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.

Rotational misalignment of two stacked honeycomb lattices produces a moiré pattern that is observable in scanning tunneling microscopy as a small modulation of the apparent surface height. This is known from experiments on highly-oriented pyrolytic graphite. Here, we observe the combined effect of three-layer moiré patterns in multilayer graphene grown on SiC (0001). Small-angle rotations between the first and third layer are shown to produce a "double-moiré" pattern, resulting from the interference of moiré patterns from the first three layers. These patterns are strongly affected by relative lattice strain between the layers. We model the moiré patterns as a beat-period of the mismatched reciprocal lattice vectors and show how these patterns can be used to determine the relative strain between lattices, in analogy to strain measurement by optical moiré interferometry.

No abstract