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

Todor M. Mishonov, Albert M. Varonov, Kaloian D. Lozanov

TL;DR

The work addresses the metal–insulator transition in a half-filled CuO chain within a Kondo–Zener exchange framework inspired by Abrikosov's SDW scenario. It develops a reduced, separable Kondo exchange model and employs a self-consistent (BCS-like) mean-field approach to obtain a Bragg-gap in the 1D conduction band. A self-consistent gap equation is derived, yielding a sizable gap of order a few hundred meV (e.g., ≈330 meV for $J_{sd} obreak = obreak 5.87$ eV) and highlighting a mechanism by which exchange interactions can drive insulating behavior. The results illuminate how exchange-induced density waves can produce metal–insulator transitions in cuprate chains and suggest pathways to extend the analysis to two-dimensional cuprate systems, potentially linking insulating behavior to superconducting tendencies.

Abstract

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$_{7-δ}$, 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.

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

TL;DR

The work addresses the metal–insulator transition in a half-filled CuO chain within a Kondo–Zener exchange framework inspired by Abrikosov's SDW scenario. It develops a reduced, separable Kondo exchange model and employs a self-consistent (BCS-like) mean-field approach to obtain a Bragg-gap in the 1D conduction band. A self-consistent gap equation is derived, yielding a sizable gap of order a few hundred meV (e.g., ≈330 meV for eV) and highlighting a mechanism by which exchange interactions can drive insulating behavior. The results illuminate how exchange-induced density waves can produce metal–insulator transitions in cuprate chains and suggest pathways to extend the analysis to two-dimensional cuprate systems, potentially linking insulating behavior to superconducting tendencies.

Abstract

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, YBaCuO, 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.

Paper Structure

This paper contains 6 sections, 50 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Electron band Hamiltonian
  3. Kondo exchange Hamiltonian
  4. Orthogonal $u$-$v$ transformations
  5. Self-consistent Hamiltonian and spectrum
  6. Interpretation of the results

Figures (2)

  • Figure 1: From top to bottom we have the unfilled Cu4$s$, half-filled Cu3$d_{x^2-y^2}$, and filled O2$p_x$ bands, respectively. Here it should be noted that $\epsilon_\mathrm{_F} = 1.0$ eV, for the used values of the parameters $\epsilon_s=4.0$ eV, $\epsilon_d=0.0$ eV, ${\overline\epsilon}_p=-0.9$ eV, $t_{pd}=1.5$ eV, $t_{sp}=2.0$ eV.
  • Figure 2: The eigenvector of $H^{(0)}$ Eq. (\ref{['independent_Hamiltonian']}), corresponding to the conduction band, $b=2$, plotted in Fig. \ref{['Fig:ElectronicBands']}. At the $\Gamma$-point $p=0,\, 2\pi$ we have pure Cu$3d_{x^2-y^2}$ orbital and just zero Cu$4s$ and O$2p_x$ hybridization.