Scaling theory of the Peierls charge density wave in metal nanowires

The Peierls instability in multichannel metal nanowires is investigated. Hyperscaling relations are established for the finite-size, temperature, and wave-vector scaling of the electronic free energy. It is shown that the softening of surface modes at wave vector q=2 kF,ν leads to critical fluctuations of the wire's radius at zero temperature, where kF,ν is the Fermi wave vector 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.