Transport in twisted bilayer graphene

In this project, we computed and studied multi-terminal conductance in mesoscopic samples of twisted bilayer graphene with up to one million lattice sites. Our results suggest that twisted bilayer graphene could be used for high-frequency device applications and sensitive detectors.

Twisted bilayer graphene is a material consisting of two sheets of graphene, a single layer of carbon atoms, rotated relative to each other by a certain twist angle. Around a small twist angle of about one degree, the so-called magic angle, the relevant electronic energy bands of this material become extremely flat. This enhances correlation effects between the electrons and leads, for example, to superconductivity. Even though the energy bands are very flat, they still have some substructure. In particular, they feature saddle points causing the electronic density of states do diverge at certain energies. These special points are called van-Hove singularities.

In our work, we set out to explore the correspondence between these van-Hove singularities and features in the conductance of twisted bilayer graphene as a function of the twist angle, pressure, and energy. At small angles, the relevant length scales in this material are large and the relevant energy scales are small. For this reason, we needed to simulate extremely large samples with up to one million carbon atoms to resolve potential features stemming from the mentioned singularities. Specifically, in our setup we crossed a narrow graphene junction and a wide graphene junction on top of each other at a certain angle. We then computed the multi-terminal conductance for the resulting bilayer region.

We observed how features in the conductance form and evolve as the twist angle is tuned down close to the magic angle. By analyzing the energy bands we were able to link most features to the van-Hove singularities. Interestingly, we find that the energetic position and width of these features can be tuned by varying the twist angle, by applying pressure, or by altering the size of the system. Besides these features, we observed a considerable enhancement of conductance at small twist angles overall. Based on these findings, we suggest that the combination of large conductance, strong quantum nonlinearity from the singularities, and high sensitivity to external parameters could make twisted bilayer graphene suitable for high-frequency device applications and sensitive detectors.

A. S. Ciepielewski, J. Tworzydło, T. Hyart, and A. Lau,
Transport signatures of van Hove singularities in mesoscopic twisted bilayer graphene,
Physical Review Research 4, 043145 (2022), arXiv:2208.08366