Stretching dependence of the vibration modes of a single-molecule $\mathrm{Pt}-{\mathrm{H}}_2-\mathrm{Pt}$ bridge

A conducting bridge of a single hydrogen molecule between Pt electrodes is formed in a break junction experiment. It has a conductance near the quantum unit, $G_0=2e^2∕h$, carried by a single channel. Using point-contact spectroscopy three vibration modes are observed and their variation upon isotope substitution is obtained. The stretching dependence for each of the modes allows uniquely classifying them as longitudinal or transversal modes. The interpretation of the experiment in terms of a $\mathrm{Pt}-{\mathrm{H}}_2-\mathrm{Pt}$ bridge is verified by density-functional theory calculations for the stability, vibrational modes, and conductance of the structure.

Figure 1

Differential conductance curve for ${\mathrm{D}}_2$ contacted by Pt leads. The $dI∕dV$ curve (top) was recorded over $1\min$, using a standard lock-in technique with a voltage bias modulation of $1\mathrm{meV}$ at a frequency of $700\mathrm{Hz}$. The lower curve shows the numerically obtained derivative. The spectrum for ${\mathrm{H}}_2$ in the inset shows two phonon energies, at 48 and $62\mathrm{meV}$. All spectra show some, usually weak, anomalies near zero bias that can be partly due to excitation of modes in the Pt leads, partly due to two-level systems near the contact (Ref. 19).

Figure 2

Distribution of vibration mode energies observed for ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ between Pt electrodes, with a bin size of $2\mathrm{meV}$. The peaks in the distribution for ${\mathrm{H}}_2$ are marked by arrows and their widths by error margins. These positions and widths were scaled by the expected isotope shifts, $\sqrt{2∕3}$ for HD and $\sqrt{1∕2}$ for ${\mathrm{D}}_2$, from which the arrows and margins in the upper two panels have been obtained.

Figure 3

$dI∕dV$ spectrum (top) for $\mathrm{Pt}\text{−}{\mathrm{D}}_2$ junctions and their numerical derivatives $d^{2}I∕d{V}^2$ (bottom). The spectrum (b) was obtained on the same contact as (a) after stretching the junction by $0.04\mathrm{nm}$. They are two spectra out of a series of six and the complete evolution of the two modes is shown in the inset.

Figure 4

Calculated vibrational frequencies for the hydrogen atoms in the contact as a function of elongation of the supercell. The inset shows the atomic arrangement in the supercell. The lower panel shows the calculated conductance.