Stacks of two-dimensional (2D) van der Waals monolayer materials represent a new platform for the realization of correlated and topological electronic states. By twisting 2D atomic crystals relative to each other, the interference of two lattices forms a moiré superlattice structure with an electronic bandwidth that is comparable in energy to that of Coulomb interactions. In this “strongly correlated regime,” many-body electronic phases arise that are highly tunable using electrostatic gating techniques. The prototypical example of this newly established motif is magic-angle twisted bilayer graphene (MATBG), in which experiments have discovered a rich spectrum of many-body electronic states, including correlated insulators, superconductors, and topological phases. The band structure of MATBG is characterized by two nearly flat bands close to charge neutrality, which are much narrower in energy than estimates of the Coulomb interaction for electrons separated by the moiré superlattice spacing. Much remains to be understood about the properties of this system, including the symmetry-broken nature of correlated insulating states, the pairing mechanism of superconductivity, and the intense ground-state competition amongst a diverse set of topological phases.
Our group has developed gate-dependent scanning tunneling microscopy (STM) and spectroscopy measurements that enable us to study the electronic properties of MATBG as a function of carrier concentration. When the flat bands of this system are partially full, our spectroscopic measurements show direct signatures of strong electronic correlations (Y. Xie, et al. Nature, 572, 2019). We have demonstrated that these signatures cannot be captured by a mean-field model of the interaction, and therefore require using a Hubbard-type model to understand the signatures. Further high-resolution measurements reveal a cascade of electronic transitions within this highly correlated state occurring as a function of carrier density, at each integer filling of the moiré flat bands — where insulating phases emerge at low temperatures. These transitions are a direct consequence of the confluence of Coulomb interactions and the spin/valley quantum degeneracy of this system, which split the degenerate flat bands into Hubbard sub-bands in an analogous manner to the well-established paradigm of quantum Hall ferromagnetism (D, Wong, et al. Nature, 582, 2020).
Most recently, we have developed a new approach for identifying many-body phases and measuring their characteristic topological invariants using the scanning tunneling microscope. With this new technique, we have uncovered a hierarchy of strongly correlated Chern insulating phases emanating from all integer fillings of the flat bands of MATBG. This work has provided a unique insight into the intrinsically topological electronic structure of MATBG and has recognized new mechanisms for creating correlated topological phases of matter in the rapidly expanding gamut of moiré flat-band systems (K. P. Nuckolls, et al. Nature, 588, 2020).
Currently, we are working to characterize the spectroscopic and spatial qualities of the insulating and superconducting states in MATBG using our millikelvin STM capabilities.