Spectroscopic signatures of massless gap opening in graphene

Gap opening in graphene is usually discussed in terms of a semiconductinglike spectrum, where the appearance of a finite gap at the Dirac point is accompanied by a finite mass for the fermions. In this paper we propose a gap scenario from graphene which preserves the massless characters of the carriers. This approach explains recent spectroscopic measurements carried out in epitaxially grown graphene, ranging from photoemission to optical transmission.

Figure 1

(Color online) Electronic dispersion (a) and DOS (b) for the massless $E^{\text{ml}}$ (solid black line) and massive $E^{\text{ms}}$ (dashed red line) gapped models, with $\Delta =0.13\text{eV}$. The dotted line refers to the Dirac-type dispersion $\epsilon$ in the absence of any gap.

Figure 2

(Color online) (a) Intensity map of the spectral function $A\left(k_x,k_y=0,\omega \right)$ of the massless model [Eq. (4)] for $\Delta =0.13\text{eV}$, $v_F=6\text{eV}\text{Å}$, and $\Gamma$ taken from the experiments (see text). Dashed white lines show the mismatch between the asymptotic linear behavior of the upper and lower bands. (b) Corresponding energy-distribution curves taken for $k_y=0$ and equally spaced $k_x$ values. The curves are vertically displaced for clarity. (c) Plot of the gap edge at finite $k_x$ for the massless and massive gap model [$\Delta ,v_F$ as in panel (a)]. Dark squares are experimental data taken from Ref. 1.

Figure 3

(Color online) (a) Optical conductivity $\sigma \left(\Omega \right)$ for $\mu =0.1\text{eV}$, $T=300\text{K}$, and $\Gamma =15\text{meV}$ for the massless gap model (solid black line, $\Delta =45\text{meV}$) and for the massive gap model (dashed red line, $\Delta =73\text{meV}$). Inset: reduction in the zero-frequency optical conductivity in the two cases, as a function of $\Delta /\mu$. (b): Comparison of the two models with the experimental data for $T\left(\omega \right)$ from Ref. 9.