Light-induced fractional quantum Hall phases in graphene

TL;DR

This paper proposes a method to induce and control fractional quantum Hall phases in graphene using optical driving, enabling exploration of non-Abelian topological phases and phase transitions.

Contribution

It introduces a novel optical technique to realize and manipulate two-component fractional quantum Hall states in graphene, including potential non-Abelian phases.

Findings

Optical resonance creates effective tunneling between Landau levels.

Interlayer interactions favor singlet states at specific fillings.

Potential realization of non-Abelian phases like the Fibonacci phase.

Abstract

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings $\nu=1/2$ and $\nu=2/3$. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.