Engineering Quantum Hall Phases in Synthetic Bilayer Graphene System

TL;DR

This paper demonstrates how optically driven monolayer graphene can be used to engineer and study various quantum Hall phases, including non-abelian and ferromagnetic states, by tuning system parameters.

Contribution

It introduces a synthetic quantum Hall bilayer system in monolayer graphene and explores its phase diagram using advanced numerical methods, revealing novel non-abelian and ferromagnetic phases.

Findings

Identification of a non-abelian bilayer Fibonacci phase at ν=2/3

Observation of quantum Hall ferromagnetism at ν=1

Topological skyrmion excitations in the ferromagnetic phase

Abstract

Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent driving which couples two Landau levels mimicks an effective tunneling between synthetic layers. The tunneling strength, the effective Zeeman coupling, and two-body interaction matrix elements are tunable by varying the driving frequency and the driving strength. Using infinite density matrix renormalization group (iDMRG) techniques combined with exact diagonalization (ED), we show that the system exhibits a non-abelian bilayer Fibonacci phase at filling fraction $\nu = 2/3$. Moreover, at integer filling $\nu = 1$, the SQHB exhibits quantum Hall ferromagnetism. Using Hartree-Fock theory and exact diagonalization, we show that excitations of the quantum Hall ferromagnet are topological textures known as skyrmions.