Screening and band structure effects on quasi-one-dimensional transport in periodically modulated graphene

Using ab-initio density functional theory the electronic response is studied for graphene subjected to an external superlattice potential. Different potential strengths and crystallographic directions forming one-dimensional (1D) superlattices with zigzag and armchair edges are investigated. The graphene band structure and the screening effect are self-consistently taken into account. The Dirac points appear slightly displaced in reciprocal space with a strongly anisotropic Fermi velocity. The screening tends to weaken the potential action and renormalization of the Fermi velocity. We demonstrate that the vanishing group velocity perpendicular to the superlattice as predicted for non-interacting massless Dirac fermions still occurs although somewhat modified by the self-consistent reaction of the system. Features of a quasi-1D metal remain observable.

Figure 1

Ideal 1D Kronig-Penney potential $U_{\mathrm{ext}}$ (top) and unperturbed graphene layer (bottom).

Figure 2

Band structure of periodically modulated graphene along a high-symmetry direction $\Gamma Y$ (perpendicular to the superlattice axis) of the superlattice BZ for different potential strengths. $U=0\text{eV}$ is a solid black line, $U=2.5\text{eV}$ is a dotted red line, and $U=4.5\text{eV}$ is a dashed green line.

Figure 3

Renormalized Fermi velocity perpendicular to the barriers as a function of the strength of the external Kronig-Penney potential. Ab-initio calculations, represented by red dots, results based on model Hamiltonian (1) are represented by a blue thin solid line, and similar results for a screened potential by a black solid line.

Figure 4

Electron-density modification $\Delta n\left(\mathbf{r}\right)$ (top) and induced potential $\Delta V_{\mathrm{el}}\left(z\right)$ (bottom, red) for a zigzag graphene superlattice close to the potential step $U=100\text{meV}$. For comparison, the external potential $U_{\mathrm{ext}}\left(z\right)$ is also plotted (bottom, blue). Isosurfaces (in yellow) belong to electron accumulation, whereas blue isosurfaces belong to electron depletion near the potential step. Green faces are cross sections between isosurfaces and the boundaries of the unit cell.

Figure 5

Same as Fig. 4, but for an armchair graphene superlattice. For details, see text.