Scaling Theory of the Peierls-CDW in Metal Nanowires

TL;DR

This paper develops a scaling theory for the Peierls charge density wave in metal nanowires, showing how finite size, temperature, and wavevector influence the instability and predicting experimental conditions to induce CDW states.

Contribution

It introduces a comprehensive scaling framework for the Peierls instability in nanowires, linking surface mode softening to critical fluctuations and charge density wave formation.

Findings

Surface mode softening at specific wavevectors leads to radius fluctuations.

Finite-size effects induce critical fluctuations at zero temperature.

Strain can drive nanowires into the charge-density-wave regime.

Abstract

The Peierls instability in multi-channel metal nanowires is investigated. Hyperscaling relations are established for the finite-size-, temperature-, and wavevector-scaling of the electronic free energy. It is shown that the softening of surface modes at wavevector $q=2k_{F,\nu}$ leads to critical fluctuations of the wire's radius at zero temperature, where $k_{F,\nu}$ is the Fermi wavevector of the highest occupied channel. This Peierls charge density wave emerges as the system size becomes comparable to the channel correlation length. Although the Peierls instability is weak in metal nanowires, in the sense that the correlation length is exponentially long, we predict that nanowires fabricated by current techniques can be driven into the charge-density-wave regime under strain.