Elastic Stiffnesses, Debye Temperatures, and Tc in Cuprates

Published

September 1, 2003

Author(s)

H M. Ledbetter, K Sudook

Abstract

For cuprate superconductors and related oxides, we review some aspects of their elastic constants. We consider the systematics of the bulk-modulus/atomic-volume (B/V_a) relationship. For nonsuperconducting oxides, the B-V_a diagram shows that most oxides fall in three sets: (1) rocksalt crystal structure, AO; (2) perovskite crystal structure, ACO₃; and (3) transition-metal oxides ranging through stoichiometries of AO, A₃O₄, A₂O. Seventeen oxide superconductors show a surprisingly narrow V_a range and a relatively narrow range of B=116 19 GPa. B- V_a slopes depart from expectations from a simple ionic-crystal model. Within a superconductor subgroup for example, La-O or Tl-O, higher B corresponds to higher T_c. Because the in-plane (CuO₂-plane) compressibility probably varies little among these cuprates, the out-of-plane compressibility should correlate inversely with T_c. We consider also the relationship between T_c and the Debye characteristic temperature θ, which enters the BCS T_c expression in two ways. (Theta values come simply and accurately from the elastic constants.) Contrary to BCS (electron-phonon) superconductors where lattice softening (lower θ) increases T_c, in the cuprates T_c increases with increasing θ. This implies strongly that phonons participate in the basic high-T_c mechanism in cuprates, even though most theories ignore phonons.

Citation

Elastic Stiffnesses, Debye Temperatures, and T_c in Cuprates

Publisher Info

Book Chapter ,

Pub Type

Books

Keywords

BCS theory

Citation

Ledbetter, H. and Sudook, K. (2003), Elastic Stiffnesses, Debye Temperatures, and T_c in Cuprates, Book Chapter , (Accessed December 13, 2024)