Charge Density Wave in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$

TL;DR

This paper explains the stability of odd-period charge density waves in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ by solving an effective t-J model with a novel interladder interaction term derived from the charge transfer model.

Contribution

It introduces a new interladder interaction term V in the t-J model, resolving the contradiction regarding CDW stability in coupled Cu$_2$O$_5$ ladders.

Findings

Odd-period CDWs are stable due to the interladder repulsion V.

Even-period CDWs are unstable under the same conditions.

The interaction V is derived from on-site Hubbard repulsion on oxygen sites.

Abstract

Recent experimental results [A. Rusydi et al., Phys. Rev. Lett. 97, 016403 (2006)] revealed the stability of a peculiar charge density wave (CDW) with odd period (three or five) in the coupled Cu$_2$O$_5$ spin ladders in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$, while the CDW with even period is unstable. Here we resolve this contradiction by solving the effective t-J model for the two coupled chains supplemented by the intersite interaction term V. Crucial to this finding is the novel interaction term V (responsible for the interladder repulsion between nearest neighbor holes), which is derived from the on-site Hubbard-like repulsion between electrons on the same oxygen sites but within two distinct orbitals which belong to two neighboring Cu$_2$O$_5$ ladders in the charge transfer model.