In graphene, the Dirac point is where the conduction and valence bands meet. The bands approach this point in a linear way, which means that the effective kinetic energies of the conduction electrons (and holes) are directly proportional to their momenta. This unusual relationship is normally only seen for photons, which are massless. The result is that the electrons in Dirac cones behave as though they are relativistic particles with no rest mass, travelling through the material at extremely high speeds – a property that could be exploited to make ultrafast transistors.

Now, Cinzia Casiraghi from the University of Manchester and colleagues at the Université Paris-6, have found a simple way to measure the energy of new Dirac points using Raman spectroscopy The Dirac points appear at an energy that is determined by the rotational angle (Θ) between graphene and boron nitride.

The researchers fabricated their samples by transferring graphene on top of a relatively thin boron nitride crystal. They then aligned the two material lattices with the help of an optical microscope so they could choose graphene and boron nitride crystallites with straight edges. Finally, they rotated the graphene sheets relative to the boron nitride so that the edges of the two materials were parallel.

As the graphene was rotated over the boron nitride, a Moiré pattern appears (see animated figure). This pattern – generated as the two overlapping crystals interfere – is also known as a superlattice. “The Moiré pattern is periodic and characterized by a specific wavelength,” explains Casiraghi, “which is determined by Θ. The Moiré pattern thus acts as a periodic potential.

“In a crystal, the effect of this potential associated with the nuclei in the material significantly alters the electronic energy dispersion, which leads to a bandgap opening in the sample. (Graphene does not have a bandgap to start with). However, since the electrons in graphene are massless – they are known as ‘Dirac electrons’ – the periodic potential produces locally gapped regions (or mini gaps) characterized by the new Dirac points.”

Thanks to Raman spectroscopy measurements, Casiraghi and colleagues were able to calculate the energies of these new Dirac points. The researchers did this by simply measuring the width of the 2D Raman peak (see figure), which is very sensitive to the misalignment between the graphene and hexagonal boron nitride lattices. This is the first time that Raman spectroscopy has been used to characterise a hybrid 2D structure in this way.

“To design novel optical and optoelectronic devices based on graphene and boron nitride superlattices, we need to be able to identify the energy of the Dirac points,” Casiragh told “Raman spectroscopy offers a simple and fast way to determine the wavelength of the periodic potential and the energy of the Dirac points in these superlattices.”

The team says that it is now busy investigating other types of graphene-based superlattice in which Dirac points could appear at higher energies. “Such points could be useful in optoelectronics too and should also produce strong effects on the Raman spectrum of graphene,” said Casiraghi.

The present work is detailed in Nano Lett. DOI: 10.1021/nl402679b

Further reading

Acoustic analogue to graphene announced (May 2012)
Physicists put a new twist on graphene (Mar 2011)
"Designer" graphene makes its debut (Mar 2012)