Universality in metallic nanocohesion: a quantum chaos approach

TL;DR

This paper derives semiclassical trace formulas to explain universal oscillations in the cohesive force of metallic nanoconstrictions, linking quantum chaos and classical orbit instability, with results aligning with experimental data.

Contribution

It introduces a quantum chaos approach to model nanocohesion, revealing universal force oscillations dependent on classical dynamics crossover.

Findings

Universal force oscillations depend only on a quantum parameter

Oscillation amplitudes are around 1 nano-Newton

Quantum tunneling relates to classical orbit instability

Abstract

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.