When two pieces of fine mesh are placed one on top of the other and then rotated, new, more complicated patterns appear. As you keep on twisting, the patterns change like in a kaleidoscope (figure 1). These so-called Moiré patterns have been known for a long time and were recently observed in scanning tunnelling microscope (STM) images of stacked layers of graphene (figure 2).

However, these earlier experiments completely missed the fact that, besides forming pretty patterns, such twists also cause dramatic changes in graphene's electronic properties. Now, a team led by Eva Andrei of Rutgers University has shown that the twists induce sharp peaks in the electronic density of states (or Van Hove singularities) that can be seen as peaks in the tunnelling spectra (figure 3). "Remarkably, the energy of these peaks varies continuously with the twist angle so that their position can be tuned at will," said Andrei. "This opens up the prospect of 'twist-engineering' the electronic properties of graphene."

Correlated electron phases, such as superconductivity, magnetism or density waves, are often driven by electronic instabilities, she explains. Such instabilities can occur when the energy of conduction electrons in a material (the Fermi energy) is close to the Van Hove singularity. This is because interactions between electrons – however weak – become larger thanks to enhanced densities of states at the singularity.

But these instabilities are difficult to control or predict in most materials, which makes finding correlated electronic states difficult.

"Our work demonstrates a new way of engineering correlated electronic states by introducing a twist between graphene layers," Andrei told nanotechweb.org. "Indeed, we found that the electron density becomes strongly modulated when the Van Hove singularity is brought close to the Fermi energy – indicating that a correlated electron phase, called a charge density wave, has been formed."

The experiments also prove that we can now tune the position of the Van Hove singularity by controlling the relative angle between layers, she adds. For the time being, graphene is the only material in which this can be done.

Which opens up exciting opportunities for inducing and exploring correlated electronic phases in graphene, she says. "We expect that the twist-induced charge density wave discovered in this work will have important consequences for the transport properties of graphene. We could imagine that massless Dirac fermions in the material are strongly diffracted by the charge-density waves, leading to the new features in its band structure such as mini-bands separated by gaps where the material becomes insulating."

The experiments done so far were carried out on samples that had a fixed Fermi energy because they could not be gated. The team, which includes researchers from Porto University, MIT and Boston University, now plans to extend these measurements to gated samples where the Fermi energy can be controlled. "Here, we should be able to make the Fermi energy and the Van Hove singularity coincide for any twist angle," revealed Andrei. "This should drive a strong and tuneable electronic stability that we will study by transport measurements and STM."

The work was reported in Nature Physics.