Theory of discommensurations and the commensurate-incommensurate charge-density-wave phase transition

The lowest-energy state of the incommensurate charge density wave (CDW) near the lock-in transition is found to be a distorted plane wave. An exact solution is found in the weak-coupling limit and the lock-in phase transition is continuous. A new defect is found in the commensurate CDW, a discommensuration, in which the phase of the CDW slips by 2π3 relative to the perfectly locked in CDW. The lock-in phase transition is interpreted as a defect melting transition with a finite density of discommensurations in the incommensurate state.