Stability and Symmetry Breaking in Metal Nanowires I: Toward a Theory of Metallic Nanocohesion

Capri Spring School on Transport in Nanostructures, March 29, 2007

Charles Stafford

Acknowledgements

Students:Chang-hua Zhang (Ph.D. 2004) Dennis Conner (M.S. 2006)Nate Riordan

Postdoc: Jérôme Bürki

Coauthors:Dionys Baeriswyl, Ray Goldstein, Hermann Grabert, Frank Kassubek, Dan Stein, Daniel Urban

Funding:NSF Grant Nos. DMR0072703 and DMR0312028; Research Corp.

1. How thin can a metal wire be?

Surface-tension driven instability

T. R. Powers and R. E. Goldstein, PRL 78, 2555 (1997)

Cannot be overcome in classical MD simulations!

Fabrication of a gold nanowire using an electron microscope

Courtesy of K. Takayanagi, Tokyo Institute of Technology

QuickTime™ and a YUV420 codec decompressor are needed to see this picture.

Courtesy of K. Takayanagi, Tokyo Institute of Technology

Extrusion of a gold nanowire using an STM

What is holding the wires together? A mechanical analogue of conductance quantization?

Is electron-shell structure the key to understanding stable contact geometries?

A. I. Yanson, I. K. Yanson & J. M. van Ruitenbeek, Nature 400, 144 (1999);PRL 84, 5832 (2000); PRL 87, 216805 (2001)

Corrected Sharvin conductance:

T=90K

Conductance histograms of sodium nanocontacts

2. Nanoscale Free-Electron Model (NFEM)

• Model nanowire as a free-electron gas confined by hard walls.

• Ionic background = incompressible fluid.

• Most appropriate for s-electrons in monovalent metals.

• Regime:

• Metal nanowire = 3D open quantum billiard.

Scattering theory of conduction and cohesion

Electrical conductance (Landauer formula)

Grand canonical potential (independent electrons)

Electronic density of states (Wigner delay)

Quantum suppression of Shot noise

NFEM w/disorder

Gold nanocontacts

Multivalent atoms

Adiabatic + WKB approximations

Schrödinger equation decouples:

WKB scattering matrix for each 1D channel:

,

Comparison: NFEM vs. experiment

Exp:Theory:

Weyl expansion + Strutinsky theorem

Mean-field theory:

Weyl expansion:

Electron-shell potential

→ 2D shell structure favors certain “magic radii”

Classical periodic orbitsin a slice of the wire

NFEM vs. self-consistent Jellium calculation

Different constraints possible in NFEM

# of atoms

Physical properties (e.g., tensile force) depend only on energy differences:

Example of the Strutinsky theorem: self-consistentHartree approximation

Special case: the constant-interaction model

Last term is important!

Semiclassical power counting

Planck’s constant:

→ Surface energy dominates shell correction?!

3. Conclusions to Lecture 1

Nanoscale Free Electron Model is able to describe quantumtransport and metallic nanocohesion on an equal footing,explaining observed correlations in force and conductance ofmetal nanocontacts.

Total energy calculations apparently not sufficient to addressnanowire stability.

What more is needed? See Lecture 2!