Graphene is a sheet of carbon atoms just one atom thick arranged in a honeycomb lattice. It is a semi-metal and does not contain a bandgap in its pristine state. Multilayer graphene is different from its single-layer counterpart in that we can induce a large bandgap in it using an applied electric field. This is not the case for single-layer graphene.

When layers of graphene are stacked on top of each other, they organize themselves in one of two main configurations – known as Bernal and rhombohedral. Bernal stacking occurs when the A-sublattice of one layer sits above the B-sublattice of the underlying layer. This “ABA-stacked” configuration has the lowest possible energy, so under normal circumstances, this is the structure that multilayer graphene likes to adopt.

However, other, higher-energy configurations, such as rhombohedral, can exist too. Here the sublattice of the top layer lies above the centre of the hexagon of the bottom layer. This configuration is denoted by ABC.

Multilayer graphene is unique

These two configurations have very different electronic properties and applying an electric field perpendicular to the graphene sheets breaks sublattice symmetries differently depending on how the layers in the material are stacked. This makes multilayer graphene unique in that its crystal structure – and hence its electronic properties – can be modified by applying an external voltage. Such phase transitions are usually induced by applying temperature or pressure, but being able to induce them with just an applied voltage should be a much simpler and faster option.

“When we apply an electric field to trilayer graphene, the energy of the rhombohedral stacked configuration is lowered because a bandgap opens in it,” explains team leader Brian LeRoy of the University of Arizona, Tucson. “However, no such bandgap opens in the Bernal stacked region.”

The energy of the rhombohedral stacking thus lowers relative to the energy of the Bernal stacking, he says. This causes the strain soliton (the domain wall between the two stacking configurations) to move so that the area taken up by rhombohedral stacked region increases. As the domain wall moves, elastic energy costs (like those that occur when an elastic band is stretched) come into play. These cause the domain wall to move until the elastic energy costs from stretching equal the energy gained by opening a bandgap.

Semi-metal to semiconductor

Being able to control boundaries in graphene in this way could prove very useful, he adds. “In trilayer graphene we are able to induce a transition from semi-metal to semiconductor. Since the conductivity depends on the stacking order, we reckon that we can modulate the conductivity in the material by simply applying an electric field – much like what happens in an ordinary field-effect transistor made from any conventional semiconductor.”

However, there is a difference: in a device made of trilayer graphene, modulating current in this way would be possible thanks to the domain walls moving. Similar strain solitons exist in bilayer graphene, where they are expected to host topologically protected states that can change normally insulating samples into metallic ones. “Understanding and controlling these solitons in graphene is thus also crucial for fully understanding the electronic properties observed in multilayer graphene devices,” added LeRoy.

Unique objects

Solitons in graphene multilayers are very unique objects in themselves, says team member Pablo San-Jose, and being able to manipulate them opens up a whole new world of possibilities. Structural domain walls between two crystals are usually like cracks – defects where crystalline order is broken. However, solitons – which also have the particularity of being structural domain walls – are more like smooth and elastic boundaries, where local order does not suddenly break. They can stretch and snap back to their original shape, something that does not happen with more conventional structural domain walls, such as a crack in a crystal.

Solitons are electronic domain walls too. “Usually, such structures are either mechanical or electronic, but seldom both,” he explains. “A soliton in the trilayer graphene system is a rather unique beast because it is a smooth, elastic, structural boundary that carries with it a change in electronic properties. It could be likened to a sound wave in a metal that might not only be made of pressure ripples, but which also carried insulating stripes in the pressure troughs. This wave could efficiently carry a quantized electric current, for example.”

The team, which includes researchers from the Massachusetts Institute of Technology, Harvard University, the US Army Research Lab in Maryland, the National Institute for Materials Science in Tsukuba and the ICMM-CSIC in Madrid, says that it will now try to show that it is possible to move solitons in trilayer graphene with gate electrodes (like those used in traditional graphene devices). In this work, the researchers managed to move the solitons using a scanning tunnelling microscope tip. “Using gate electrodes instead would allow us to fabricate real-world devices that exploit the movement of solitons,” LeRoy told

The current work is detailed in Nature Materials doi:10.1038/nmat3965.