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

The in-plane phonon-drag thermopowerSg, diffusion thermopowerSdand the power factor PF are theoretically investigated in a twisted bilayer graphene (tBLG) as a function of twist angleθ, temperatureTand electron densitynsin the region of lowT(1-20 K). Asθapproaches magic angleθm, theSgandSdare found to be strongly enhanced, which is manifestation of great suppression of effective Fermi velocityvF*of electrons in moiré flat band nearθm. This enhancement decreases with increasingθandT. In the Bloch-Grüneisen (BG) regime, it is found thatSg∼vF*-2,T3andns-1/2. AsTincreases, the exponentδinSg∼Tδ, changes from 3 to nearly zero and a maximumSgvalue of ∼10 mV K-1at ∼20 K is estimated.Sgis found to be larger (smaller) for smallernsin low (high) temperature region. On the other hand,Sd, taken to be governed by Mott formula withSd∼vF*-1,Tandns-1/2andSd≪SgforT> ∼2 K. The power factor PF is also shown to be stronglyθdependent and is very much enhanced. Consequently, possibility of a giant figure of merit is discussed. In tBLG,θacts as a strong tuning parameter of bothSgandSdand PF in addition toTandns. Our results are qualitatively compared with the measured out-of-plane thermopower in tBLG.