Graphene may have seemed a poor candidate for any kind of correlated electron physics not so long ago, but studies of bilayer graphene revealed a twist in the tale. Experimenting with the angle of orientation between one layer and another, revealed both Mott insulating and superconducting behaviour at different magic angles, and the potential for a new “twistronics” approach to engineering device properties. Theorists have been quick to snap up on the action with a recent paper suggesting more revelations to come.

“Graphene may become not only a venue for strong correlation physics, but also topological superconductivity,” suggest Cenke Xu at University of California, Santa Barbara, and Leon Balents at the Kavli Institute of Theoretical Physics, Santa Barbara, in the US in a recent Physics Review Letters report. Their theoretical treatment of the bilayer graphene systems points towards the existence of topological “Majorana” states at the edge of the material, of particular interest for quantum computing since they offer a system for quantum bits that is more robust to environmental perturbations than many others.

Three is the magic number of lattice sides

Following the experimental observations of superconductivity in bi- and multilayer graphene Xu and Balents aimed to “understand the nature of the observed superconducting phases”. They describe the twisted multilayer graphene as a superlattice with three-sided triangular lattice units much larger than the original honeycomb microscopic lattice. They then apply the “Hubbard model” – one of the simplest models for interacting particles in a lattice with just two terms in the Hamiltonian to describe the kinetic energy in terms of hopping from one site to another and the potential at the lattice sites.

“We argue that even in the simplest situation, the valley degree of freedom of graphene leads to dramatic modifications to the superconductivity: the preferred states are topological superconductors with a valley singlet structure,” explain Xu and Balents. “The compelling simplicity of the triangular framework suggests that graphene Moiré heterostructures which realize the single band triangular regime are favourable for realizing topological physics,” they conclude.

Among the recent work on this topic Noah F. Q. Yuan and Liang Fu a MIT published a report that also applied the Hubbard model to twisted bilayer graphene but based on a honeycomb lattice, leading to more intricate nuances in the results. Their work helps towards understanding the recent observations of transitions from metal to Mott insulator, Landau level degeneracy lifting, and unconventional superconductivity. What Xu and Balents add to the discussion is the potential for topological superconducting phenomena in these systems.

Full details are reported in Physical Review Letters.