A unified treatment of the cohesive and conducting properties of metallic nanostructures in terms of the electronic scattering matrix is developed. A simple picture of metallic nanocohesion in which conductance channels act as delocalized chemical bonds is derived in the jellium approximation. Universal force oscillations of order´F͞l F are predicted when a metallic quantum wire is stretched to the breaking point, which are synchronized with quantized jumps in the conductance.[S0031-9007(97)04243-9] PACS numbers: 73.20.Dx, 03.40.Dz, 62.20.Fe, 73.40.Jn Cohesion in metals is due to the formation of bands, which arise from the overlap of atomic orbitals. In a metallic constriction with nanoscopic cross section, the transverse motion is quantized, leading to a finite number of subbands below the Fermi energy´F. A striking consequence of these discrete subbands is the phenomenon of conductance quantization [1]. The cohesion in a metallic nanoconstriction must also be provided by these discrete subbands, which may be thought of as chemical bonds which are delocalized over the cross section. In this Letter, we confirm this intuitive picture of metallic nanocohesion using a simple jellium model. Universal force oscillations of order´F͞l F are predicted in metallic nanostructures exhibiting conductance quantization, where l F is the Fermi wavelength. Our results are in quantitative agreement with the recent pioneering experiment of Rubio, Agraït, and Vieira [2], who measured simultaneously the force and conductance during the formation and rupture of an atomic-scale Au contact. Similar experimental results have been obtained independently by Stalder and Dürig [3].Quantum-size effects on the mechanical properties of metallic systems have previously been observed in ultrasmall metal clusters [4], which exhibit enhanced stability for certain magic numbers of atoms. These magic numbers have been rather well explained in terms of a shell model based on the jellium approximation [4]. The success of the jellium approximation in these closed nanoscopic systems motivates its application to open (infinite) systems, which are the subject of interest here. We investigate the conducting and mechanical properties of a nanoscopic constriction connecting two macroscopic metallic reservoirs. The natural framework in which to investigate such an open system is the scattering approach developed by Landauer [5] and Büttiker [6]. Here, we extend the formalism of Ref.[6], which describes electrical conduction, to describe the mechanical properties of a confined electron gas as well.For definiteness, we consider a constriction of length L in an infinitely long cylindrical wire of radius R, as shown in Fig. 1. We neglect electron-electron interactions, and assume the electrons to be confined along the z axis by a hard-wall potential at r r͑z͒. This model is considerably simpler than a self-consistent jellium calculation [4], but should suffice to capture the essential physics of the problem. Outside the constriction, the Schrödinger equation ...

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.

When a macroscopic metallic wire is subject to tensile stress, it necks down smoothly as it elongates. We show that nanowires with radii comparable to the Fermi wavelength display remarkably different behavior. Using concepts from fluid dynamics, a partial differential equation for nanowire shape evolution is derived from a semiclassical energy functional that includes electron-shell effects. A rich dynamics involving movement and interaction of kinks connecting locally stable radii is found, and a new class of universal equilibrium shapes is predicted.

The cohesion and conductance of a point contact in a two-dimensional metallic nanowire are investigated in an independent-electron model with hard-wall boundary conditions. All properties of the nanowire are related to the Green's function of the electronic scattering problem, which is solved exactly via a modified recursive Green's function algorithm. Our results confirm the validity of a previous approach based on the WKB approximation for a long constriction, but find an enhancement of cohesion for shorter constrictions. Surprisingly, the cohesion persists even after the last conductance channel has been closed. For disordered nanowires, a statistical analysis yields well-defined peaks in the conductance histograms even when individual conductance traces do not show well-defined plateaus. The shifts of the peaks below integer multiples of $2e^2/h$, as well as the peak heights and widths, are found to be in excellent agreement with predictions based on random matrix theory, and are similar to those observed experimentally. Thus abrupt changes in the wire geometry are not necessary for reproducing the observed conductance histograms. The effect of disorder on cohesion is found to be quite strong and very sensitive to the particular configuration of impurities at the center of the constriction.Comment: 10 pages, 7 figures, submitted to Phys. Rev. B, discussions of the equilibrium geometry and of the effects of disorder on the cohesion have been modifie