Superfluidity and geometry of Bloch bands

Speaker: Sebastiano Peotta. Seminar presented by Centres of Excellence in Computational Nanoscience & Low Temperature Quantum Phenomena and Devices

Band structure theory and the BCS theory of superconductivity are two cornerstones of modern condensed matter physics. They have been used to explain many properties of crystalline solids and have found important practical applications. It is believed that the interplay between the atomic lattice and the attractive force between electrons, whose origin is still matter of debate, is at the root of the useful properties of known high-Tc superconductors. In weakly-coupled superconductors the effect of the lattice amounts to a simple renormalization of the electron mass, equivalent to a renormalization of the density of states. On the contrary in high-Tc superconductors the coherence length is of the order to the lattice spacing and one may expect new phenomena to occur. An extreme example in this sense are “flat bands”, namely bands where the electron effective mass diverges. As proposed in Ref. [1] flat bands are an attractive platform for high-temperature superconductors since the critical temperature is linear in the coupling constant rather then being exponentially suppressed as for a conventional superconductor. In a recent work [2] we have provided a general theory of superfluidity that can be used even for flat band systems. Surprisingly, we find that in the flat band limit the superfluid density is not controlled by the effective mass but rather by a geometric invariant of the band, the quantum metric. This implies that the superfluid density can be nonzero even for a band which is strictly flat. We provide predictions for a model Hamiltonian with flat bands that can be realized with ultracold gases, the Harper model [2]. The Harper model is relevant for the theory of the quantum Hall effect and provides an example of the connection between superfluidity and a topological invariant of the band structure, the Chern number, which is an interesting consequence of our theory. Our results are potentially relevant for condensed matter systems other than ultracold gases.

References
[1] Kopnin, N. B., Heikkilä, T. T. & Volovik, G. E., Phys. Rev. B 83, 220503(R) (2011).
[2] S. Peotta & P. Törmä, Nature Communications 6, 8944 (2015).