Engineering flux-controlled flat bands and topological states in a Stagome lattice

TL;DR

This paper introduces the Stagome lattice, a tunable variant of the Kagome lattice, enabling the creation of flat bands and topological states through magnetic flux control, with potential applications in superconductivity and photonics.

Contribution

The study presents a novel lattice design allowing external control of flat bands and topological properties, with analytical calculations and robustness analysis.

Findings

Flat bands can be tuned to the Fermi level via magnetic flux.

The lattice exhibits nontrivial topological phases with varying Chern numbers.

Flat band localization remains robust under small disorder.

Abstract

We present the Stagome lattice, a variant of the Kagome lattice, where one can make any of the bands completely flat by tuning an externally controllable magnetic flux. This systematically allows the energy of the flat band to coincide with the Fermi level. We have analytically calculated the compact localized states associated to each of these flat bands appearing at different values of the magnetic flux. We also show that, this model features nontrivial topological properties with distinct integer values of the Chern numbers as a function of the magnetic flux. We argue that this mechanism for making any of the bands exactly flat could be of interest to address the flat-band superconductivity in such a system. Additionally, we show that our results are robust even in the presence of a small amount of disorder. Furthermore, we believe that the phenomenon of photonic flat band localization could be studied in the Stagome lattice structure, designed for instance using femtosecond laser induced single-mode waveguide arrays.