Intrinsically coupled stripes within the CuO2 planes of the high-Tc materials

Analysis of the electronic state of the CuO2 planes of high-Tc materials has been performed with special regard to the influence of the coulomb interactions separated after moments. Using this analysis to derive the basic structure of the electronic states within the CuO2 planes of the high-Tc materials, different symmetry breaking effects were revealed. First of all, a commensurate charge and bonding fluctuation state (CBF) with the period (2a, 2b) is established which exists collinearly with the antiferromagnetic spin state. It is concluded that the CBF state and the antiferromagnetic spin state are results of the same electronic renormalizations. Furthermore, the existence of localized topological hole states under hole doping is established. As a natural consequence of this, the local symmetry is broken. It is proven that a quadrupolar polarization induced attractive hole–hole interaction can exist between such topological hole states. This interaction creates an ordered topological hole structure which leads to a global symmetry breaking. This highly ordered topological hole structure, which will be referred as bonded holes (b-holes), can be characterized as parallel one-dimensional electronic states (stripes) along particular ⋯Cu–O–Cu⋯ bonding directions which are intrinsically coupled to each other. The highly ordered topological b-hole state exists undisturbed for hole concentrations nh in the range of 0.125 holes/copper ⩽ nh ⩽ 0.25 holes/copper. The total correlation energy per b-hole |ECtot||ECtot| was deduced to be ⩾160 meV. In addition to b-holes, holes which are not intrinsically bonded exist in the concentration range of nh > 0.125 holes/copper. These non-bonded holes are termed as free holes (f-holes). The inevitable consequence is an electronic two fluid behaviour (b-holes, f-holes) within the hole concentration range of 0.125 holes/copper < nh ⩽ 0.25 holes/copper. The characteristics of the electronic state deduced here, enable a more complex understanding of various experimental results, and gives in particular insight into the foundations of the 1/8 problem and the creation of checkerboard structures.