First-order transition into a charge-density wave phase

The transition into a charge-density wave phase is analyzed theoretically. We argue that, for commensurate or nearly-commensurate charge-density wave, the transition may become first order. Such a remarkable departure from the more common second-order transition scenario is associated with additional `umklapp' terms one can include in the Landau free energy expansion in the commensurate or nearly-commensurate cases. The proposed mechanisms may be relevant for certain alloys demonstrating first-order transition into charge-density wave state. It may be generalized for spin-density wave phases as well.