Current-Voltage Curves of Atomic-Sized Transition Metal Contacts: An Explanation of Why Au is Ohmic and Pt is Not

We present an experimental study of current-voltage ($I\text{−}V$) curves on atomic-sized Au and Pt contacts formed under cryogenic vacuum (4.2 K). Whereas $I\text{−}V$ curves for Au are almost Ohmic, the conductance $G=I/V$ for Pt decreases with increasing voltage, resulting in distinct nonlinear $I\text{−}V$ behavior. The experimental results are compared with first principles density functional theory calculations for Au and Pt, and good agreement is found. The difference in conductance properties for Pt vs Au can be explained by the underlying electron valence structure: Pt has an open $d$ shell while Au has not.

Figure 1

Representative $I\text{−}V$ curves on ASCs of (a) Au and (b) Pt. The $I\text{−}V$ curves are fitted to the third-order polynomial from Eq. (1), and fits are plotted as dotted lines. Curves have been labeled by the low bias conductance $G$ obtained from the fit. For Pt, the low bias conductance $G$ for the curves is represented by the straight, dashed lines. Note that the voltage scale for Pt is a factor of 2.5 smaller than for Au. The inset in (b) shows a sketch of the MCBJ. The sample is made from a notched wire of Au or Pt with a purity of 99.999% and a diameter of 0.1 mm which is glued to a bendable substrate. The sample is mounted in a three-point bending device and placed in a vacuum pot which is lowered into liquid helium obtaining cryogenic vacuum. Then the wire is broken at the notch by bending the substrate with the center rod as indicated in the sketch. The break exposes clean fracture surfaces of bulk material from which ASCs can be formed and controlled using the stacked piezoelement.

Figure 2

Nonlinear term $G^{\prime \prime }$ vs low bias conductance $G$ for Au and Pt ASCs. Each point represents a fit to Eq. (1) of one $I\text{−}V$ curve on one ASC. There are points from 1240 Au and 834 Pt $I\text{−}V$ curves. The solid curve represents the mean value of $G^{\prime \prime }$ for Pt. It is drawn through points found by averaging over 50 successive Pt points.

Figure 3

(a) The atomic structure of a symmetric monatomic contact of Au and Pt between (100) electrodes and corresponding calculated $I\text{−}V$ curves. (b) Eigenchannel decomposition of the total transmission through the atoms for Au for 0 and 1 V (left panels) and Pt for 0 and 0.8 V (right panels). Because of the complicated structure for Pt the graphs are split with the $s$, $d_{z^2}$ channels in the upper window and the remaining channels in the lower window. The channels are labeled by their main orbital components ($z$ is the direction perpendicular to the electrode surfaces). $E_F$ is the Fermi energy at equilibrium. Dashed lines indicate the “voltage window” spanning $\pm \mathrm{e}\mathrm{V}/2$ on each side of $E_F$.