Abstract
The effects of the spin-orbit coupling and its interplay with the Aharonov-Bohm flux on the Peierls instability and the persistent currents in one-dimensional mesoscopic rings are studied. Within the mean-field approximation, it is shown that the spin-orbit coupling will suppress the Peierls instability in one-dimensional mesoscopic rings, and if the spin-orbit coupling is strong enough, the Peierls instability will be destroyed completely even in the mean-field approximation. The parity effect on the Peierls instability is also discussed.
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