Electronic properties of structural twin and antiphase boundaries in materials with strong electron-lattice couplings

Recent advances in imaging techniques have revealed the presence of rich elastic textures in functional materials such as colossal magnetoresistive sCMRd manganites,1,2 ferroelectrics,3 ferroelastics,4 and shape memory alloys.5 In particular, experiments on certain perovskite manganite compounds2 have shown the correlation between electronic transport properties and the presence of meandering antiphase boundaries sAPBsd within insulating charge ordered domains, interpreted as the existence of metallic regions forming around APBs. It is also reported that strains near grain boundaries in thin film can significantly modify electronic properties in manganites.6 The interplay between elastic texture and electronic heterogeneity is thus central to understanding multiphase coexistence and resultant electronic properties in CMR and other functional electronic materials. In this work we illustrate the importance of elastic heterogeneities in modifying electronic properties in materials with strong electron-lattice coupling. In particular, we study the electronic properties of APBs and twin boundaries sTBsd on a two-dimensional s2Dd lattice. We first show how our recently developed symmetry-based atomic-scale theory of lattice distortions can be used to find atomic configurations of twin and antiphase boundaries. Within our framework, we illustrate the differences and similarities between TBs and APBs from the point of view of localization of long sshortd wavelength modes inside APBs sTBsd, evolution upon energy relaxation and roughness7 ssmoothnessd of APBs sTBsd. We subsequently perform a tight binding calculation with a Su-Schrieffer-Heeger sSSHd type model of electron-lattice coupling to predict the distribution of electronic density of states, which can be related to the results of scanning tunneling microscope sSTMd measurements. Our work thus forms the basis for predicting electronic properties from predesigned materials microstructures. Twin boundaries separate domains related by the rotation of crystalline axes, whereas APBs represent boundaries at which the sequence of alternating distortions, such as alternating rotational directions of oxygen octahedra in perovskite oxides, change their phase si.e., broken translational symmetryd. Although our method can be applied to 2D or 3D lattices with monatomic or multiatomic bases, we illustrate our ideas with a square lattice in 2D space splanar P4mmd with a monatomic basis, for which the appropriate atomic scale distortion variables are the modes shown in Fig. 1. These modes have important advantages over displacement variables—they reflect the symmetries of the lattice and can serve as order parameters sOPsd in structural phase transitions.8 Therefore, energy expressions with desired ground states can be written in a simpler way in these variables than in usual displacement variables. Moreover, since the lattice distortions are decomposed into the modes at kW = s0,0d slong-wavelength or intercell modesd and kW = sp ,pd sshort-wavelength or intracell modesd, the approach using these modes reveals the differences between long and short wavelength lattice distortions in a natural way. We consider APBs, such as the one shown in Fig. 2 where open circles represent the distorted atomic positions, for sx or sy modes. 9 The simplest energy expression yielding a ground state with either pure sx or sy mode lattice distortion is