Conductivity of twin walls - surface junctions in ferroelastics:   interplay of deformation potential, octahedral rotations, improper   ferroelectricity and flexoelectric coupling
  Electronic and structural phenomena at the twin domain wall-surface junctions in the ferroelastic materials are analyzed. Carriers accumulation caused by the strain-induced band structure changes originated via the deformation potential mechanism, structural order parameter gradient, rotostriction and flexoelectric coupling is explored. Approximate analytical results show that inhomogeneous elastic strains, which exist in the vicinity of the twin walls - surface junctions due to the rotostriction coupling, decrease the local band gap via the deformation potential and flexoelectric coupling mechanisms. This is the direct mechanism of the twin walls static conductivity in ferroelastics and, by extension, in multiferroics and ferroelectrics. On the other hand, flexoelectric and rotostriction coupling leads to the appearance of the improper polarization and electric fields proportional to the structural order parameter gradient in the vicinity of the twin walls - surface junctions. The "flexo-roto" fields leading to the carrier accumulation are considered as indirect mechanism of the twin walls conductivity. Comparison of the direct and indirect mechanisms illustrates complex range of phenomena directly responsible for domain walls static conductivity in materials with multiple order parameters. 
Eugene A. Eliseev, Anna N. Morozovska, Albina Y. Borisevich, Yijia Gu,   Long-Qing Chen and Venkatraman Gopalan, and Sergei ...
cond-mat.mtrl-sci