Transport through normal-metal–graphene contacts

Conductance of zigzag interfaces between a graphene sheet and a normal metal is investigated in the tight-binding approximation. Boundary conditions, valid for a variety of scattering problems, are constructed and applied to the normal-metal–graphene–normal-metal junctions. At the Dirac point, the conductance is determined solely by the evanescent modes and is inversely proportional to the length of the junction. It is also independent of the interface resistance. Away from the Dirac point, the propagating modes’ contribution dominates. We also observe that even in the junctions with high interface resistance, for certain modes, ideal transmission is possible via Fabry-Pérot-like resonances.

Figure 1

(a) Typical experimental contact configuration: metallic leads overlaying graphene. The contact occurs over many microlinks, which leads to equilibration of the chemical potentials in the metal and in graphene. In the case of tight coupling under the contact, the band structures of graphene and the metal are expected to “fuse.” (b) Theoretical model of a contact—tunneling between the metal leads and graphene zigzag edges. It can be thought of as a limiting case of strong coupling (a) with the tunable hybridization between contact and the edge.

Figure 2

(a) A zigzag interface between square and graphene lattices. Sites belonging to the two sublattices in graphene are indicated by $a$ and $b$. On the top, boundary conditions are sketched: We introduced two columns of fictitious amplitudes, $c_1$ in graphene and $d_{-1}^b$ in the square lattice, used them for wave-function matching at the interface. [(b) and (c)] A NGN contact of width $L=a_g(3N+1)∕2$ with (b) an odd-integer or (c) an even-integer value of $N$.