Measuring In-Plane Electrostatic Potentials In 2D Systems and Correlating them with Electronic Structure

Accurately mapping the local electrostatic potential of 2D materials is critical in understanding how the electronic structure changes due to a perturbing potential. In-plane potentials produced by superlattices and defects are of particular importance given the effects they may have on transport properties and on the formation of localized states. However, characterizing the electrostatic potential with local probes (including STM and AFM) is challenging for 2D materials as these measurements are typically invasive, locally doping the material as they probe it. Kelvin Probe Force Microscopy (KPFM) does not induce local perturbations but suffers from inaccuracies due to the contributions of long-range electrostatic fields. We present a calibration scheme for KPFM that allows for the potential of 2D materials to be obtained accurately and with nanometer resolution. This new methodology is used to reconstruct the potential profile of electrostatically defined quantum dots in graphene/hexagonal boron nitride heterostructures. Experimentally extracted energy level spacings measured by scanning tunneling spectroscopy compare well to reconstructed KPFM data. This approach allows for the response of quasiparticles as a function of carrier concentration to be determined in a self-consistent way.