Thermal stability of mode-locking steps in charge density waves

We examine the stability of mode-locking steps in incommensurate charge density waves in the presence of finite temperature. The steps turn out to be quite stable by showing a series of definite plateaus in the current-voltage characteristics. We also study the dynamical phase transition from a mode-locked state to an unlocked state by assuming the fact that there exists a similar power-law scaling hypothesis as in a pinning-depinning phase transition. The critical exponents around both the edges of the mode-locking steps are found to have similar values for the depinning transition.