Writable and tunable Landau level quantum dots in graphene devices

In graphene devices supported by hexagonal boron nitride (hBN), local charge pockets can be written by pulsing the bias voltage of a scanning tunneling microscope (STM) tip. In a strong magnetic field, discrete Landau levels (LLs) replace the continuous graphene density of states, and the charge pocket is characterized by a concentric series of compressible and incompressible rings, as successive LLs cross the Fermi energy. Here, Coulomb blockade peaks appear in the scanning tunneling dI/dV spectra, revealing the addition of single electrons to the confined Landau island, and encoding the capacitances between it and the tip and back-gate electrodes. When two highly-gapped LLs cross the Fermi energy, two series of peaks appear, experiencing avoided crossings within the dot. The observed avoidance pattern of these anti-crossings is unusual and defies conventional explanation. We present a new phenomenological electrostatic model, taking into account the self-contained geometry of this double-quantum dot system, and are able to reproduce the most striking features of the experimental data.