta$, changes from 3 to nearly zero and a maximum $S^g$ value of the order of $\sim$ 10 mV/K at $\sim$ 20 K is estimated. Simple relations of 'Kohn anomaly temperature' $T_{KA}$ with $\theta$ and $n_s$ are obtained. $S^g$ 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 is much greater than that in MLG. $S^g$ dominates $S^d$ very significantly for $T > \sim$ 2 K. In tBLG, $\theta$ acts as a strong tuning parameter of both $S^g$ and $S^d$, in addition to $T$ and $n_s$. Moreover, in the BG regime Herring's law is found to be satisfied in tBLG. The power factor $PF$ is also found to be strongly $\theta$ dependent and is very much larger than that in MLG. $PF$ as a function of $T$ is found to exhibit a broad maximum, which is, for example, $\sim$75 W/m-K$^2$ for $\theta = 1.2^\circ$. Consequently, possibility of a giant figure of merit is discussed.