Quantum Geometry and superconductivity in flat bands

We have found that superconductivity and superfluidity have a connection to quantum geometry [1,2]. Namely, the superfluid weight in a multiband system has a previously unnoticed component which we call the geometric contribution. It is proportional to the minimal 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. Recently, we and other groups have shown [3,4] that these results may be essential in explaining the observation of superconductivity in bilayer graphene and may eventually help realize superconductors at elevated temperatures. In addition to the promise of high critical temperatures and strong correlation effects, also the quantum transport in flat band shows unique behavior [5]. In the normal state above the superconducting critical temperature, a new type of insulator can be found [6]. We have also explored the effect of quantum geometry on Bose-Einstein condensation and shown that the quantum distance and quantum metric determine the stability of the condensate, and quantum fluctuations dominate over mean-field effects [7]. Light-matter interactions become strongly enhanced by quantum geometry in flat bands [8].

[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] K.-E. Huhtinen, J. Herzog-Arbeitman, A. Chew, B.A. Bernevig, P. Törmä, Phys. Rev. B 106 , 014518 (2022); J. Herzog-Arbeitman, A. Chew, K.-E. Huhtinen, P. Törmä, B.A. Bernevig, arXiv:2209.00007 (2022)

[3] A. Julku, T.J. Peltonen, L. Liang, T.T. Heikkilä, P. Törmä, Phys. Rev. B 101, 060505(R) (2020)

[4] P. Törmä, S. Peotta, B.A. Bernevig, Nat. Rev. Phys.  4, 528 (2022)

[5] V.A.J. Pyykkönen, S. Peotta, P. Fabritius, J. Mohan, T. Esslinger, P. Törmä, Phys. Rev. B 103, 44519 (2021)

[6] K.-E. Huhtinen, P. Törmä, Phys. Rev. B 103, L220502 (2021)

[7] A. Julku, G.M. Bruun, P. Törmä, Phys. Rev. Lett., 127, 170404 (2021), ibid Phys. Rev. B 104, 144507 (2021)

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