Researchers at the University of Manchester found a mechanism that could explain unusual electronic and optical behaviour in graphene, and another route to give it a bandgap.
The work involved spreading mono-layer flakes of graphene on a thin (20nm) layer of boron nitride (BN).
Both materials have a hexagonal two-dimensional structure – there is increasing interest in the interaction of various 2-d materials, phosphorene and molybdenum di-sulphide are others. LINK
Some language is required here: when two layers of graphene are aligned with one another exactly, atoms from the layers attract each other and lock the alignment, and they are said to be ‘commensurate’.
Boron nitride’s lattice constant is 1.8% larger than graphene.
“There has been work done to see if graphene and boron nitride would become commensurate. Everyone had assumed they would stay incommensurate – there would be no way to click together,” project scientist Colin Woods told Electronics Weekly.
Monolayer graphene flakes were known to stick to boron nitride, by the same van der Waals’ forces that hold two aligned graphene layers together, but the lattice mis-match was thought to be enough that they would always remain incommensurate.
Woods’ examined graphene flakes flat on the boron nitride in various rotational orientations, using atomic force microscopy, scanning tunnelling microscopy and Raman spectroscopy.
He discovered that when the lattices were clearly misaligned, they were incommensurate.
However when the axes of the hexagons were aligned exactly, the graphene locally stretched to match the boron nitride and became commensurate, and also developed a bandgap.
“The badgap is small. We don’t know if it exists in un-aligned state, where there is a very small bandgap or no bandgap,” said Woods, “but the commensurate/incommensurate transition definitely opens a bandgap. This is a new mechanism for creating a bandgap in graphene.”
Strain build-up cannot continue forever across the graphene, and periodically carbon atoms within the graphene bunch together in a strain-relieving dislocation. Viewed from above, the dislocations form a sharply-defined hexagonal grid (see image), where the hexagons within are perfectly-aligned graphene/boron nitride.
Maximum size for the hexagonal super-lattice is 14nm, compared with the 0.25nm graphene lattice constant.
Sadly, “the area of bandgap not enough for electronic logic”, he said, but this is new fundamental understanding in the behaviour of graphene, which could explain certain electronic and optical behaviours.
Where flakes are not perfectly aligned, the super-lattice quickly de-focusses to the incommensurate state with increasing rotation.
“It was extremely exciting to see that the properties of graphene can change so dramatically by simply twisting the two crystals only a fraction of a degree,” said Woods.
Having observed the effect, the team is looking to get a theoretical handle on the two-dimensional forces and stretches.
“Generally, the previous model used to describe the sort of interaction which has been observed in our experiments describes only the one-dimensional case, but even there it produces very non-trivial solutions. We hope that our system will push the mathematical development of the model to two-dimensions, where even more exciting mathematics is to be expected,” said Woods.
The work is described in a Nature Physics paper: ‘Commensurate–incommensurate transition in graphene on hexagonal boron nitride‘, and was led by graphene co-discoverer Sir Kostya Novoselov.
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