Evidence of Fermi level pinning at the Dirac point in epitaxial multilayer graphene

We investigate the temperature-dependent conductivity of epitaxial multilayer graphene using THz time-domain spectroscopy and find evidence that the Fermi level in quasineutral graphene layers is pinned at the Dirac point by midgap states. We demonstrate that the scattering mechanisms result from the interplay between midgap states that dominate in the vicinity of the Dirac point and short-range potentials that govern at higher energies (>8 meV). Our results highlight the potential of multilayer epitaxial graphene for probing low-energy Dirac particles and also for THz optics.

Figure 1

(a) Transmitted THz electric field through the graphene sample at 5 K (blue) and 300 K (black). Insert: Corresponding amplitude spectrum of the THz electric field at $T=300\mathrm{K}$ obtained by fast Fourier transform. (b) Transmittance as a function of the temperature for different frequencies. (c) Amplitude transmittance spectrum $\left|t\left(\omega \right)\right|$ of the graphene multilayers at 5 K measured (top) and predicted (bottom) for $E_F=7\mathrm{meV}$. (d) Calculation of the intraband conductivity in graphene as a function of $k_{B}T/E_{\mathrm{F}}$ [16].

Figure 2

(a) Experimental transmission spectra of MEG at 5 K, 50 K, 100 K, 200 K, and 300 K. The error bars are the standard deviation in the measurements. (b) Corresponding calculated transmission spectra of graphene layers considering scattering on short-range potentials only (dashed line) and considering both scattering on short-range potentials and on mid-gap states (solid line). (c) Deviation in percent from calculated to experimental data $\mathrm{\Delta }t=|t_{\exp }|-|t_{\mathrm{theo}}|$ as a function of frequency. Black symbols result from calculations assuming scattering on short-range potentials only and open symbols on both scattering processes. (d) Peak-to-peak electric field transmitted through the graphene sample normalized to that of the SiC substrate as a function of temperature (symbols are experimental data; dashed and solid lines are the calculated data, assuming one and two scattering mechanisms, respectively).

Figure 3

(a) Schematic of the density of states of graphene without and with vacancies. (b) Scattering times as a function of carrier energies: scattering time on short-range potentials (red line), scattering time on channels related to the presence of vacancy defects (blue line), and the total scattering time including both scattering mechanisms (black line). (c) The predicted intraband conductivity of the quasineutral layers for $E_F=0$ of the highly-doped layers and the total intraband conductivity at 5 K and 300 K. (d) The interband conductivity of the quasineutral layers at 5 K (blue line) and 300 K (black line).