Electrostatic Modeling of Bilayer Graphene Band Structure for Scanning Tunneling Spectroscopy

Bilayer graphene (BLG) is known to have a dynamic electronic structure including a continuously tunable bandgap, and correlated electron behavior under a variety of conditions. To better understand these phenomena, it is important to develop local probes that can directly determine how these effects manifest in the presence of defects and impurities. In many semiconducting or metallic systems, scanning tunneling spectroscopy (STS) can serve as such a local probe. However, STS necessarily applies a local electric field to the system it measures. For BLG, this field can alter the local band structure by breaking the symmetry of the two layers and simultaneously doping the surface. This dynamic band structure modification makes STS measurements of BLG difficult to interpret and prevents straightforward extraction of the material parameters. In this talk, we show how these effects can be modeled and understood by computing the expected voltage-dependent tunneling spectrum of a BLG sheet between two gate electrodes. We compare this model to STS data taken from BLG/SiO₂ and BLG/h-BN systems under UHV conditions at a temperature of 4 K and show how to extract the BLG bandgap from STS measurements performed at different back-gate voltages.