Spectroscopic imaging of graphene in the quantum hall regime with the scanning tunneling microscope

In strong magnetic fields, the kinetic energy becomes suppressed and Dirac fermions in graphene form a highly interactive system that resides in quantized Landau levels. In this limit, a myriad of interaction-driven phenomena can emerge in the zeroth Landau level, including quantum Hall ferromagnetism, Wigner crystallization and skyrmionic excitations, some of which that have been studied in transport and capacitance measurements. With its capability to determine the electronic density of states in real space, the scanning tunneling microscope (STM) is a robust tool to shed light on the interactions in both occupied and unoccupied levels. Landau orbits have been previously imaged near point defects on the surface of Bismuth at high magnetic fields with the STM. We aim at extending such spectroscopic imaging techniques to graphene in the quantum Hall limit, by measuring its local density of states as we tune the carrier density with electrostatic gating. Our energy-resolved measurements detect signatures of quantum Hall ferromagnetism that arise from broken valley and spin symmetries. We seek to complement these measurements with spatially resolved studies that will unveil real-space features of these and other interacting electronic states that form in graphene in high fields.