Energetics, forces, and quantized conductance in jellium-modeled metallic nanowires

Abstract

Physical Review B 57, 4872 [1998]) Energetics and quantized conductance in jellium-modeled nanowires are investigated using the local-density-functionalbased shell correction method, extending our previous study of uniform-in-shape wires [C. Yannouleas and U. Landman, J. Phys. Chem. B 101, 5780 (1997)] to wires containing a variable-shaped constricted region. The energetics of the wire (sodium) as a function of the length of the volumeconserving, adiabatically shaped constriction, or equivalently its minimum width, leads to formation of self-selecting magic wire configurations, i.e., a discrete configurational sequence of enhanced stability, originating from quantization of the electronic spectrum, namely, formation of transverse subbands due to the reduced lateral dimensions of the wire. These subbands are the analogs of shells in finite-size, zero-dimensional fermionic systems, such as metal clusters, atomic nuclei, and 3 He clusters, where magic numbers are known to occur. These variations in the energy result in oscillations in the force required to elongate the wire and are directly correlated with the stepwise variations of the conductance of the nanowire in units of 2e 2 /h. The oscillatory patterns in the energetics and forces, and the correlated stepwise variation in the conductance are shown, numerically and through a semiclassical analysis, to be dominated by the quantized spectrum of the transverse states at the narrowmost part of the constriction in the wire.

Observation of Shell Structure in Sodium Nanowires

“…Second, the mechanism of level-bunching leading to fluctuations Ω(R) should also give rise to fluctuation corrections to G(R), which by itself would lead to peaks in the histograms even for a perfectly smooth distribu- , where R is given in units k −1 F ). The radii at the peak positions are compared with the radii corresponding to the magic numbers for sodium metal clusters (filled circles) [11] and with those expected from a semiclassical description for the fluctuations in the free energy for the nanowire (open triangles) [18,19].…”

Materials by numbers: Computations as tools of discovery

“…The propensity of materials systems of reduced size to undergo selfselection of size and shape, as well as their ability to spontaneously adopt optimal configurations by self-organization, are among the unique properties of nanoscale materials systems. Examples include magic number sequences that reflect enhanced stabilities of particular sizes [e.g., number of cluster atoms (20)(21)(22) or radii of nanowires (23)(24)(25)] originating from electronic shell effects (a concept familiar from nuclear structure studies) and͞or from particular geometrical atomic packing arrangements; shape deformations effects (21,22), akin to Jahn-Teller distortions (familiar in molecular and nuclear systems) that lift spectral degeneracies with consequent stabilization gained through such spontaneous symmetry-lowering (or breaking); and self-assembly processes underlying formation of nanostructures and nanoparticle arrays (10,(26)(27)(28)(29)(30).…”

Phase-Controlled Force and Magnetization Oscillations in Superconducting Ballistic Nanowires

“…The aperiodic variations of the AF originating from the change in the number of open channels upon elongation, are particularly pronounced at lower temperatures. Note however, that such aperiodic variations occur also for normal metal NW [4,6] and consequently separation of the SC-induced contribution may be difficult.…”

“…For normal metals the oscillatory behavior of the elongation forces [1] with the size of a NW formed between a surface and a retracting tip have been shown to be correlated with a quantized staircase behavior of the electrical conductance [3][4][5][6][7]. However, the influence of superconductivity (SC) on the nanomechanical properties of such NWs has not been explored yet, and these effects are the focus of this Letter.…”

“…The force oscillations (portrayed by the dependence of the force on the contact size) are determined by two distinct contributions: (i) a large phase-independent term ( operative also in normal-metal NWs ) of the order of N ⊥ ε F /λ F originating from incoherent contributions of all the conducting electrons to the thermodynamic potential [4][5][6], and (ii) a coherent SC-induced force (Eq. (4)- (6)).…”