The effect of dislocations on the roughening transition in the weak coupling approximation

The analysis of the roughening transition proposed by Nozieres and Gallet is extended to interfaces threaded with either randomly placed screw dislocations or dislocation loops. In both cases we consider a low density of dislocations which intersect normally with the surface leading to a local deformation of the crystal planes and to the formation of small steps in the interface. We show that dislocation loops do not change the roughening transition significantly: it still remains within the Kosterlitz-Thouless universality, class of phase transitions. In contrast, randomly placed screw dislocations modify the phase transition: the Kosterlitz-Thouless transition is rounded on a length scale of order the spacing of dislocations. However there is a transition at a slightly lower temperature for randomly placed screw dislocations: the super-roughening transition. This conclusion is only valid if the dislocations are randomly placed, not if they are distributed as closely spaced pairs of opposite sign.