Effective contact model for transport through weakly-doped graphene

Recent investigations address transport through ballistic charge-neutral graphene strips coupled to doped graphitic leads. This paper shows that identical transport properties arise when the leads are replaced by quantum wires. This duality between graphitic and metallic leads originates in the selection of modes with transverse momentum close to the $K$ points, and can be extended to a wide class of contact models. Among this class, we identify a simple, effective contact model, which provides an efficient tool to study the transport through extended weakly-doped graphitic systems.

Figure 1

A graphene sample, modeled as a hexagonal lattice (lattice constant $a$), is attached to leads formed either by doped graphene (top) or by a quantum wire, modeled as a commensurably matched square lattice with lattice constant $\sqrt{3}a$ (bottom). The charge carrier density in the leads is controlled by a gate potential $V_g$, while the central graphitic region is held close to the charge-neutrality point. The paper demonstrates that both leads are equivalent when the gate potential is suitably adjusted and further extends this duality to a broad class of leads and contacts, which all share the properties of a simple effective contact model.

Figure 2

Gate-voltage dependence of the conductivity $\sigma =(\mathcal{L}∕\mathcal{W})G$ (in units of $e^2∕h$) and the shot-noise Fano factor $F$ of an undoped graphene strip of width $\mathcal{W}=152\sqrt{3}a$ and length $\mathcal{L}=30a$. The open data points are obtained by numerical computations for square-lattice leads (left) and hexagonal-lattice leads (right). The solid curves are the prediction of the effective contact model [Eq. (18)] with $\mu$ given by Eq. (10, 11), respectively. The dashed curves are the analytical expressions (12, 13, 14, 15) obtained within the saddle-point approximation.

Figure 3

Gate-voltage dependence of the conductance $G$ (in units of $e^2∕h$) and the shot-noise Fano factor $F$ for a weakly-doped circular graphene sample $(E_F=\gamma ∕10)$ of radius $\mathcal{R}=100\sqrt{3}a$, connected to leads of width $\mathcal{W}=60\sqrt{3}a$. The data points are obtained by numerical computations for square-lattice leads (left) and hexagonal-lattice leads (right). The curves are the predictions of the effective contact model [Eq. (18)] with $\mu$ given by Eq. (10) or (11), respectively.

Figure 4

(a) Brillouin zone for a square lattice with lattice constant $\sqrt{3}a$. (b) Hexagonal Brillouin zone for a honeycomb lattice with lattice constant $a$ (dashed) and its rearrangement into a rectangular Brillouin zone (solid). The numbered triangles denote regions which are transported with reciprocal lattice vectors. The solid dots denote the $K$ points.