Resonant scattering in graphene with a gate-defined chaotic quantum dot

We investigate the conductance of an undoped graphene sheet with two metallic contacts and an electrostatically gated island (quantum dot) between the contacts. Our analysis is based on the matrix Green function formalism, which was recently adapted to graphene by Titov et al. [Phys. Rev. Lett. 104, 076802 (2010)]. We find pronounced differences between the case of a stadium-shaped dot (which has chaotic classical dynamics) and a disk-shaped dot (which has integrable classical dynamics) in the limit that the dot size is small in comparison to the distance between the contacts. In particular, for the stadium-shaped dot the two-terminal conductance shows Fano resonances as a function of the gate voltage, which cross over to Breit-Wigner resonances only in the limit of completely separated resonances, whereas for a disk-shaped dot sharp Breit-Wigner resonances resulting from higher angular momentum remain present throughout.

Figure 1

Stadium quantum dot (parameters $R$,$a$) in a rectangular graphene sample of dimensions $L\times W$. The sample is attached to metallic leads on the left and right sides, defining a two-terminal geometry.

Figure 2

Conductance versus gate voltage $U$ for an undoped graphene sheet with a gate-defined stadium-shaped quantum dot. The parameters of the numerical calculation are $2a/R=\sqrt{3}$ and $L/R=5$. The curves correspond to the numerical calculation using the method of Sec. 2, with contributions to the $T$ matrix up to $d$ wave (blue, solid), and to a direct numerical solution of the Dirac equation (red, points; data taken from Ref. 20).

Figure 3

First four conductance resonances: The conductance has been calculated using Eq. (10) with the $T$ matrix truncated after the $s$-wave (blue, dashed), $p$-wave (red, dotted), and $d$-wave (green, solid) angular momentum channel, corresponding to $M^{\prime }=0,1,2$, respectively. In the upper panel, we set $L/R=5$, while in the lower panel, $L/R=10$. The ratio $a/R$ remains the same as in Fig. 2.

Figure 4

Dependence of the first and second resonances on the ratio of dot size versus system size $R/L$.