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

Abstract

Analysis of the electronic state of the CuO 2 planes of high-T c 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 CuO 2 planes of the high-T c 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 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 n h in the range of 0.125 holes/copper ≤ n h ≤ 0.25 holes/copper. The total correlation energy per b-hole E C(tot)  was found to be greater than 160 meV. In addition to b-holes, holes which are not intrinsically bonded exist in the concentration range of n h > 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 < n h ≤ 0.25 holes/copper. A comparison with experimental results is given with particular respect to peculiarities of µSR experiments, neutron scattering results (1/8 problem), Hall-effect anomalies and scanning tunneling microscopy (STM). The characteristics of the electronic state deduced by the new methodology described here enable a more in depth understanding of these experimental results.

Interpretation of the Dispersion of the Electron States of High-$T_{c}$ Cuprate Superconductors Based on the Theory of Topological Resonance

“…In a more stringent ab initio approach, however, we could show that the initial electronic states are already symmetry broken in various ways leading to new ordered macroscopic electronic structures but which are still dynamic (TR state). 6,7 Basically, the two-dimensionality of the energetically highest valence bands is removed in favour to two arrays of one-dimensional bands {I x , I ′…”

“…1). Asymmetric hole doping on particular oxygen sites requires horizontal electronic transformations in real space with the result that every local state u i related to a given copper site i is split up into a left and right part which are separately associated to the neighbouring left and right oxygen atom in a O-Cu-O bonding unit, respectively, subsequently abbreviated by L and R. 6,13 In consequence, the initial Hilbert spaces are additionally split up according to…”

“…Topological hole configuration of a CuO2 plane for a nominal hole concentration n h = 1 8 holes/copper forming an ordered topological hole state over oxygen sites, termed as b-hole state. 6 The valence bands, usually being two-dimensional, are renormalized into two perpendicular arrays of one-dimensional bands, along the x coordinate {Ix, I ′…”

“…x , Īx, Ī′ x } and the y coordinate {Iy, I ′ y , Īy, Ī′ y }. 6 The +,− signs indicate two different copper sites within every onedimensional band resulting from renormalized electronic basis states, CBF states, which define new lattice periodicities of 2a and 2b in x and y direction, respectively. The b-hole topology results from attractive b-hole−b-hole pair couplings EC < 0 6 depicted, e.g., within the shadowed one-dimensional bands.…”

“…Within this range the states are dispersionless also in k ⊥ direction for nominal hole densities n h (≡ x) = 0.12 − 0.3 holes/copper. 2−4 These extraordinary experimental findings will be proven here by a new theoretical concept, termed as topological resonance (TR) theory 6,7 , which defines new quantum states in high-T c cuprates.…”