Reststrahl band-assisted photocurrents in epitaxial graphene layers

We report on the observation of the reststrahl band-assisted photocurrents in epitaxial graphene on SiC excited by infrared radiation. The peculiar spectral dependence for frequencies lying within the reststrahl band of the SiC substrate provides a direct and noninvasive way to probe the electric field magnitude at atomic distances from the material's surface. Furthermore our results reveal that nonlinear optical and optoelectronic phenomena in two-dimensional crystals and other atomic scale structures can be giantly enhanced by their deposition on a substrate with negative dielectric constant.

Figure 1

(a) Experimental geometry. (b) Reflection of a plane wave from a graphene layer on a SiC substrate deposited at distances of about 2 Å from the surface.

Figure 2

Spectra of the photocurrent excited by (a) linearly and (b) circularly polarized radiation.

Figure 3

Spectra of the longitudinal photocurrent $j_x^L$ measured for $\left|\theta \right|={30}^{\circ }$ and the azimuth angle $\alpha =0^{\circ }$. The data are obtained applying linearly polarized radiation of the free electron laser “FELIX.” Gray area indicates the range of the reststrahl band of SiC. The inset shows the experimental geometry.

Figure 4

Dashed and solid lines show the reflection spectra of graphene on SiC substrate and pure SiC, respectively. Dotted line shows the difference between the two curves. The spectra are measured with a Fourier spectrometer. Gray area shows the range of the reststrahl band of SiC limited by the energies of transverse and longitudinal optical phonons.

Figure 5

(a) Photocurrent $j_y/I$ as a function of $\hslash \omega$ and angle $\phi$ (polarization states are sketched above). (b) and (c) show corresponding dependencies obtained for fixed $\hslash \omega$.

Figure 6

(a) Experimental geometry. (b)–(d) Calculated spectra of the linear (solid) and circular (dashed) photocurrents. (b) Photon drag effect. (c) and (d) Photogalvanic effect caused by the electric field in the SiC side, ${\mathit{E}}^{\mathrm{in}}$, and in the air side of the air/SiC interface, ${\mathit{E}}^{\mathrm{out}}$, respectively. The calculations are performed for ${\theta }_0={30}^{\circ }$, $\gamma /\chi =0.9$, and $T^{\prime }/T=18$, as well as obtained from the reflection data $\Gamma =0.01{\omega }_{\text{TO}}$, ${\varepsilon }_{\infty }=6.52$, and ${\varepsilon }_0=9.66$ for SiC (see also Ref. [43]). The insets shows the electric field components considered in the calculations.

Figure 7

Spectral behavior of the linear (solid lines) and circular (dashed lines) photocurrents. (a) Experimental results. (b) Calculations of the total photocurrent considering electric field components $E_x,E_y$ and electric field component in the air side of the air/SiC interface $E_z^{\mathrm{out}}$. Here we used a ratio of circular PDE to circular PGE equal to $({\omega }_{TO}/c)T^{\prime }/\chi =0.3$ and the parameters given in the caption of Fig. 6.