Quantum Dots in Graphene

We suggest a way of confining quasiparticles by an external potential in a small region of a graphene strip. Transversal electron motion plays a crucial role in this confinement. Properties of thus obtained graphene quantum dots are investigated theoretically for different types of the boundary conditions at the edges of the strip. The (quasi)bound states exist in all systems considered. At the same time, the dependence of the conductance on the gate voltage carries information about the shape of the edges.

Figure 1

Upper curve: Conductance of the graphene quantum dot as a function of Fermi energy for the metallic armchair edges for $L=4\xi$, Eq. (4). Lower curve: Contribution to conductance from the transmission channels with $p_y=\pm \pi \hslash /L$. All calculations are carried out for zero temperature, $T=0$.

Figure 2

Examples of trajectories described in the text drawn on the $x$, $p_x$ plane (arbitrary units). Solid lines show the trajectories with $\epsilon <0$ either bouncing inside the barrier or reflected by it from the left or right. Tunneling events between the bounded and unbounded trajectories are shown schematically (t). Thick dashed lines show the trajectories with $\epsilon >0$ either transmitted for $|p_y|<\epsilon /c$ or reflected for $|p_y|>\epsilon /c$.

Figure 3

Conductance of the graphene quantum dot for the semiconductor armchair edge (solid line) compared to the metallic armchair edge (dashed line) for $L=2\xi$ (4). The nonresonant conductance at $\epsilon <0$ is $G\approx G_0$ for the metallic strip and $G\approx 0$ for the semiconducting one. At $\epsilon >0$ the conductance steps in the semiconductor case are 2 times smaller, $\Delta G\approx G_0$, and have alternating lengths.