Geometric distribution of CuO chains in YBa 2Cu 3O 6+ x

Abstract

Statistics of CuO chains in basal planes of YBa 2Cu 3O 6+ x high- T c superconductor has been studied in terms of two dimensional asymmetric next-to-nearest-neighbor Ising (ASYNNNI) model, with accentuation on distribution of CuO chains per different chain lengths. It has been shown that the fraction p( l) of CuO chains containing l oxygen ions (i.e., having the length equal to l), satisfies so-called “law of geometric distribution” p( l) = ω(1 − ω) l−1 , where the quantity ω is equal to the inverse of average chain length l av in the system, for given values of oxygen content x and temperature T. In the case of ortho-II (OII) structural phase, the geometric chain probability distribution is shown to hold separately for each of two different sublattices of oxygen sites, commonly known as α 1 and α 2, with respectively defined l av α 1 ( x , T ) and l av α 2 ( x , T ) . The theoretically derived result of the chain probability distribution p( l) is shown to be in a remarkable agreement with the results obtained out of extensive Monte Carlo calculations that were made within region of stability of orthorhombic structural phases in ( x, T) space. The relevance of chain length distribution for accurate count of the number of transferred electronic holes to superconducting CuO 2 layers has been pointed out and expression for hole concentration has been derived. The concept of critical chain length for charge transfer mechanism was briefly discussed.