Dynamic band structure and capacitance effects in scanning tunneling spectroscopy of bilayer graphene

We develop a fully self-consistent model to describe scanning tunneling spectroscopy (STS) measurements of Bernal-stacked bilayer graphene (BLG), and we compare the results of our model with experimental measurements. Our results show that the STS tip acts as a top gate that changes the BLG band structure and Fermi level, while simultaneously probing the voltage-dependent tunneling density of states (TDOS). These effects lead to differences between the TDOS and the local density of states; in particular, we show that the bandgap of the BLG appears larger than expected in STS measurements, that an additional feature appears in the TDOS that is an artifact of the STS measurement, and that asymmetric charge distribution effects between the individual graphene layers are observable via STS.