Fig. 3: Expected thermopower from the local moments and comparison with the experiment.
From: Thermopower probes of emergent local moments in magic-angle twisted bilayer graphene
a, Theoretically calculated thermopower in a strongly correlated regime using the atomic limit38,39,40 at different temperatures with U = 20 meV. The additional crossings, νcross around ±1.3, are indicated by vertical black arrows. b, The extracted νcross from Fig. 3a as a function of temperature is shown in a solid violet line. For contrast, νcross from non-interacting band electrons using semi-classical theory (for W ≈ 10 meV) is shown by a black line. c, Evolution of the crossing points (within 0 < ∣ν∣ < 4) with T for MATBLG (red circles) and near MATBLG (blue triangles). Note that, for the strongly correlated MATBLG with flatter bands, νcross remains almost constant, resembling the thermopower from the local moments in Fig. 3b. However, for the near MATBLG device with bands that are not as flat, there is greater variation in νcross. d, TDBLG with weaker correlation exhibits notable νcross variations with T: in the valence band, νcross shifts to lower ν and disappears by 20 K, while in the conduction band, νcross approaches ν = 0 around 35 K and qualitatively resembles the solid black line that is non-interacting band electrons in b. e, The temperature evolution of the crossing points of thermopower calculated using DMFT for U, W = 6, 10 meV (blue), U, W = 12, 20 meV (black) and U, W = 20, 20 meV (red) contrasted with crossing points evolution for HF thermopower at U, W = 12, 20 meV (green). Even DMFT with U ≲ W (blue plot) has only weak temperature dependence over a broad range, unlike the HF thermopower, where the crossing point varies significantly with temperature and merges to a single crossing point at much lower temperature.
