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

The in-plane phonon-drag thermopowerS^g, diffusion thermopowerS^dand the power factor PF are theoretically investigated in a twisted bilayer graphene (tBLG) as a function of twist angleθ, temperatureTand electron densityn_sin the region of lowT(1-20 K). Asθapproaches magic angleθ_m, theS^gandS^dare found to be strongly enhanced, which is manifestation of great suppression of effective Fermi velocityv_F^*of electrons in moiré flat band nearθ_m. This enhancement decreases with increasingθandT. In the Bloch-Grüneisen (BG) regime, it is found thatS^g∼v_F^*-2,T³andn_s^-1/2. AsTincreases, the exponentδinS^g∼T, changes from 3 to nearly zero and a maximumS^gvalue of ∼10 mV K^-1at ∼20 K is estimated.S^gis found to be larger (smaller) for smallern_sin low (high) temperature region. On the other hand,S^d, taken to be governed by Mott formula withS^d∼v_F^*-1,Tandn_s^-1/2andS^d≪S^gforT> ∼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 bothS^gandS^dand PF in addition toTandn_s. Our results are qualitatively compared with the measured out-of-plane thermopower in tBLG.