Quantum geometry, namely quantities such as quantum metric, Berry curvature, and Chern number, have become increasingly important in understanding interacting many-body systems. We have shown that supercurrents and superfluidity in a flat band are governed by quantum geometry [1], which opens new prospects for achieving high temperature superconductivity. These findings have become relevant for superconductivity in twisted bilayer graphene and other moiré materials [2]. We present our newest results on the topic, showing that flat band superconductivity is governed by the minimal quantum metric, which can be obtained by utilizing the system symmetries [3]. We discuss how effects unique to flat bands appear also in the normal state above the superconducting critical temperature [4,5]. Further, we show that quantum geometry governs the behaviour of bosonic condensates in flat bands as well, making quantum fluctuation effects remarkably strong [6].

References

1. S. Peotta, P. Törmä, Nature Communications 6, 8944 (2015)
2. P. Törmä, S. Peotta, B.A. Bernevig, arXiv:2111.00807, review article aNat.  Rev. Phys. in press (2022)
3. K.-E. Huhtinen, J. Herzog-Arbeitman, A. Chew, B.A. Bernevig, P. Törmä,  arXiv:2203.11133 (2022)
4. K.-E. Huhtinen, P. Törmä, Phys. Rev. B 103, L220502 (2021)
5. P. Kumar, S. Peotta, Y. Takasu, Y. Takahashi, P. Törmä, Phys. Rev. A 103, L031301 (2021)
6. A. Julku, G.M. Bruun, P. Törmä, Phys. Rev. Lett. 127, 170404 (2021)