Physical Science Laboratory, *Materials Science Laboratory
Graphene, a two-dimensional honeycomb lattice of carbon
atoms, is known to have the relativistic energy band called Dirac cone.
Accordingly, the density of states in graphene depends on the Fermi energy,
whereas those in the conventional two-dimensional systems (2DESs) do not
rely on the Fermi level. This then indicates that the quantum capacitance,
which is defined to be proportional to the density of states, is quite
different for graphene and conventional 2DESs. In this study, using a top-gated
device fabricated from epitaxial graphene on SiC, we demonstrate that the
interplay between quantum capacitances of graphene and interface states
in the device changes the appearance of the fan diagram in epitaxial graphene,
which consequently represents the relativistic graphene Landau level. This
indicates that our transport measurements serve as a kind of energy spectroscopy
[1], and thus enables us to deduce the energy broadening of the Landau
levels in graphene [1].
The sample is a top-gated Hall-bar device, fabricated
from graphene on SiC. At low temperature and low fields, we observe the
quantum Hall (QH) state, where the Hall resistance becomes quantized at
h/{(4N+2)e2} and longitudinal resistance Rxx becomes zero at the Landau level filling factor ν = 4N + 2 (N: integer). The observed QH states are illustrated in a fan diagram
[Fig. 1(a)], where Rxx is mapped as a function of gate voltage Vg and magnetic field B. At ν = 2, a wide region with zero Rxx, indicating the ν = 2 QH state, appears and clear Rxx peaks are observed at ν = 0, 4, and 8. In contrast to the usual case,
in which Rxx peaks appear as an equidistant linear fan diagram in the Vg - B plane, in our epitaxial graphene device, the trajectories of the Rxx peaks are curved and unequally spaced. This can be explained by our model
[Fig. 1(c)], in which not only graphene but also the interface states nearby
graphene, such as dangling-bond states at SiC or those in the gate insulator,
serve as charge reservoirs when Vg is swept. As a result, the quantum capacitance of graphene and that of the interface states associated with the density of states play a significant role in the Vg dependence of the graphene carrier density. Analyzing the Vg dependence with this model allows us to deduce the interface state densities. Furthermore, when the interface state density is much larger than the graphene carrier density, the Fermi level in graphene becomes proportional to Vg. Consequently, Rxx peaks in the Vg - B plane represents the graphene Landau-level structure. Filling factor calculated
vs. Vg and B in Fig. 1(b) nicely reproduces the experimentally observed peak positions
of Rxx in Fig. 1(a).
[1] K. Takase et al., Phys. Rev B 86 (2012) 165435.
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