Landau Level Spectroscopy of Electron-Electron Interactions in Graphene

We present magneto-Raman scattering studies of electronic inter-Landau level excitations in quasineutral graphene samples with different strengths of Coulomb interaction. The band velocity associated with these excitations is found to depend on the dielectric environment, on the index of Landau level involved, and to vary as a function of the magnetic field. This contradicts the single-particle picture of noninteracting massless Dirac electrons but is accounted for by theory when the effect of electron-electron interaction is taken into account. Raman active, zero-momentum inter-Landau level excitations in graphene are sensitive to electron-electron interactions due to the nonapplicability of the Kohn theorem in this system, with a clearly nonparabolic dispersion relation.

Figure 1

Gray scale map of the electronic response in the magneto-Raman scattering spectra as a function of the magnetic field ($B$) for suspended graphene (G-S, top panel), graphene encapsulated in hBN (G-BN, middle panel), and graphene on graphite (G-Gr, bottom panel). Each map represents the collection of differential spectra (the $B=0$ spectrum has been subtracted from each spectrum measured in a magnetic field $B$). Dashed white lines account for the $B$ evolutions of the two most pronounced inter-LL excitations, expected within a single-particle approach, when assuming a $B$-independent but different for each sample band velocity $v$. Upper inset: scheme of the Landau level fan chart in graphene; two, $L_{-1,1}$ and $L_{-2,2}$, inter-Landau level excitations, well visible in the experiments on all samples, are indicated by red arrows. Middle panel inset: characteristic spectra due to $L_{-1,1}$ excitations measured at $B=8\mathrm{T}$ for G-Gr (black symbols), G-BN (red symbols), and G-S (blue symbols). Gray curves are Lorentzian functions. Light gray horizontal ribbons on gray scale maps are to mask the (residual) contribution to Raman scattering due to phonons of graphene or graphite at $\sim 1600$ and $\sim 2700{\mathrm{cm}}^{-1}$ as well as of the Si substrate ($\sim 520$ and $\sim 1000{\mathrm{cm}}^{-1}$ of hBN at $\sim 1370{\mathrm{cm}}^{-1}$.

Figure 2

Magnetic field dependence ($B_0=1\mathrm{T}$) of the velocities associated with $L_{-1,1}$ and $L_{-2,2}$ inter-Landau level excitations shown with, correspondingly, open circles (solid lines) and open stars (dashed lines), as derived from the experiment (data modeling), for G-S, G-hBN, and G-Gr specimens. Straight lines follow Eq. (4) [see also Eq. (2)], with ${ϵ}_{*}=3.9$, 7.0, and 12 for G-S, G-hBN, and G-Gr species, respectively, and the corresponding values for ${ϵ}_{\delta v}=1.3$, 3.7, and 12.