Abstract
We investigate effects of a magnetic flux $\ensuremath{\Phi}$ threading mesoscopic Peierls rings. Both isolated rings and ensembles of rings are considered and quantum phonon fluctuations are accounted for. Significant qualitative and quantitative modifications to the mean field results are obtained. Quantum fluctuations yield a continuous structural Peierls change occurring without symmetry breaking and a $\ensuremath{\Phi}$-dependent tunneling splitting. The latter yields a $\ensuremath{\Phi}$-modulated ultrasound or hypersound absorption that could be detected experimentally. Important differences exist between an isolated ring and an ensemble of rings. To perform ensemble averaging, we propose a new and simple method. Unlike isolated rings, ensembles possess structural and magnetic properties that do not distinguish between average sizes $N=4n$ and $N=4n+2$ but rather between smaller and larger N. In ensembles, the flux period is $hc/2e,$ half the period for an isolated ring. An appealing magnetic behavior with an interplay between dia- and paramagnetism is found in ensembles that could be experimentally investigated by means of a SQUID technique.
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