Superconductivity in repulsively interacting fermions on a diamond chain: flat-band induced pairing

TL;DR

This study demonstrates that flat-band systems with repulsive interactions can host superconductivity, with pairing driven by the interaction between dispersive and flat bands in a diamond chain, revealing topological insulating phases at specific fillings.

Contribution

It shows that flat bands in a quasi-one-dimensional diamond chain can support superconductivity through repulsive interactions, a novel insight into flat-band physics and pairing mechanisms.

Findings

Significant Cooper pair binding energy near 1/3 filling

Long-range pair correlations across outer sites

Topological insulating phase at exact 1/3 filling

Abstract

To explore whether a flat-band system can accommodate superconductivity, we consider repulsively interacting fermions on the diamond chain, a simplest quasi-one-dimensional system that contains a flat band. Exact diagonalization and the density-matrix renormalization group (DMRG) are used to show that we have a significant binding energy of a Cooper pair with a long-tailed pair-pair correlation in real space when the total band filling is slightly below $1/3$, where the dispersive band interacts with the flat band that is empty but close to $E_F$. Pairs selectively formed across the outer sites of the diamond chain are responsible for the pairing correlation. At exactly $1/3$-filling an insulating phase emerges, where the entanglement spectrum indicates the particles on the outer sites are highly entangled and topological. These come from a peculiarity of the flat band in which "Wannier orbits" are not orthogonalizable.