Theory of Metastability in Simple Metal Nanowires

Thermally induced conductance jumps of metal nanowires are modeled using stochastic Ginzburg-Landau field theories. Changes in radius are predicted to occur via the nucleation of surface kinks at the wire ends, consistent with recent electron microscopy studies. The activation rate displays nontrivial dependence on nanowire length, and undergoes first- or second-order-like transitions as a function of length. The activation barriers of the most stable structures are predicted to be universal, i.e., independent of the radius of the wire, and proportional to the square root of the surface tension. The reduction of the activation barrier under strain is also determined.

Figure 1

Electron-shell potential $V(R)$ at zero temperature. The top axis shows the conductance values of the most stable wires in units of the conductance quantum, $G_0=2e^2/h$.

Figure 2

The activation energy $\Delta E$ as a function of the wire length $L$, for the cubic potential with Neumann boundary conditions (top). The dashed line indicates the critical wire length $L_c$ at which the transition takes place. The bottom panel shows the prefactor ${\Gamma }_0$, and the inset displays the activation barrier for the full potential $U(\varphi )$ for $k_F{R}_0=12.79$, exhibiting a succession of first order phase transitions.

Figure 3

The activation energy $\Delta E_{\infty }$ as a function of radius for a typical stable zone in Au. Solid curve: numerical result for the full potential $U(\varphi )$, Eq. (6); dashed curve: result from Eq. (13) using the best cubic-polynomial fit to $U(\varphi )$. The wire radius is related to the tensile stress (upper axis).