Statistical properties of charged interfaces

Abstract

We consider the equilibrium statistical properties of interfaces submitted tocompeting interactions: a long-range repulsive Coulomb interaction inherent tothe charged interface and a short-range, anisotropic, attractive one due to eitherelasticity or confinement. We focus on one-dimensional interfaces such as strings.Model systems considered for applications are mainly aggregates of solitons inpolyacetylene and other charge-density wave systems, domain lines inuniaxial ferroelectrics and the stripe phase of oxides. At zero temperature,we find a shape instability which leads, via phase transitions, to tiltedphases. Depending on the regime, elastic or confinement, the order of thezero-temperature transition changes. Thermal fluctuations lead to a pure Coulombroughening of the string, in addition to the usual one, and to the presenceof angular kinks. We suggest that such instabilities might explain thetilting of stripes in cuprate oxides. The three-dimensional problem of thecharged wall is also analysed. The latter experiences instabilities towardsvarious tilted phases separated by a tricritical point in the elastic regime. Inthe confinement regime, the increase of dimensionality favours either themelting of the wall into a Wigner crystal of its constituent charges or astrongly inclined wall which might have been observed in nickelate oxides.