Localized Excitations and Anisotropic Directional Ordering in a Two-Dimensional Morse Lattice Model of Cuprate Layers
We study here localized excitations in a Morse lattice model of two-dimensional CuO 2 layers (cuprates in short). The Cu-atoms are positioned motionless in a square lattice and the oxygen atoms are able to oscillate around originally equilibrium positions
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Abstract We study here localized excitations in a Morse lattice model of twodimensional CuO2 layers (cuprates in short). The Cu-atoms are positioned motionless in a square lattice and the oxygen atoms are able to oscillate around originally equilibrium positions on another superposed square lattice. After studying regular oxygen lattices we investigate lattices with bonds which are weakly distorted. We estimate the density of compressions (strain density) in dependence of the misfit of the Cu–O-bonds. We show that with increasing misfit the nonlinear oscillations of the O-atoms yield stripes hence patches exhibiting anisotropic directional ordering with an overall yet transient tessellated structure.
1 Introduction The model system which we study here is a square lattice with lattice constant (equilibrium distance between lattice units), formed by oxygen atoms, which is embedded or superposed into another square lattice, consisting of copper atoms.
M.G. Velarde () Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, Madrid-28040, Spain Fundación Universidad Alfonso X El Sabio, Villanueva de la Cañada-28691, Madrid, Spain e-mail: [email protected],[email protected] W. Ebeling Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, Madrid-28040, Spain Institut für Physik, Humboldt-Universität Berlin, Newtonstrasse 15, Berlin-12489, Germany e-mail: [email protected] A.P. Chetverikov Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, Madrid-28040, Spain Department of Physics, Saratov State University, Astrakhanskaya 83, Saratov-410012, Russia e-mail: [email protected] R. Carretero-González et al. (eds.), Localized Excitations in Nonlinear Complex Systems, Nonlinear Systems and Complexity 7, DOI 10.1007/978-3-319-02057-0__10, © Springer International Publishing Switzerland 2014
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Fig. 1 Model CuO2 cuprate layer. Two superposed square lattices, one with oxygens (red color dots) and another with coppers (green color dots)
We assume that the interaction potential parameters are such that the distances between minima of Cu and of O – atoms are related like the geometrical distances as p 1= 2 [1, 2]. This case is denoted as “regular”; otherwise, if the distances deviate from such value we speak about “irregular” cases. The case of a regular lattice exhibiting breathers was already considered by Russell and colleagues [3–5]. For other works on breathers for two-dimensional lattices see Refs. [6–11]. Here we shall explore stripe structures and soliton-like localized excitations rather than breathers. In the case of heated lattices, irregular configurations may appear as time proceeds, so the term regular and irregular refers only to the initial equilibrium situation. Note that we give only the initial square lattice configuration and then we allow the O-units to freely move, but the Cu-units are held fixed in the time scale considered here which agrees with available experimental observations [12, 13]. Figur
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