Description du sujet de thèse

Title: Inhomogeneities in Flat band superconductors: what is the length scale?

Recent experimental studies on twisted bilayer graphene (TBG) and other twisted materials have revealed unexpectedly complex phase diagrams with exotic phases of quantum matter [1]. Among them, they revealed highly unconventional superconducting phases with ultra-flat bands, which cannot be described by the conventional BCS theory. Due to their very low Fermi velocity, the superconducting coherence length  predicted by BCS theory (which is proportional to the Fermi velocity) is more than 20 times shorter than the measured values. Recent theoretical developments [2] show that the coherence length is instead governed by the quantum metric of the Bloch states (which measures the distance between two adjacent Bloch states).
When a magnetic impurity is embedded in a superconductor, its local moment acts as a Cooper pair breaker, creating intra-gap bound state excitations whose spatial extent can be extremely large and is governed by . This is also true for other bound states in superconductors such as Andreev bound states in superconducting-Normal junctions or Majorana bound states in topological superconductors. In this PhD, we would like to theoretically study how the superconducting order parameter responds to various inhomogeneities. More specifically, we would like to analyze first the problem of a magnetic impurity in a flat-band superconductor and decipher if and how the quantum metric shows up in the bound state equation. Then we will extend it to many impurities and other source of inhomogeneities.
In the longer term, our understanding of hybrid systems (Josephson junctions) involving such flat-band superconductors needs to be completely revised: this includes all the quantum engineering that has been developed with mesoscopic superconductors.

[1] Y. Cao et al., Unconventional superconductivity in magic-angle graphene superlattices, Nature 556, 43 (2018).
[2] S. A. Chen and K. T. Law, Ginzburg-Landau Theory of Flat-Band Superconductors with Quantum Metric, Phys. Rev. Lett. 132, 026002 (2024).
[3] G. C. Ménard et al., Coherent long-range magnetic bound states in a superconductor, Nature Physics 11, 1013 (2015).

Contexte de travail

The Laboratoire de Physique des Solides is a joint research unit (UMR 8502) of the Université Paris-Saclay and the CNRS. It is affiliated to the Institut de Physique du CNRS and to the 28th section of the Conseil National des Universités. The LPS is a member of the Friedel-Jacquinot Federation, a coordinating structure for physics on the Moulon plateau in Orsay (IdF). It employs around one hundred researchers and teacher-researchers, both experimentalists and theoreticians, and its research activities are supported by some sixty engineers, technicians and administrative staff. Every year, the laboratory welcomes a large number of undergraduate and graduate students, including many PhD students, as well as post-doctoral researchers and visiting scientists. The laboratory covers a wider range of topics than its name suggests, and aims to address the full diversity of condensed matter physics. Research activity is organized around three main axes, each involving roughly the same number of scientists: - New electronic states of matter - Physical phenomena in reduced dimensions - Soft matter and the physics-biology interface The first area covers experimental and theoretical studies into the properties of systems in which electronic correlations are generally strong, and which are home to remarkable properties and unconventional electronic states such as superconductivity, magnetism, metal-insulator transitions and so on. The second section covers activities relating to the “nanosciences” in the broadest sense. Here, they are approached from the point of view of fundamental properties, when an object's dimensions become as small as certain characteristic distances (coherence length, mean free path, etc.). The third axis extends the concept of “soft matter” to biological systems. Topics range from complex systems to living tissues, from liquid crystals to foams, from polymers to granular systems. These physical studies are at the interface with physical chemistry and biology. The research work will be carried out within the THEORIE team of the Laboratoire de Physique des Solides (CNRS-UMR 8502). This research project is funded by the CNRS from 01/10/2025 to 30/09/2028.

Contraintes et risques

No risks