Flat Bands and Electronic Correlations in Graphene with and without a Twist

Van der Waals bilayers with an interlayer twist are an excellent platform towards achieving gate-tunable electronic flat bands. A number of emergent phases driven by electron-electron interactions have been observed when tuning the Fermi level through these flat bands. I will present atomically-resolved doping-dependent scanning tunneling spectroscopy studies of two graphene-based systems with emergent correlated phases due to flat bands – magic angle twisted bilayer graphene (tBG) and ABCA graphene, a simple system with a flat band without a moire potential. Our spectroscopy shows that magic angle tBG features two flat bands separated by 40-55 meV. Correlated states emerge when tuning the Fermi level through an individual flat band with minimized bandwidth suggesting the importance of maximized electronic correlations at the magic angle. We measure the correlated insulator gap at half filling and show evidence of nematicity near half-filling in magic angle tBG. I will then show that twisted double bilayer graphene (tDBG) features a fundamentally different moire pattern than tBG, hosting rhombohedral (ABCA) stacking sites. At tiny tDBG angles this creates micron-scale ABCA graphene domains, a robust platform to stabilize the ABCA graphene. Our spectroscopy reveals that ABCA graphene hosts a flat band of 3-4 meV half-width (versus 9-10 meV in magic angle tBG). The unprecedentedly narrow electronic band enhances electronic correlations inducing a correlated gap at charge neutrality making ABCA graphene a model graphene-based correlated system with no moire superlattice potential or integer fillings. Finally, I will show that ABCA graphene hosts topological surface helical edge states which can be turned on and off with gate voltage.