Kevin D. Kubista

Observing the quantization of zero mass carriers in graphene.

Resolving Landau Levels in Graphene The charge carriers in a two-dimensional conductor, when placed in a magnetic field, can develop an additional set of quantized energy levels. These Landau levels correspond to the carriers now moving in cyclotron orbits. In graphene, which consists of single-atom-thick sheets of graphite, an unusual set of Landau levels with nonequal energy spacing can develop in graphene layers that have undergone symmetry breaking caused by rotation between adjacent layers. Miller et al. (p. 924) used scanning tunneling microscopy at cryogenic temperatures to map out Landau levels in graphene grown on silicon carbide with high energy and momentum resolution, including the characteristic level in graphene that can occur at zero energy. Scanning tunneling microscopy on graphene reveals non-equally spaced Landau energy levels induced by a magnetic field. 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.