Melting of crystalline films with quenched random disorder

Abstract

According to the Kosterlitz-Thouless-Theory two-dimensional solid films melt by the unbinding of dislocation pairs. A model including quenched random impurities was already studied by Nelson [Phys. Rev. B 27 (1983) 2902], who predicted a reentrance into the disordered phase at low temperatures and weak disorder. New investigations of the physically related XY-model [e.g. T. Nattermann et al., J. Phys. (France) 5 (1995), 565] and a work of Cha and Fertig [Phys. Rev. Lett. 74 (1995) 4867] refuse this reentrant melting. In this work we map the system onto a two-dimensional vector Coulomb gas and via a renormalization we derive flow equations both for the square and for the triangular lattice. An analysis of these flow equations shows a new behaviour in the low-temperature range, where the reentrance into the non-crystalline phase with short-range order is not found, but the crystalline phase with quasi-long-range order is preserved below a critical disorder strength of \barσ_c = 1/16 π. Finally we estimate the influence of commensurate substrates and obtain phase diagrams, which show that the melting by dislocation unbinding can only be expected, if the lattice constant of the crystalline film is a multiple of the lattice constant of the substrate potential.