Title Handle with care: Gapping fragile topological bands by interactions
Abstract Twisted bilayer graphene (TBG) has emerged as a new, fascinating platform to study the interplay of band topology and electron-electron interactions. In particular, the narrow bands of TBG are characterized by a subtle form of symmetry-protected structure known as fragile topology. Without electron-electron interactions, this topological structure enforces a band touching between the two bands, that cannot be lifted without breaking the protecting space-time symmetry. In contrast, we show that when the fragile bands are half filled, interactions can open a gap in the many-body spectrum without breaking any symmetry or mixing degrees of freedom from remote bands. Furthermore, the resulting ground state is not topologically ordered. Thus, a fragile topological band structure does not present a fundamental obstruction to forming a “featureless insulator” ground state. We will then turn to discuss sign problem free quantum Monte Carlo simulations of a realistic model of TBG at charge neutrality, showing signatures of a transition from a Kramers Inter-Valley Coherent (KIVC) state to a semi-metal.