Quantum pumping in graphene

We show that graphene-based quantum pumps can tap into evanescent modes, which penetrate deeply into the device as a consequence of Klein tunneling. The evanescent modes dominate pumping at the Dirac point, and give rise to a universal response under weak driving for short and wide pumps, in close analogy to their role in the minimal conductivity in ballistic transport. In contrast, evanescent modes contribute negligibly to normal pumps. Our findings add an incentive for the exploration of graphene-based nanoelectronic devices.

Figure 1

(Color online) Left panels: Illustration of a graphene quantum pump with highly doped (metallic) contacts. Two gates at voltage $V_1\left(t\right)$ and $V_2\left(t\right)$ control the time-dependent on-site energy $U_1\left(t\right)$ and $U_2\left(t\right)$ in the graphene flake over a pumping cycle. This induces a charge transport between two contact electrodes, separated by a distance $L$. The working point of the device can be further controlled by an additional back gate with voltage $V_0$. Right panels: Snapshots of the onsite potential along the quantum pump, for highly doped (metallic) contacts (top) and undoped contacts (bottom). The solid base line shows the potential at the working point. We show that evanescent modes induced by metallic contacts enable finite charge pumping at vanishing nominal charge-carrier density, in striking contrast to the case of normal pumps where the nanoribbon is replaced by a normal conductor.

Figure 2

(Color online) Momentum distribution of pumped charge per mode ${\chi }_q^u$ as a function of mode index $q$ for varying carrier concentration (parametrized by the Fermi momentum $k_F$). Blue and brown represent opposite directions of pumping (left to right or right to left). In graphene, the propagating mode with $q=0$ (normal incidence) cannot be pumped due to the Klein paradox. In the case of graphene with heavily doped leads, however, significant pumping is possible due to the contribution of the evanescent modes ($\left|q\right|>k_F$, delineated by the dashed line), which dominate around the Dirac point $\left(k_F=0\right)$. The other pumps can only drive current through the propagating modes.

Figure 3

(Color online) Total dimensionless response per mode ${\chi }^u$ for short and wide pumps $\left(W⪢L\right)$, as a function of the carrier concentration (parametrized by the Fermi momentum $k_F$). Left panel: graphene pumps. Right panel: Normal-conducting pumps. Solid lines correspond to pumps with highly doped leads (which tend to 1/4 at $k_{F}L⪢1$), while dashed lines correspond to pumps with undoped leads (which tend to 1/2). At the charge neutrality ($k_{F}L\to 0$, see inset), evanescent modes allow for a finite charge transfer in the highly doped-leads graphene pump, whose response saturates at a universal (sample independent) value of 0.0288.