Spin-orbit interactions may relax the rigid conditions leading to flat bands

TL;DR

This paper shows that including tunable spin-orbit interactions in conducting polymers relaxes the strict conditions needed for flat band formation, allowing for more flexible engineering of flat bands in real materials.

Contribution

It demonstrates that spin-orbit interactions can significantly relax the mathematical constraints for flat band realization, broadening the possibilities for flat band engineering.

Findings

Spin-orbit interactions relax flat band conditions by 20-30%.

External magnetic fields increase this relaxation to about 80%.

Flat bands can be achieved with parameter variations previously considered too large.

Abstract

Flat bands are of extreme interest in a broad spectrum of fields since given by their high degeneracy, a small perturbation introduced in the system is able to push the ground state in the direction of an ordered phase of interest. Hence the flat band engineering in real materials attracts huge attention. However, manufacturing a flat band represents a difficult task because its appearance in a real system is connected to rigid mathematical conditions relating a part of Hamiltonian parameters. Consequently, whenever a flat band is desired to be manufactured, these Hamiltonian parameters must be tuned exactly to the values fixed by these rigid mathematical conditions. Here we demonstrate that taking the many-body spin-orbit interaction (SOI) into account -- which can be continuously tuned e.g. by external electric fields --, these rigid mathematical conditions can be substantially relaxed. On this line we show that a $\sim 20-30 \%$ variation in the Hamiltonian parameters rigidly fixed by the flat band conditions can also lead to flat bands in the same or in a bit displaced position on the energy axis. This percentage can even increase to $\sim 80 \%$ in the presence of an external magnetic field. The study is made in the case of conducting polymers. These systems are relevant not only because they have broad application possibilities, but also because they can be used to present the mathematical background of the flat band conditions in full generality, in a concise, clear and understandable manner applicable everywhere in itinerant systems.