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

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

Electronic and atomic shell structure in aluminum nanowires

We report experiments on aluminum nanowires in ultra-high vacuum at room temperature that reveal a periodic spectrum of exceptionally stable structures. Two "magic" series of stable structures are observed: At low conductance, the formation of stable nanowires is governed by electronic shell effects whereas for larger contacts atomic packing dominates. The crossover between the two regimes is found to be smooth. A detailed comparison of the experimental results to a theoretical stability analysis indicates that while the main features of the observed electron-shell structure are similar to those of alkali and noble metals, a sequence of extremely stable wires plays a unique role in Aluminum. This series appears isolated in conductance histograms and can be attributed to "superdeformed" non-axisymmetric nanowires.Comment: 15 pages, 9 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 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

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.

Finite Temperature Theory of Metastable Anharmonic Potentials

The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a function of temperature. The family of classical paths, saddle points for the action, is derived in terms of Jacobian elliptic functions whose periodicity sets the energy-temperature correspondence. The period of the classical oscillations varies monotonically with the energy up to the sphaleron, pointing to a smooth crossover from the quantum to the activated regime. The softening of the quantum fluctuation spectrum is evaluated analytically by the theory of the functional determinants and computed at low $T$ up to the crossover. In particular, the negative eigenvalue, causing an imaginary contribution to the partition function, is studied in detail by solving the Lam\`{e} equation which governs the fluctuation spectrum. For a heavvy particle mass, the decay rate shows a remarkable temperature dependence mainly ascribable to a low lying soft mode and, approaching the crossover, it increases by a factor five over the predictions of the zero temperature theory. Just beyond the peak value, the classical Arrhenius behavior takes over. A similar trend is found studying the quartic metastable potential but the lifetime of the latter is longer by a factor ten than in a cubic potential with same parameters. Some formal analogies with noise-induced transitions in classically activated metastable systems are discussed.Comment: European Physical Journal B EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 200