Signature of chirality in scanning-probe imaging of charge flow in graphene

We theoretically propose to directly observe the chiral nature of charge carriers in graphene mono- and bilayers within a controlled scattering experiment. The charge located on a capacitively coupled scanning-probe microscope (SPM) tip acts as a scattering center with controllable position on the graphene sheet. Unambiguous features from the chirality of the particles in single and bilayer graphene arise in the ballistic transport in the presence of such a scattering center. To model the scattering from the smooth potential created by the SPM tip, we derive the space-dependent electron Green function in graphene and solve the scattering problem within the first-order Born approximation. We calculate the current through a device with a SPM tip between two constrictions (quantum point contacts) as a function of the tip position.

Figure 1

The proposed setup. An applied bias voltage $V$ between the source S and the middle region M injects a current into the graphene sheet. The injected electrons scatter from an artificial scatterer created by a SPM tip above the surface. The flux of electrons that are coherently scattered into the drain D can be detected in the drain current $I$.

Figure 2

Formulation of the scattering problem: an incoming plane wave propagating along the $x$ direction hits the scattering potential. A detector measures the outgoing flux of the scattered wave as a function of the deflection angle $\varphi$.

Figure 3

Differential cross section normalized by $2\pi {\left(kR\right)}^4{(U_0∕E)}^2$ in units of $1∕k$ for a circular scatterer of the Gaussian shape. For single layer graphene, the Berry phase of $\pi$ prohibits backscattering, while for bilayer graphene, the Berry phase of $2\pi$ prohibits rectangular deflection. The radius of the scatterer is chosen $kR=0.5$ for this plot.

Figure 4

Relative change $\Delta I∕I_0$ of the drain (D) current as a function of the tip position $(x,y)$ in units of ${\lambda }_F$. The existence of two possible trajectories, one directly from source (S) to drain, the other via the scatterer at $(x,y)$, generates an interference pattern. Since scattering under an angle of $\pi ∕2$ is forbidden for a bilayer, a circle without signal (dashed white line) appears. The scattering potential radius and strength were chosen to be $Rk=1$ and $U_0∕E=0.3$, respectively.

Figure 5

Alternative setup where the QPCs have been replaced by two additional SPM tips playing the role of the source and drain contacts.