# $2\pi$-flux loop semimetals

## TL;DR

This paper introduces a new class of $2 ext{-} ext{} ext{ extpi}$-flux loop semimetals with winding number 2, explores their relation to Hopf-link semimetals, and studies their Floquet-driven topological phase transitions under circularly polarized light.

## Contribution

It models $2 ext{-} ext{ extpi}$-flux loops, connects them to Hopf-link semimetals, and proposes simple physical implementations and Floquet control methods.

## Key findings

- $2 ext{-} ext{ extpi}$-flux loops characterized by winding number 2.
- Transformation of $2 ext{-} ext{ extpi}$-flux loops into Hopf-link semimetals.
- Floquet driving can split loops into $ ext{ extpi}$-flux loops or Weyl points.

## Abstract

We introduce a model of $2\pi$-flux loop semimetals which holds nodal loops described by a winding number $\nu=2$. By adding some extra terms, this model can be transformed into a recently discovered Hopf-link semimetal, and the symmetries distinguishing these two phases are studied. We also propose a simpler physical implementation of $2\pi$-flux loops and of the Hopf-link semimetals which only involves nearest-neighbor hoppings, although in the presence of spin-orbit interaction. Finally, we investigate the Floquet properties of the $2\pi$-flux loop, and find that such a loop may be driven into two separated $\pi$-flux loops or four Weyl points by light with circular polarization in certain directions.