Front propagation into unstable metal nanowires

Long, cylindrical metal nanowires have recently been observed to form and be stable for seconds at a time at room temperature. Their stability and structural dynamics is well described by a continuum model, the nanoscale free-electron model, which predicts cylinders in certain intervals of radius to be linearly unstable. In this paper, I study how a small, localized perturbation of such an unstable wire grows exponentially and propagates along the wire with a well-defined front. The front is found to be pulled, and forms a coherent pattern behind it. It is well described by a linear marginal stability analysis of front propagation into an unstable state. In some cases, nonlinearities of the wire dynamics are found to trigger an invasive mode that pushes the front. Experimental procedures that could lead to the observation of this phenomenon are suggested.Comment: 6 pages, 4 figure

Noisy Classical Field Theories with Two Coupled Fields: Dependence of Escape Rates on Relative Field Stiffnesses

Exit times for stochastic Ginzburg-Landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined, the potential in which the fields deterministically evolve, and the relative stiffness of the fields themselves. The latter is of particular importance in that physical applications will generally require different relative stiffnesses, but the effect of varying field stiffnesses has not heretofore been studied. In this paper, we explore the complete phase diagram of escape times as they depend on the various problem parameters. In addition to finding a transition in escape rates as the relative stiffness varies, we also observe a critical slowing down of the string method algorithm as criticality is approached.Comment: 16 pages, 10 figure

On the Stability and Structural Dynamics of Metal Nanowires

This article presents a brief review of the nanoscale free-electron model, which provides a continuum description of metal nanostructures. It is argued that surface and quantum-size effects are the two dominant factors in the energetics of metal nanowires, and that much of the phenomenology of nanowire stability and structural dynamics can be understood based on the interplay of these two competing factors. A linear stability analysis reveals that metal nanocylinders with certain magic conductance values G=1, 3, 6, 12, 17, 23, 34, 42, 51, 67, 78, 96, ... times the conductance quantum are exceptionally stable. A nonlinear dynamical simulation of nanowire structural evolution reveals a universal equilibrium shape consisting of a magic cylinder suspended between unduloidal contacts. The lifetimes of these metastable structures are also computed.Comment: 8 pages, 6 figure

Quantum Necking in Stressed Metallic Nanowires

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 PDE 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.Comment: 4 pages, 3 postscript figures. New result on universal equilibrium shape

Stability and Symmetry Breaking in Metal Nanowires

A general linear stability analysis of simple metal nanowires is presented using a continuum approach which correctly accounts for material-specific surface properties and electronic quantum-size effects. The competition between surface tension and electron-shell effects leads to a complex landscape of stable structures as a function of diameter, cross section, and temperature. By considering arbitrary symmetry-breaking deformations, it is shown that the cylinder is the only generically stable structure. Nevertheless, a plethora of structures with broken axial symmetry is found at low conductance values, including wires with quadrupolar, hexapolar and octupolar cross sections. These non-integrable shapes are compared to previous results on elliptical cross sections, and their material-dependent relative stability is discussed.Comment: 12 pages, 4 figure

Universality in metallic nanocohesion: a quantum chaos approach

Convergent semiclassical trace formulae for the density of states and cohesive force of a narrow constriction in an electron gas, whose classical motion is either chaotic or integrable, are derived. It is shown that mode quantization in a metallic point contact or nanowire leads to universal oscillations in its cohesive force: the amplitude of the oscillations depends only on a dimensionless quantum parameter describing the crossover from chaotic to integrable motion, and is of order 1 nano-Newton, in agreement with recent experiments. Interestingly, quantum tunneling is shown to be described quantitatively in terms of the instability of the classical periodic orbits.Comment: corrects spelling of one author name on abstract page (paper is unchanged

The Order of Phase Transitions in Barrier Crossing

A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the transition can be first or second-order, but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier. In this paper, we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary both in space and time, and whose zero-noise dynamics are governed by a smooth polynomial potential. We show that a quartic potential barrier can only have second-order transitions, confirming an earlier conjecture [1]. We then derive, through a combination of analytical and numerical arguments, both necessary conditions and sufficient conditions to have a first-order vs. a second-order transition in noise-induced activation behavior, for a large class of systems with smooth polynomial potentials of arbitrary order. We find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version accepted for publication by Phys. Rev.

Stability of Metal Nanowires at Ultrahigh Current Densities

We develop a generalized grand canonical potential for the ballistic nonequilibrium electron distribution in a metal nanowire with a finite applied bias voltage. Coulomb interactions are treated in the self-consistent Hartree approximation, in order to ensure gauge invariance. Using this formalism, we investigate the stability and cohesive properties of metallic nanocylinders at ultrahigh current densities. A linear stability analysis shows that metal nanowires with certain {\em magic conductance values} can support current densities up to 10^11 A/cm^2, which would vaporize a macroscopic piece of metal. This finding is consistent with experimental studies of gold nanowires. Interestingly, our analysis also reveals the existence of reentrant stability zones--geometries that are stable only under an applied bias.Comment: 12 pages, 6 figures, version published in PR

The Escape Problem in a Classical Field Theory With Two Coupled Fields

We introduce and analyze a system of two coupled partial differential equations with external noise. The equations are constructed to model transitions of monovalent metallic nanowires with non-axisymmetric intermediate or end states, but also have more general applicability. They provide a rare example of a system for which an exact solution of nonuniform stationary states can be found. We find a transition in activation behavior as the interval length on which the fields are defined is varied. We discuss several applications to physical problems.Comment: 24 page