Structural and magnetic transitions in ensembles of mesoscopic Peierls rings in a magnetic flux

We investigate effects of a magnetic flux Phi threading mesoscopic Peierls rings. Both isolated rings and ensembles of rings are considered and quantu m phonon fluctuations are accounted for. Significant qualitative and quanti tative modifications to the mean field results are obtained. Quantum fluctu ations yield a continuous structural Peierls change occurring without symme try breaking and a Phi-dependent tunneling splitting. The latter yields a P hi-modulated ultrasound or hypersound absorption that could be detected exp erimentally. Important differences exist between an isolated ring and an en semble of rings. To perform ensemble averaging, we propose a new and simple method. Unlike isolated rings, ensembles possess structural and magnetic p roperties 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 i s hc/2e, half the period for an isolated ring. An appealing magnetic behavi or with an interplay between dia- and paramagnetism is found in ensembles t hat could be experimentally investigated by means of a SQUID technique. [S0 163-1829(99)09825-2].