Title: New perspectives on quantum geometry, superconductivity and Bose-Einstein condensation

Abstract: 

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. Recently, we and other groups have shown [2,3] that these results are essential in explaining the intriguing observation of superconductivity in bilayer graphene and may eventually help realize superconductors at elevated temperatures. We have also explored the effect of quantum geometry on Bose-Einstein condensation [4].

Bose-Einstein condensation has been realized for various particles or quasi-particles, such as atoms, molecules, photons, magnons and semiconductor exciton polaritons. We have experimentally realized a new type of condensate: a BEC of hybrids of surface plasmons and light in a nanoparticle array [5]. The condensate forms at room temperature and shows ultrafast dynamics, and the system provides easy tunability of the lattice and unit cell geometry and symmetries. Recently, we have observed formation of polarization textures and domain walls, and obtained the BEC phase for the first time using a phase retrieval algorithm [6]. Our measurements of spatial and temporal coherence show a change from exponential decay to powerlaw or streched-exponential when crossing to the BEC phase [7]. We have also observed that when the nanoparticles are made of magnetic material, chiral modes and magnetic switching of lasing become possible [8]. This paves the way for future studies of topological effects in these systems.   

[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) https://physics.aps.org/articles/v13/23

[3] P. Törmä, S. Peotta, B.A. Bernevig, review article to appear in Nat. Rev. Phys., arXiv:2111.00807 (2022)

[4] A. Julku, G.M. Bruun, P. Törmä, Phys. Rev. Lett., 127, 170404 (2021)

[5] T.K. Hakala, A.J. Moilanen, A.I. Väkeväinen, R. Guo, J.-P. Martikainen, K.S. Daskalakis, H.T. Rekola, A. Julku, P. Törmä, Nature Phys. 14, 739 (2018); A.I. Väkeväinen, A.J. Moilanen, M. Necada, T.K. Hakala, P. Törmä, Nature Commun. 11, 3139 (2020)

[6] J.M. Taskinen, P. Kliuiev, A.J. Moilanen, P. Törmä, Nano Letters 21, 5202 (2021)

[7] A.J. Moilanen, K.S. Daskalakis, J.M. Taskinen, P. Törmä, Phys. Rev. Lett. 127, 255301 (2021)

[8] F. Freire-Fernandez, J. Cuerda, K.S. Daskalakis, S. Perumbilavil, J.-P. Martikainen, K. Arjas, P. Törmä, S. van Dijken, Nature Photonics in press, Nature Phot. 16, 27 (2021)