Graphene is a two-dimensional material made up of carbon atoms arranged in a hexagonal pattern that is only one atom layer thick. When two layers of graphene are stacked on top of each other, with one layer rotated relative to the other, the hexagonal patterns in each layer interact and create a new, larger pattern visible on the surface of the material. This is called a moiré pattern, and the resulting material is an example of a moiré material.

Recently, moiré materials have become particularly interesting to researchers and engineers. The twist angle alters how the layers interact with each other and creates a new type of material with unique properties. For example, layers of graphene stacked in this way can produce a so-called "magic angle" that makes the material exhibit unusual electronic properties like superconductivity. Normally, when electricity flows through a material, some energy is lost as heat due to the material's resistance. However, a superconductor can conduct current without energy loss, which has opened new avenues for researching more efficient electronic components and even new types of computers.

To understand the mechanism that makes twisted layers of graphene superconductors at a magic angle, much deeper mathematical understanding of this phenomenon is required than we have today. Therefore, in this project, we aim to investigate it more closely by developing new mathematical tools and models of moiré materials. Specifically, we will use models to obtain precise information on what characterizes magic angles, and then we will use this to build advanced simulations where we can numerically explore phenomena such as superconductivity. We will also investigate a type of magnetic conduction that arises when moiré materials are deformed through strain. Such knowledge could lead to the creation of new materials with surprising properties, which could have far-reaching effects in electronics, engineering, and materials science.

The project is one of those selected to describe the Swedish Research Council's research funding. Read more at the Swedish Research Council's webpage (in Swedish)