Preformed pairs in flat Bloch bands

Aalto Quantum Physics Seminar (Nanotalo). Speaker: Dr. Sebastiano Peotta (Aalto University, Quantum Dynamics).

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 [3-8], motivated by the expectation that the diverging density of states of a flat band should boost the superconductive critical temperature [9]. We have found that the ground state is well described by the BCS wavefunction [3,5], whereas the normal state of a flat band superconductor is expected to be is very different from a Fermi liquid and in this sense similar to the pseudogap phase of high-Tc superconductors. The purpose of this talk is to present our most recent results that provide strong evidence for a non-Fermi liquid normal state in a flat band superconductor [8]. We show for some lattice models with flat bands that only pairs of particles (Cooper pairs) are mobile and can carry a current, while single Bogoliubov quasiparticles remain localized even in the presence of interactions. This result is valid at arbitrary temperature and is a consequence of the existence of exact local integral of motions in these lattice models, which imply that the single-particle propagator is short-ranged. Therefore, Cooper pairs dominate transport even in the normal state and are in this sense “preformed”. Preformed pairs have been put forward as a possible explanation for the anomalies observed in the pseudogap phase in underdoped copper-based superconductors [10]. Our results can serve as a benchmark for the approximations used to tackle the pseudogap phase. Moreover the possibility of implementing these lattice models with flat bands in a number of physical platforms will be discussed.
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] S. Peotta, P. Törmä, Nature Communications 6 , 8944 (2015).
[4] A. Julku, SP, T. Vanhala, D.-H. Kim, P. Törmä, Phys. Rev. Lett. 117 , 045303 (2016).
[5] M. Tovmasyan, SP, P. Törmä, S. D. Huber, Phys. Rev. B 94 , 245149 (2016).
[6] L. Liang, T. I. Vanhala, SP, T. Siro, A. Harju, P. Törmä, Phys. Rev. B 95 , 024515 (2017).
[7] L. Liang, SP, A. Harju, P. Törmä, Phys. Rev. B 96 , 064511 (2017).
[8] M. Tovmasyan, SP, L. Liang, P. Törmä, S. D. Huber, arXiv:1805.04529.
[9] N. B. Kopnin, T. T. Heikkilä, G. E. Volovik, Phys. Rev. B 83 , 220503 (2011).
[10] M. Randeria, “Precursor pairing correlations and pseudogaps,” in Proceedings of the
International School of Physics “Enrico Fermi” Vol. 136, edited by G. Iadonisi, J.R. Schrieffer, and
M.L. Chiofalo (IOS Press, 1998) pp. 53 – 75, arXiv:cond-mat/9710223.