SDR Deposit of the Week: Tunable properties of graphene

Aaron Sharpe with experimental setup

It's likely not news to you that Stanford researchers are undertaking all manner of cutting-edge and groundbreaking work. Applied Physics graduate student Aaron Sharpe is one such researcher who has become intrigued by a single-atom-thick layer of carbon called graphene that he says has, "continuously shaken up the field of condensed matter physics." Graphene sheets, as well as stacks of these sheets, show "unique and tunable electronic properties." We see why Aaron couldn't resist! We talked to Aaron about the research he and his colleagues have been undertaking with graphene and that has recently been published in Science.

Outreach by Stanford science librarians led Aaron to the Stanford Digital Repository (SDR), which he used to make the data and code for this publication publicly-available. "We chose the SDR because it was an easy process to make our data publicly available and permanent and to obtain a digital object identifier (DOI) to reference it in our publication." We completely agree with Aaron's comment that "with any publication, it is important that the data be publicly available."

One way they help to make this easier for others is by using Jupyter notebooks, which Aaron says is "a fantastic platform." In his research group, they use them "for everything from data acquisition and talking with instruments to data analysis and generating figures. On top of that, Jupyter is open-source, making it an obvious choice" for their lab.

Jupyter notebooks combined with the SDR are a great combination. "We hope that by sharing our data along with the Jupyter notebook that anyone can easily download and look more closely into the data presented in our paper," Aaron told us. "This is important not just for other groups trying to replicate and build on our work, but also because others might find something important in our data that we’ve missed, which could advance the field as a whole."

If you're interested in using the Stanford Digital Repository to share your research, please contact us at Requests for DOIs for SDR content should be sent to

Continue reading to find out more about the details of Aaron's work and the challenges they still face.

Briefly describe your research and why it is important.

Aaron Sharpe with experimental setup

Experiments with graphene, a single-atom-thick layer of carbon, have continuously shaken up the field of condensed matter physics. First, individual graphene sheets, and then stacks of multiple sheets have displayed unique and tunable electronic properties. 

It was predicted and recently experimentally realized that when two graphene layers are stacked with a relative twist angle of about one degree, the electrons no longer travel freely, but are instead localized to individual moiré cells about 10 nanometers in size. This localization in so-called “magic-angle twisted bilayer graphene” makes interactions between electrons very important, as two electrons on the same site strongly repel each other. As a result, an increase in resistivity is seen experimentally when there are exactly two electrons per moiré site, so that any rearrangement would require squeezing a third electron onto some site. Even more surprisingly, when an average of a tenth of an electron per site is added by applying a potential to a nearby “gate” electrode, twisted bilayer graphene becomes superconducting below 2 Kelvin. No one expected superconductivity to emerge from such a system, and even in retrospect, it’s puzzling that it occurs at such a “high” temperature (relative to the extremely low density of electrons in the sheets compared to other superconductors). Strong interactions in so-called “correlated” materials, similar to those thought to occur in twisted bilayer graphene, are believed to be at the root of many interesting and poorly understood phenomena, such as high-temperature superconductivity.

Seeing these exciting results, we decided to make twisted bilayer graphene samples to attempt to replicate the superconductivity and see what other interesting physics could appear. During preliminary measurements on our first sample, we saw a striking behavior when adding three rather than two electrons per moiré site: a very large anomalous Hall effect, a voltage perpendicular to the direction of an applied current that is normally proportional to the applied magnetic field but here occurred strongly near zero magnetic field. This suggested that the sample was magnetized despite having no elements like iron or nickel, which are traditionally associated with magnetism! Sweeping the applied magnetic field back and forth, we found that the anomalous Hall voltage is hysteretic, indicating that a finite applied field is required to flip the magnetization of the sample. This hysteretic magnetization is consistent with a ferromagnetic state. 

The nature of this observed magnetic state is still an open question. The magnetism could come from either the spin of the electrons (as in iron) or the circulating motion of the electrons. Because in twisted bilayer graphene the electrons are restricted to moving in two-dimensions, one way to distinguish between the two is to apply a magnetic field in the plane of the device. An in-plane magnetic field can couple to the spins of the electrons but not to the orbital motion, allowing us to distinguish the nature of the magnetism.

It is theoretically challenging to make predictions of the behavior of strongly interacting systems. Twisted bilayer graphene is an exciting testbed for probing interactions in a highly tunable system, where experiments are needed to guide theoretical understanding. Our research has revealed new, unexpected behavior arising from enhanced electron interactions and our future experiments may further elucidate the nature of these correlated states.

What are some of the challenges that you continue to face in your research?

The main challenge we and other groups working on twisted bilayer graphene are facing is making samples of consistent quality. The overall physics of twisted bilayer graphene seems to depend on the relative twist angle down to roughly the ten millidegree scale and samples with the same nominal twist angle do not consistently exhibit the same phenomenology. This inconsistency is due to inhomogeneity within the sample from strain in the lattice; the local twist angle can vary significantly within a single sample. While this sample to sample variation has not inhibited the community from learning a lot extremely quickly, it will surely need to be solved before we can understand the more subtle details of the physics in twisted bilayer graphene.