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

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.

Phys. Rev. B, to be published

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• Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band
• Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system
• Theoretical study of spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band
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• Hidden Ladder in SrMoO${}_3$/SrTiO${}_3$ Superlattices: Experiments and Theoretical Calculations