Superfluidity and geometry of flat Bloch bands

Sebastiano Peotta, Aalto University School of Science, Finland

09.07.2018 at 14:00 

Correlated many-body states of fermions in a lattice are at the root of many fascinating phenomena in
condensed matter, which are at present still poorly understood. An example in this sense is high-Tc
superconductivity. Understanding the low energy properties of a system of many fermions in a lattice, even in
its simplest realization, the Fermi-Hubbard model, is challenging both from the conceptual and the
computational point of view [1]. Therefore it is of paramount importance to find ways to simplify the problem.
One possibility is to consider lattices with flat bands, that is Bloch bands with vanishing bandwidth (infinite
effective mass). In the case of flat band models it is possible to obtain remarkable exact results. For example
Mielke and Tasaki have rigorously proved that a maximally polarized ferromagnet is the unique ground state
(up to rotations) for a half-filled flat band in a repulsive Hubbard model [2]. On the other hand we have focused
on the attractive case, motivated by the expectation that the diverging density of states of a flat band should
boost the superconductive critical temperature [3]. We find that the ground state is well described by the BCS
wavefunction [6], whereas the normal state of a flat band superconductor is very different from a Fermi liquid
and in this sense similar to the pseudogap phase of high-Tc superconductors. Indeed we provide evidence that
only pairs of particles are mobile in a flat band in the presence of interactions, while unpaired particles remain
localized [9]. We have also related the superfluid weight of a flat band superconductor to geometric and
topological invariants of the band structure, respectively the quantum metric and the Chern number [4-8]. In
particular we find that the superfluid weight of a flat band is bounded from below by the Chern number. Our
results are not limited to the attractive case since in the flat band limit a superconductor can be mapped exactly
into a ferromagnet of the Mielke and Tasaki type [5,6]. Ultracold gases are the most promising platform to verify
these predictions, but our results are potentially important also for solid state superconductors.

References
[1] J. P. F. LeBlanc et al., Phys. Rev. X 5 , 041041 (2 015 ).
[2] A. Mielke, H. Tasaki, Commun. Math. Phys. 158 , 341 (1993).
[3] N. B. Kopnin, T. T. Heikkilä, G. E. Volovik, Phys. Rev. B 83 , 220503 (2011).
[4] S. Peotta, P. Törmä, Nature Communications 6 , 8944 (2015).
[5] A. Julku, SP, T. Vanhala, D.-H. Kim, P. Törmä, Phys. Rev. Lett. 117 , 045303 (2016).
[6] M. Tovmasyan, SP, P. Törmä, S. D. Huber, Phys. Rev. B 94 , 245149 (2016).
[7] L. Liang, T. I. Vanhala, SP, T. Siro, A. Harju, P. Törmä, Phys. Rev. B 95 , 024515 (2017).
[8] L. Liang, SP, A. Harju, P. Törmä, Phys. Rev. B 96 , 064511 (2017).
[9] M. Tovmasyan, SP, L. Liang, P. Törmä, S. D. Huber, arXiv:1805.04529.