Superconductivity with Wannier-Stark Flat Bands

TL;DR

This paper explores how applying a DC field to a lattice can create flat bands that significantly enhance superconductivity, especially the superfluid weight, under optimal interaction conditions.

Contribution

It proposes a practical method to realize flat bands via a DC field, avoiding precise Hamiltonian tuning, and systematically studies their impact on superconducting properties.

Findings

Superfluid weight is dramatically enhanced at optimal interaction and weak DC fields.

Flat bands can be realized by applying a DC field in a commensurate lattice direction.

Superconducting properties depend on the interplay between the DC field strength and interaction.

Abstract

We investigate superconducting transport in the DC field induced Wannier-Stark flat bands in the presence of interactions. Flat bands offer the possibility of unconventional high temperature superconductivity, where the superfluid weight, $D_s$, is enhanced by the density overlap of the localized states. However, construction of flat bands typically requires very precise tuning of Hamiltonian parameters. To overcome this difficulty, we propose a feasible alternative to realize flat bands by applying a DC field in a commensurate lattice direction. We systematically characterize the superconducting behavior on these flat bands by studying the effect of the DC field and attractive Hubbard interaction strengths on the wavefunction, correlation length, pairing order parameter and the superfluid weight $D_s$. Our main result is that the superfluid weight is dramatically enhanced at an optimal value of the interaction strength and weak DC fields.