Tuning the charge-transfer energy in hole-doped cuprates

Chuck-Hou Yee and Gabriel Kotliar

Phys. Rev. B 89, 094517 – Published 24 March 2014

Abstract

Chemical substitution, combined with strain, allows the charge-transfer energy in hole-doped cuprates to be broadly tuned. We theoretically characterize the structural and electronic properties of the family of compounds $R_{2}$ CuO $_{2}$ S $_{2}$ , constructed by sulfur replacement of the apical oxygens and rare-earth substitutions in the parent cuprate La $_{2}$ CuO $_{4}$ . Additionally, the enthalpies of formation for possible synthesis pathways are determined.

Received 23 April 2013
Revised 11 March 2014

DOI:https://doi.org/10.1103/PhysRevB.89.094517

Authors & Affiliations

Chuck-Hou Yee^*

Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA

Gabriel Kotliar

Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854-8019, USA

^*cyee@kitp.ucsb.edu

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Vol. 89, Iss. 9 — 1 March 2014

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Images

Figure 1
Scatterplot of the charge-transfer energy $ε_{d} - ε_{p}$ and the apical atom distance from the CuO $_{2}$ plane $d_{apical}$ for the family of hypothetical copper oxysulfides $R$ $_{2}$ CuO $_{2}$ S $_{2}$ (squares) and the actual compound La $_{2}$ CuO $_{4}$ (circle). The oxysulfides are formed by the substitution of apical oxygens by sulfur (arrows in inset figure of crystal structure), and the structure is obtained by full relaxation in DFT. Chemical substitution allows us to span nearly the entire range of charge-transfer energies (shaded bar) found in the cuprates.
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Figure 2
Fully relaxed conventional cell lattice parameters for the $R_{2}$ CuO $_{2}$ S $_{2}$ family of compounds (squares) compared to La $_{2}$ CuO $_{4}$ (dot). Sulfur substitution increases both the $a$ and $c$ lattice parameters. The decrease in the cation's ionic radii from La $\to$ Y $\to$ Lu $\to$ Sc $\to$ Ga accounts for the contraction of $a$ and $c$ within the family of oxysulfides. The dotted line is a guide to the eye.
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Figure 3
The effect of uniaxial $c$ -axis strain on the charge-transfer energy (circles) for (top) the actual compound La $_{2}$ CuO $_{4}$ and (bottom) the oxysulfide La $_{2}$ CuO $_{2}$ S $_{2}$ . The dotted line shows the equilibrium $d_{apical}$ . In LCO, uniaxial compression increases $ε_{d} - ε_{p}$ and consequently suppresses $T_{c}$ , as observed experimentally [30], while we predict pressure should hardly affect $T_{c}$ in the oxysulfide. To disentangle crystal fields from the Madelung potential, we show the effect of tweaking $d_{apical}$ with all other atoms fixed (squares). The effects due to the Madelung potential, roughly quantified by the difference between the two curves, are the same order of magnitude as the crystal fields.
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Figure 4
Octahedral rotations in Sc $_{2}$ CuO $_{2}$ S $_{2}$ as shown by (a) a view along the $a$ axis and (b) a section of the CuO $_{2}$ plane. We structurally relaxed a $2 \times 2 \times 1$ supercell with no symmetry constraints. While there is no out-of-plane buckling of the Cu-O bonds, the small Sc ion causes strong in-plane rotations of the octahedral cages (denoted $a^{0} a^{0} c_{p}^{-}$ in Glazer notation). The compound remains in the tetragonal $T$ -type phase.
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Figure 5
The energy splitting $Δ E = E_{x^{2} - y^{2}} - E_{z^{2}}$ between the on-site energies of the $d_{x^{2} - y^{2}}$ and $d_{z^{2}}$ orbitals among the copper oxysulfide family (squares). For comparison, the actual compound La $_{2}$ CuO $_{4}$ (circle) is shown. The physical range of $Δ E$ spanned by the single-layer cuprates is shown with a shaded bar (from Sakakibara et al. [20]). $Δ E$ in the oxysulfides is generally smaller, implying stronger mixing of the $d_{z^{2}}$ orbital with the in-plane $d_{x^{2} - y^{2}}$ orbital. Thus, barring other competing orders, sulfur substitution should enhance $T_{c}, \max$ according to the charge-transfer theory, while $T_{c}, \max$ will be suppressed according to the two-orbital theory.
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