ARPES signatures of few-layer twistronic graphenes

Abstract: Diverse emergent correlated electron phenomena have been observed in twisted graphene layers due to electronic interactions with the moir\'e superlattice potential. Many electronic structure predictions have been reported exploring this new field, but with few momentum-resolved electronic structure measurements to test them. Here we use angle-resolved photoemission spectroscopy (ARPES) to study the twist-dependent ($1^\circ < \theta < 8^\circ$) electronic band structure of few-layer graphenes, including twisted bilayer, monolayer-on-bilayer, and double-bilayer graphene (tDBG). Direct comparison is made between experiment and theory, using a hybrid $\textbf{k}\cdot\textbf{p}$ model for interlayer coupling and implementing photon-energy-dependent phase shifts for photo-electrons from consecutive layers to simulate ARPES spectra. Quantitative agreement between experiment and theory is found across twist angles, stacking geometries, and back-gate voltages, validating the models and revealing displacement field induced gap openings in twisted graphenes. However, for tDBG at $\theta=1.5\pm0.2^\circ$, close to the predicted magic-angle of $\theta=1.3^\circ$, a flat band is found near the Fermi-level with measured bandwidth of $E_w = 31\pm5$ meV. Analysis of the gap between the flat band and the next valence band shows significant deviations between experiment ($\Delta_h=46\pm5$meV) and the theoretical model ($\Delta_h=5$meV), indicative of the importance of lattice relaxation in this regime.