Graphene is a simple material containing only a single layer of carbon atoms, but when two sheets of it are stacked together and offset at a slight angle, this twisted bilayer material produces numerous intriguing effects, notably superconductivity.

Now Cornell researchers are making headway into understanding how the material achieves this state by identifying its highest achievable superconducting temperature – 60 Kelvin. The finding is mathematically exact, a rare feat in the field, and is spurring new insights into the factors that fundamentally control superconductivity. 

“Looking ahead, this paves the way for understanding what are the possible degrees of freedom that one should try to control and optimize in order to enhance the tendency towards superconductivity in these two-dimensional material platforms,” said Debanjan Chowdhury, the Joyce A. Yelencsics Rosevear ’65 and Frederick M. Rosevear ’64 Assistant Professor of physics in the College of Arts and Sciences (A&S).

Chowdhury is a co-author of “Low-Energy Optical Sum-Rule in Moiré Graphene,” which published Nov. 4 in Physical Review Letters. The first author of the study is Juan Felipe Mendez-Valderrama, Ph.D. ’24, now at Princeton University; the second author is Dan Mao, who was a Bethe/KIC Theory Fellow at Cornell’s Laboratory of Atomic and Solid State Physics from 2021-2024 and is now at the University of Zürich.

“Taking two layers of graphene and setting them at 1.1 degrees, a magic angle, leads to dramatic effects,” Chowdhury said. “One such effect is that by simply varying an electric field, experimentalists can turn twisted bilayer graphene into either a superconductor or an insulator, which have wildly different electrical properties. Of course, we want to know theoretically what is the highest possible temperature at which the electrons can superconduct in twisted layers of graphene, and what sets the interplay between the various insulators and superconductors.”

In 2023, Chowdhury and Mao developed a new theoretical formalism to compute the highest possible superconducting transition temperature in any material obtained by stacking and twisting two-dimensional materials. For the current work, they applied it to twisted bilayer graphene.

“They had developed these rigorous expressions in 2023, which at the time you could only calculate approximately,” Mendez-Valderrama said. “What we tried to do here is precisely calculate this in a realistic model of twisted bilayer graphene, which leads to new insights into the factors that fundamentally control superconductivity.”

One of the most sought-after properties at physics labs worldwide, superconductivity is a phenomenon in which electrons can flow through a material without energy loss. Currently, this can only be achieved at very low temperatures.

Superconductivity is well understood in conventional materials, such as aluminum, where the electrons travel with such high kinetic energies that they barely feel each other’s presence. This vastly simplifies the description of superconductivity, Chowdhury said. The temperatures at which conventional materials transition into a superconducting state are also low compared to the intrinsic energy scales in the materials.

The situation is the complete opposite in twisted bilayer graphene, as the motion of every electron is highly coordinated with every other electron, Chowdhury said. Moreover, the material’s transition temperature – starting around 5 Kelvin – is relatively high compared to the intrinsic energy scales, providing hope for designing superconductors with even higher temperatures in the future.

“One of the remarkable properties of twisted bilayer graphene is the associated tunability,” Chowdhury said. “You have unprecedented control over temperature and the twist angle – the tiny electric fields that are applied to switch the material from being an insulator versus a superconductor – making it very easy to explore all sorts of exciting regimes in this material.”

The theoretical framework the team developed can be applied to other materials in the future, according to Mao.

“We are thinking about other promising material combinations beyond twisted bilayer graphene to identify possibly higher temperature superconductors, and also trying to extend these ideas to other desirable opto-electronic properties that can be measured via experiment,” Mao said.

This research was supported in part by a National Science Foundation grant and a Sloan Research Fellowship.

Kate Blackwood is a writer for the College of Arts and Sciences.