Periodic Reporting for period 1 - SUPERLAND (A new SUPERconducting LANDscape: using nanoscale inhomogeneity for enhanced superconductivity)
Reporting period: 2023-09-01 to 2026-02-28
Superconductivity is a uniquely quantum mechanical phenomenon that despite decades of intense research is still very hard to control. It is heavily dependent on the density of states (DOS) around zero energy, but this DOS tunability has so far remained largely untapped. This project aims to theoretically create and enhance superconductivity by producing large DOS peaks at zero energy using nanoscale inhomogeneity, thereby creating an entirely new, spatial and figurative, landscape for superconductivity. A rare, not yet understood, example is twisted bilayer graphene, an all-carbon material not assumed to be superconducting. Here small twist angles produce an inhomogeneous moiré structure hosting large zero-energy DOS peaks that have recently been shown to create superconductivity. In this project we will understand, as well as enhance, superconductivity in moiré structures in both graphene and topological insulators. In this project we will also establish superconductivity driven entirely by other types of nanoscale inhomogeneity generating zero-energy DOS peaks. We will also use zero-energy DOS peaks to create a superconducting phase crystal in different superconductors, generalizing findings from high-temperature cuprate superconductor surfaces. Due to its nanoscale phase modulations and spontaneous supercurrents, the phase crystal dramatically enriches the superconducting properties. To succeed with this project, we will use and further develop our own state-of-the-art numerical tools to self-consistently study superconductivity at the atomistic level in very large inhomogeneous systems. Taken together, this project will create an entirely new, inhomogeneous, landscape for superconductivity.
During the first two years of the project we have successfully started work within all objectives of the project.
For the first objective we started with developing an understanding of the quantum metric in inhomogeneous systems. This is a crucial step for us to later be able to understand the superfluid weight in flat band-like systems. Here we have already both established that disorder in the form of random vacancies in graphene increases the quantum metric, that the quantum metric can be used to understand localization in quasicrystals, and that amorphous systems easily host topological features. We have also used our developed understanding of the importance of the quantum metric for the superfluid weight in predicting a diamagnetic Meissner response in odd-frequency superconductors, which also used results from a previous ERC project. For the second objective we have almost finished a project considering how the DOS in moiré twisted bilayer graphene is influenced by strain and buckling. We have also developed our understanding the possible chiral and nematic superconducting states in twisted bilayer graphene, as well as studied the general properties of the edge states of the chiral phase. Finally, within the third objective, we progressed in our understanding of phase crystals, how it can survive disorder and how changes of the bulk topology changes its possibilities to survive, important for future work within the project.
For the first objective we started with developing an understanding of the quantum metric in inhomogeneous systems. This is a crucial step for us to later be able to understand the superfluid weight in flat band-like systems. Here we have already both established that disorder in the form of random vacancies in graphene increases the quantum metric, that the quantum metric can be used to understand localization in quasicrystals, and that amorphous systems easily host topological features. We have also used our developed understanding of the importance of the quantum metric for the superfluid weight in predicting a diamagnetic Meissner response in odd-frequency superconductors, which also used results from a previous ERC project. For the second objective we have almost finished a project considering how the DOS in moiré twisted bilayer graphene is influenced by strain and buckling. We have also developed our understanding the possible chiral and nematic superconducting states in twisted bilayer graphene, as well as studied the general properties of the edge states of the chiral phase. Finally, within the third objective, we progressed in our understanding of phase crystals, how it can survive disorder and how changes of the bulk topology changes its possibilities to survive, important for future work within the project.
We have developed formalism and understanding of the quantum metric in real space, crucial for any inhomogeneous system. The quantum metric has been formulated before in real space but our work has established how it can be used to bring new understanding in several different settings. We are continuing to develop these concepts and applying them to superconductors.