Equilibrium-state currents in Quantum Hall graphene quantum dots and pn junctions

Charge carriers in a quantum Hall state, when subjected to a spatially dependent electrostatic confining potential, arrange themselves in a characteristic pattern of alternating compressible and incompressible regions. By delineating the individual contribution of each Landau level (LL) to electric currents in these regions, we elucidate the microscopic origin of the currents flowing in thermodynamic equilibrium. We focus on the case of a graphene quantum dot and a pn junction geometry. We find, both theoretically and experimentally, non-zero currents flowing in both compressible and incompressible regions, which alternate in sign between neighboring regions. Whilst all occupied Landau levels contribute to the incompressible currents equally, as expected, the compressible currents receive a contribution only from the last occupied LL with the contribution proportional to its energy. This peculiar dependence of compressible currents on the LL energy is best exemplified by the 0^th LL, which due to graphene’s band structure, is expected to carry no current in the compressible region. This behavior is in agreement with experimental observations.