Twisted bilayer graphene under spin pumping reveals its flat bands

The salient property of the electronic band structure of twisted bilayer graphene (TBG), at the so-called magic angle (MA), is the emergence of flat bands around the charge neutrality point. These bands are associated with the observed superconducting phases and the correlated insulating states near the MA. Scanning tunneling microscopy (STM) and spectroscopy (STS) combined with angle resolved photoemission spectroscopy (ARPES) are usually used to visualize the electronic density of states and the flatness of the band structure of the TGB at the MA. Here, we theoretically propose that spin pumping (SP) can provide direct evidence of the flat bands of TBG. We first derive the continuum model of TBG with spin orbit coupling (SOC) induced by proximity effect by a monolayer of a transition metal dichalcogenide (TMD) aligned with one of the graphene layers of TBG. We then consider a junction between this heterostructure and a ferromagnetic insulator (FI). We show that the Gilbert damping, characterizing the SP effect of such a junction, drops at the MA, which provides evidence of the emergence of the flat band and a possible accurate measurement of the MA.