Maxime Thumin : Flat band superconductivity: Quantum geometry, disorder and nanostructuration

 In the last decade, flat band (FB) superconductivity has gained considerable interest for its remarkable features such as a direct connection to the concept of quantum geometry [1], the possibility of high critical temperatures, and possible realization in twisted bilayer graphene and other carbon-based materials [2].

The main purpose of this talk is to give a selective overview of this unconventional type of superconductivity. For this, we will first define the basic properties of FB states in the single electron picture and introduce the concept of quantum geometric tensor. Then, after showing the reliability of our mean field Bogoliubov-de-Gennes approach, we will discuss what characterizes this superconductivity (in terms of pairing and phase coherence) and what connects it with the quantum metric [3,4]. In particular, we will show how the latter can provide an efficient strategy to reinforce the superconducting phase in nanostructured systems [5]. Finally, we will address the impact of disorder in the two-dimensional Lieb lattice. Our results on the pairing amplitudes and BKT temperature reveal a striking robustness of flat band superconductivity against disorder, which contrasts with the conventional intraband superconductivity [6].

[1] S. Peotta and P. Törmä, Nature communications, (2015)
[2] Y. Cao et al, Nature, (2018)
[3] M. Thumin and G. Bouzerar, Phys. Rev. B (2023)
[4] G. Bouzerar and M. Thumin, SciPost Physics (2024)
[5] M. Thumin and G. Bouzerar, Phys. Rev. B (2024)
[6] G. Bouzerar and M. Thumin, Phys. Rev. B Letter (2025)