Light-Induced Fractional Quantum Hall Phases in Graphene

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 nonzero relative angular momentum can become dominant, resembling a hollow-core pseudopotential. 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.

Figure 1

(a) A single graphene layer driven by light at Rabi frequency $\mathrm{\Omega }$. (b) LL structure with partial filling and optical transitions ${\mathrm{LL}}_{0-1}$ and ${\mathrm{LL}}_{1-2}$. (c) Formation of dressed states due to coupling between two LLs.

Figure 2

(a) Pseudopotentials for scattering of two particles in the same graphene LL, $n=0$, $n=1$, and $n=2$. (b) Pseudopotentials for scattering in different LLs, as defined in Eq. (4). If $n=1$ is coupled to $n=2$, $V_j^{\text{inter}}$ is dominated by the contribution $j=1$.

Figure 3

(a),(b) Energy levels (above the ground state in units of $e^2/\epsilon l_B$) vs Rabi frequency $\mathrm{\Omega }$, for coupling ${\mathrm{LL}}_{0\text{−}1}$ (a) and ${\mathrm{LL}}_{1\text{−}2}$ (b). (c),(d) Ground state overlaps with trial wave functions (particle-hole conjugate $1/3$ Laughlin state and a singlet phase obtained from the hollow-core model). Trial states are constructed in three different bases: (i) LL basis. All the electrons reside in the lower LL. (ii) Dressed basis. All electrons reside in lower eigenstates of Eq. (2), i.e., $|j⟩\propto (\delta -\sqrt{{\delta }^2+4{\mathrm{\Omega }}^2})|M+1,j⟩+2\mathrm{\Omega }|M,j⟩$. (iii) Antisymmetric basis. All electrons reside in the singlet state, i.e., $|j⟩\propto -|M+1,j⟩+|M,j⟩$. (e),(f) Spin polarization $S_{\alpha }=1/2N\sum _j⟨\sum _j{\tau }_{\alpha }^{(j)}⟩$ of the ground state vs $\mathrm{\Omega }$ for ${\mathrm{LL}}_{0\text{−}1}$ (e) and ${\mathrm{LL}}_{1\text{−}2}$ (f). Data in all panels (a)–(f) were obtained for eight electrons on the torus, and $\delta =0.02$.