Metal-insulator transition in a CuO chain created by Kondo interaction

Over twenty years ago Alexei Abrikosov [A.A. Abrikosov, Metal-insulator transition in layered cuprates (SDW model), Physica C: Supercond. Vol. 391, 2, 147-159 (2003)] considered the Spin-Density-Waves (SDW) model for the metal-insulator transition in layered cuprates. In one of those cuprates, YBa${}_2$Cu${}_3$O${}_{7-\delta }$, there are one-dimensional (1D) CuO chains of copper and oxygen ions. In the present work we consider the metal-insulator transition in the model case of a 1D CuO chain in the regime of half-filling of the band. Our model is essentially the same, but as an exchange interaction causing the metal-insulator transition, we consider Kondo-Zener two-electron exchange, which successfully describes many of the electronic properties of the layered cuprates.