Interplay of moiré and Landau level physics in twisted double bilayer graphene

After superconductivity was first observed in magic-angle twisted bilayer graphene, a new field of moiré materials quickly formed. Moiré materials are weakly coupled 2D crystals where a new periodicity is created due to a small lattice parameter or angle mismatch. Moiré systems can host a variety of quantum phases due to the flatness of the electronic bands and enhanced electron-electron interaction. Small-angle twisted double bilayer graphene (TDBG) made up of two Bernal-stacked bilayers is tunable by electric field which can drive the system into a correlated phase for a continuous range of twist angles. Here, we use a multi-mode instrument combining force microscopy, tunneling microscopy, and electrostatic gating to study TDBG at 10 mK under magnetic field up to 15 T. We demonstrate the interplay between the band physics, electron-electron correlations, and field-induced Landau levels in TDBG with atomic resolution. We use the experimental data and theoretical calculations to further unravel the complexity of quantum phases in this tunable moiré system.