1. quantum geometry effects on superconductivit, interacting bose-einstein condensest, and light-matter interactions in flat bands

Päivi Törmä

Aalto University, Finland

16 November 2021 Tue 5 pm

                                      IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

Superconductivity, superfluidity and Bose-Einstein condensation (BEC) are many-body phenomena where quantum statistics are crucial and the effect of interactions may be intriguing. Superconductors are already widely applied, but theoretical understanding of superconductivity and condensation in several real-world systems is still a challenge, and superconductivity at room temperature remains a grand goal. We have discovered that superconductivity (superfluidity) has a connection to quantum geometry [1]. Namely, the superfluid weight in a multiband system has a previously unnoticed component which we call the geometric contribution. It is proportional to the quantum metric of the band. Quantum metric is connected to the Berry curvature, and this allows to relate superconductivity with the topological properties of the band. Using this theory, we have shown that superconductivity is possible also in a flat band where individual electrons would not move. We and other groups have shown [2] that these results are essential in explaining the observation of superconductivity in bilayer graphene and may eventually help realize superconductors at elevated temperatures. Recently, we have shown that quantum geometry can enhance also light-matter coupling [3], and quantum correlations of a weakly interacting Bose-Einstein condensate [4].

[1] S. Peotta, P. Törmä, Nature Commun. 6, 8944 (2015); A. Julku, S. Peotta, T.I. Vanhala, D.-H. Kim, P. Törmä, Phys. Rev. Lett. 117, 045303 (2016); P. Törmä, L. Liang, S. Peotta, Phys. Rev. B 98, 220511(R) (2018) 

[2] A. Julku, T.J. Peltonen, L. Liang, T.T. Heikkilä, P. Törmä, Phys. Rev. B 101, 060505(R) (2020); X. Hu, T. Hyart, D.I. Pikulin, E. Rossi, Phys. Rev. Lett. 123, 237002 (2019); F. Xie, Z. Song, B. Lian, B.A. Bernevig, Phys. Rev. Lett. 124, 167002 (2020); for a news article see L. Classen, Physics 13, 23 (2020)

[3] G. Topp, C.J. Eckhardt, D.M. Kennes, M.A. Sentef, P. Törmä, Phys. Rev. B 104, 064306 (2021)

[4] A. Julku, G.M. Bruun, P. Törmä, arXiv:2104.14257 (2021), to appear in Phys. Rev. Lett. and Phys. Rev. B as two related papers.