Evidence for interlayer electronic coupling in multilayer epitaxial graphene from polarization-dependent coherently controlled photocurrent generation

Most experimental studies to date of multilayer epitaxial graphene on C-face SiC have indicated that the electronic states of different layers are decoupled as a consequence of rotational stacking. We have measured the third-order nonlinear tensor in epitaxial graphene as a novel approach to probe interlayer electronic coupling, by studying THz emission from coherently controlled photocurrents as a function of the optical pump and THz beam polarizations. We find that the polarization dependence of the coherently controlled THz emission expected from perfectly uncoupled layers, i.e. a single graphene sheet, is not observed. We hypothesize that the observed angular dependence arises from weak coupling between the layers; a model calculation, treating the interlayer coupling as bilayer coupling with variable strength, qualitatively reproduces the polarization angular dependence, providing evidence for coupling.

Figure 1

Schematic energy-momentum band diagram of doped and undoped layers of epitaxial graphene near the Dirac point. Solid line is associated with the ω beam, dash line with the 2ω beam. Asymmetric electron populations at $\pm k$, and hence current generation, is indicated by shaded patches. The dash line goes across the Fermi level of doped and undoped graphene layers.

Figure 2

(a) Time-dependent electro-optic signals of THz fields emitted from coherently controlled photocurrent; (b) terahertz field as a function of the phase relationship between 2ω and ω beams for constant time delay marked by the arrow in (a).

Figure 3

Experimentally measured $X$ (solid line) and $Y$ (dash line) components of relative peak THz amplitude as a function of the polarization angle between ω and 2ω pulses illustrated by the coordinates on the right corner on multilayer epitaxial graphene.

Figure 4

Theoretical predictions of current injection with linearly polarized ω and 2ω beams: polar plots of the projections of $\dot{\mathbf{J}}$ parallel ($X$) and perpendicular ($Y$) to ${\widehat{\mathbf{e}}}_{2\omega }$ as a function of the angle θ between the polarization vectors: (a) single-layer graphene (${\eta }_{XYYX}/{\eta }_{XXXX}=-1$); (b) bilayer graphene using graphite's value of ${\gamma }_1=0.4$ eV (${\eta }_{XYYX}/{\eta }_{XXXX}=-0.5$); and (c) a mixture of 70$\%$ uncoupled-layer (${\eta }_{XYYX}/{\eta }_{XXXX}=-1$) and 30$\%$ coupled-layer behavior with variable coupling strength ( ${\eta }_{XYYX}/{\eta }_{XXXX}=2.8$). The shade circles represent unit amplitude.