The surface dynamics and thermodynamics of metal nanowires are investigated in a continuum model. Competition between surface tension and electron-shell effects leads to a rich stability diagram, with fingers of stability extending to extremely high temperatures for certain magic conductance values. The linearized dynamics of the nanowire's surface are investigated, including both acoustic surface phonons and surface self-diffusion of atoms. On the stability boundary, the surface exhibits critical fluctuations, and the nanowire becomes inhomogeneous. Some stability fingers coalesce at higher temperatures, or exhibit overhangs, leading to reentrant behavior. The nonlinear surface dynamics of unstable nanowires are also investigated in a single-mode approximation. We find evidence that some unstable nanowires do not break, but rather neck down to the next stable radius.
A linear stability analysis of metallic nanowires is performed in the free-electron model using quantum chaos techniques. It is found that the classical instability of a long wire under surface tension can be completely suppressed by electronic shell effects, leading to stable cylindrical configurations whose electrical conductance is a magic number 1, 3, 5, 6,... times the quantum of conductance. Our results are quantitatively consistent with recent experiments with alkali metal nanowires.
The conducting and mechanical properties of a metallic nanowire formed at the junction between two macroscopic metallic electrodes are investigated. Both two-and three-dimensional wires with a W(ide)-N(arrow)-W(ide) geometry are modelled in the free-electron approximation with hard-wall boundary conditions. Tunneling and quantum-size effects are treated exactly using the scattering matrix formalism. Oscillations of order EF /λF in the tensile force are found when the wire is stretched to the breaking point, which are synchronized with quantized jumps in the conductance. The force and conductance are shown to be essentially independent of the width of the wide sections (electrodes). The exact results are compared with an adiabatic approximation; the later is found to overestimate the effects of tunneling, but still gives qualitatively reasonable results for nanowires of length L ≫ λF , even for this abrupt geometry. In addition to the force and conductance, the net charge of the nanowire is calculated and the effects of screening are included within linear response theory. Mesoscopic charge fluctuations of order e are predicted which are strongly correlated with the mesoscopic force fluctuations. The local density of states at the Fermi energy exhibits nontrivial behavior which is correlated with fine structure in the force and conductance, showing the importance of treating the whole wire as a mesoscopic system rather than treating only the narrow part.
Convergent semiclassical trace formulas for the density of states and the 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 nN, in agreement with recent experiments. PACS numbers: 73.40.Jn, 03.65.Sq, 05.45.Mt, An intriguing question posed by Kac [1] is the following: "Can one hear the shape of a drum?" That is, given the spectrum of the wave equation [1] or Schrödinger's equation for free particles [2] on a domain, can one infer the domain's shape? This question was answered in the negative [1,2]; nevertheless there is an intimate relation between the two. In the context of metallic nanocohesion [3-10], a related question has recently emerged: "Can one feel the shape of a metallic nanocontact?" It was shown experimentally [3] that the cohesive force of Au nanocontacts exhibits mesoscopic oscillations on the nano-Newton scale, which are synchronized with steps of order 2e 2 ͞h in the contact conductance. In a previous article [4], it was argued that these mesoscopic force oscillations, like the corresponding conductance steps [11], can be understood by considering the nanocontact as a waveguide for the conduction electrons (which are responsible for both conduction and cohesion in simple metals). Each quantized mode transmitted through the contact contributes 2e 2 ͞h to the conductance [11] and a force of order´F͞l F to the cohesion, where l F is the de Broglie wavelength at the Fermi energy´F. It was shown by comparing various geometries [4] that the force oscillations were determined by the area and symmetry of the narrowest cross section of the contact, and depended only weakly on other aspects of the geometry. Subsequent studies confirmed this observation, both for generic geometries [5,7,8,10], whose classical dynamics is chaotic, and for special geometries [6,9], whose classical dynamics is integrable. The insensitivity of the force oscillations to the details of the geometry, along with the approximate independence of their rms size on the contact area, was termed universality in Ref. [4]. A fundamental explanation of the universality observed in both the model calculations [4-10] and the experiments [3] has so far been lacking.In this Letter, we derive semiclassical trace formulas for the force and charge oscillations of a metallic nanocontact, modeled as a constriction in an electron gas with hardwall boundary conditions (see Fig. 1, inset), by adapting methods from quantum chaos [12][13][14][15] to describe the quantum mechanics of such an open system. It is found that Gutzwiller-type trace formulas [12][13][14][15], which typically do not converge for closed systems, not only converge but give quantitatively accurate results for open quant...
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