Observing the Quantization of Zero Mass Carriers in Graphene

Application of a magnetic field to conductors causes the charge carriers to circulate in cyclotron orbits with quantized energies called Landau levels (LLs). These are equally spaced in normal metals and two-dimensional electron gases. In graphene, however, the charge carrier velocity is independent of their energy (like massless photons). Consequently, the LL energies are not equally spaced and include a characteristic zero-energy state (the n = 0 LL). With the use of scanning tunneling spectroscopy of graphene grown on silicon carbide, we directly observed the discrete, non-equally–spaced energy-level spectrum of LLs, including the hallmark zero-energy state of graphene. We also detected characteristic magneto-oscillations in the tunneling conductance and mapped the electrostatic potential of graphene by measuring spatial variations in the energy of the n = 0 LL. The two-dimensional (2D) form of carbon(i.e., graphene) is of interest not onlybecause of its potential in nanoelectronics (1, 2), but also because it displays several in-triguing fundamental properties. One of these, the half-integer quantumHall effect (QHE) (3, 4), results from the symmetry of graphene’s honey-comb crystal structure, which can be viewed a