Conduction Mechanism in a Molecular Hydrogen Contact

We present first principles calculations for the conductance of a hydrogen molecule bridging a pair of Pt electrodes. The transmission function has a wide plateau with $T\approx 1$ which extends across the Fermi level and indicates the existence of a single, robust conductance channel with nearly perfect transmission. Through a detailed Wannier function analysis we show that the ${\mathrm{H}}_2$ bonding state is not involved in the transport and that the plateau forms due to strong hybridization between the ${\mathrm{H}}_2$ antibonding state and states on the adjacent Pt atoms. The Wannier functions furthermore allow us to derive a resonant-level model for the system with all parameters determined from the fully self-consistent Kohn-Sham Hamiltonian.

Figure 1

Calculated transmission for the molecular hydrogen contact shown in the inset. For comparison both the $\mathbf{k}$-point sampled transmission and the $\Gamma$-point transmission are shown. The $\Gamma$-point transmission has more structure; however, the qualitative features of the curves are essentially the same. The wide plateau with $T\approx 1$ extending across the Fermi level indicates a single, very robust conductance channel with nearly perfect transmission.

Figure 2

Calculated transmission for the structure shown in the inset of Fig. 1 when all coupling to the bonding, respectively, the antibonding, ${\mathrm{H}}_2$ state has been cut. The full transmission has been repeated for comparison. The narrow peak around $-7\mathrm{e}\mathrm{V}$ is clearly due to the bonding state, while the peak at $-2\mathrm{e}\mathrm{V}$ and the wide plateau around the Fermi level almost exclusively involve the antibonding state.

Figure 3

Contour plots of the orbitals determining the transport properties of the hydrogen contact: the ${\mathrm{H}}_2$ antibonding state, $|a⟩$, and the corresponding left and right group orbitals, $|g_L⟩,|g_R⟩$. The left (right) group orbital has been constructed by applying the DFT Hamiltonian to $|a⟩$ and then projecting onto the Wannier functions of the left (right) part of the contact.

Figure 4

The upper panel shows the transmission together with the projected DOS for the ${\mathrm{H}}_2$ antibonding state and the corresponding left group orbital. The lower panel shows the same quantities obtained from the single-level model when ${\rho }_g^0$ is approximated by a semielliptical band, and we use the coupling, $V$, and on-site energy, ${\epsilon }_a$, from the first principles calculation.