Moiré assisted fractional quantum Hall state spectroscopy

Intra-Landau level excitations in the fractional quantum Hall regime are not accessible via optical absorption measurements. We point out that optical probes are enabled by the periodic potentials produced by a moiré pattern. Our observation is motivated by the recent observations of fractional quantum Hall incompressible states in moiré-patterned graphene on a hexagonal boron nitride substrate, and is theoretically based on $f-\mathrm{sum}$ rule considerations supplemented by a perturbative analysis of the influence of the moiré potential on many-body states.

Figure 1

(a) Schematic illustration of a periodic potential in real space due to a moiré pattern formed between 2D crystals with triangular Bravais lattices. (b) The first shell of moiré reciprocal lattice vectors.

Figure 2

Schematic illustration of the perturbation theory analysis. (a) Energy spectrum of the Coulomb-only model at filling factor 1/3. The red dot represents the $\nu =1/3$ Laughlin incompressible ground state, the blue line marks the magnetoroton mode, and the gray bar the excitation continuum. In the presence of a moiré superlattice potential, the perturbed ground state contains admixtures of unperturbed excited states at momenta $\mathbf{G}$. This admixture enables intra-LL optical response. (b) Schematic illustration of the optical conductivity. When perturbation theory applies and $\left|\mathbf{G}\right|{\ell }_B$ is close to 1.5, the SMA is accurate. Thus the intra-LL optical response is dominated by a single peak. When $\left|\mathbf{G}\right|{\ell }_B>1.5$, weaker optical responses are expected at multiple frequencies. Tuning $\left|\mathbf{G}\right|$ provides a momentum-resolved spectroscopy of FQH excitations.