Wavefunction symmetry in graphene at the nanometre scale

vendredi 30 avril 2010

Graphene is an unconventional two dimensional system with fascinating electronic properties. These properties - for example the half integer Quantum Hall Eff ect - come from the honeycomb crystal structure, which imposes special symmetry relations on the electronic wavefunctions, corresponding to the so-called “electronic chirality”. A priori, this chirality is specific to the ideal graphene plane, but was found to be preserved for graphene on a SiO2 substrate, as shown by magnetotransport measurements. We have found that the property of electronic chirality is also preserved in a single plane of graphene grown epitaxially on a silicon carbide (0001) substrate.

We have studied a SiC (0001) sample that was graphitized at the Néel Institute. It shows alternating terraces of monolayer and bilayer graphene. The two types of layer are weakly doped with electrons and have almost identical Fermi surfaces consisting of small circular pockets of radius qF ≈ 0.6 nm-1, centred on the corners of the Brillouin zone. To probe the electronic chirality we measured the local density of states of the surface using a low temperature (4.2 K) Scanning Tunneling Microscope at Max Planck Institute, Stuttgart. Native surface disorder elastically scatters the electrons of the graphene layer, creating quantum interferences. We obtained 4.2 K STM images at low bias voltage (i.e. at the Fermi level) on monolayer and bilayer terraces of graphene (Figs 1a and 1b). Comparing these images, we observe that certain quantum interferences are not detected for the monolayer case. Specifically, these are the “2qF” interferences (i.e. of wavelength π/qF ≈ 5.2 nm), associated with intravalley backscattering processes (coupling between electron states with wavevectors qF and –qF). The absence of such processes in the monolayer is seen more markedly in the Fourier Transforms (Figs 1c and 1d). A circle of radius 2qF ≈ 1.2 nm-1 is present at the centre of the FT for the bilayer (d) but absent for the monolayer (c). The absence of this circle for the monolayer is direct consequence of the electronic chirality. This result was predicted theoretically but never demonstrated experimentally until now. It shows clearly that the characteristic symmetry of a graphene monolayer inhibits formation of quantum interferences at 2qF. This work was done in collaboration with Klaus Kern’s group at MPI Stuttgart and with Christina Bena of the Laboratoire de Physique des Solides, Orsay.
Fig. 1 : STM images at very low bias voltage (a few mV) of (a) a monolayer and (b) a bilayer of graphene on SiC(0001). Such images are maps of the local electronic density of states at the Fermi level. Quantum interferences of wavelength π/qF (5.2 nm), generated by disorder, are observed on the graphene bilayer but never on the graphene monolayer. Figs (c) and (d) show the central regions of the 2D Fourier transforms of STM images (a) and (b) respectively. A ring of radius 2qF ≈ 1.2 nm-1 associated with the λ= 5.2 nm quantum interferences is present for the bilayer (d) but absent for the monolayer (c). These results show the absence of certain elastic scattering processes for low energy electrons, due to the symmetry of the electronic wavefunctions.

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