Pinning of stripes in cuprate superconductors

We examine the effects of disorder on striped phases in high-temperature superconductors and related materials. In the presence of quenched disorder, pinning by the atomic lattice - which might give rise to commensuration effects - is irrelevant for the stripe array on large length scales. As a consequence, the stripes have divergent displacement fluctuations and topological defects are present at all temperatures. Therefore the positional order of the stripe array is short ranged, with a finite correlation length even at zero temperature. Thus lock-in phenomena can exist only as crossovers but not as transitions. In addition, this implies the glassy nature of stripes observed in recent experiments.