Fragile Insulator and Electronic Nematicity in a Graphene Moiré System**

Graphene heterostructures, which can host narrow moiré electron bands that amplify the correlation effect, represent a new setting to study the organizing principles of strongly correlated systems. In such correlated moiré systems, an insulating state is a prominent feature of the phase diagram which may hold the key to understanding the basic physics. Here [1] we advance the notion of a fragile insulator, a correlation-driven insulating state that is on the verge of a delocalization transition into a bad metal. Using a realistic multiorbital Hubbard model as a prototype for narrow band moiré systems, we realize such a fragile insulator and demonstrate a nematic order in this state as well as in the nearby bad metal regime. Our results provide a natural understanding of the observed electronic anisotropy [2] as well as the behavior when the insulator is tuned into a bad metal. We propose the fragile insulator and the accompanying bad metal as competing states at integer fillings that analogously anchor the overall phase diagram of the correlated moiré systems and beyond.

[1] L. Chen, H. Hu, Q. Si, arXiv:2007.06086
[2] e.g. A. Kerelsky et al, Nature 572, 95 (2019)
[3] e.g. H.S. Arora et al, Nature 583, 379 (2020).