Y1-xPrxBa2Cu3O6+y: Pr Effects in Cuprate Superconductors

• Y1-xPrxBa2Cu3O6+y is a high-Tc cuprate system where Pr substitution alters the crystal structure and disrupts superconductivity.
• Pr incorporation induces strong 4f–2p orbital hybridization that enhances interplanar electronic coherence and stabilizes 3D charge order.
• Site-sensitive spectroscopy distinguishes two orders—static Pr-driven Q1 and CDW-like Q2—that compete with superconducting pairing.

The cuprate system Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$ is a member of the "123" family of high-temperature superconductors, in which praseodymium (Pr) is substituted for yttrium (Y) within the perovskite-derived YBa$_2$Cu$_3$O$_{6+y}$ lattice. Pr substitution is well known to have a unique and pronounced influence on the structural, electronic, and ordering phenomena in these cuprates, often resulting in the suppression of superconductivity and the emergence of competing orders. The system thereby provides a fertile ground for exploring the interplay between superconductivity, charge and lattice ordering, dimensionality, and the impact of rare-earth magnetism.

1. Crystal Structure, Substitution Effects, and Lattice Dynamics

Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$ crystallizes in the orthorhombic perovskite (Pmmm) structure, composed of CuO$_2$ planes sandwiched by rare earth (RE) layers (Y or Pr), CuO chains, and BaO layers. The substitution of Pr for Y primarily perturbs the RE layer, but also affects the electronic landscape of the adjacent CuO$_2$ planes through hybridization effects. The rare-earth ionic radius and electronic configuration influence lattice constants and phonon spectra.

Raman studies across RBa$_2$Cu$_3$O$_{6+\delta}$ (R = Y, Dy, Gd, Sm, Nd) indicate that the B$_{1g}$ optical phonon energy ($\nu_{B_{1g}}$) decreases systematically with increasing in-plane lattice parameter $a$. For Y-123, $\nu_{B_{1g}} \approx 335$ cm$^{-1}$, falling for larger RE ions. However, the antiferromagnetic superexchange coupling $J$ remains essentially constant for Y, Dy, Gd, and Sm, regardless of lattice parameter, implying robust magnetic interactions despite lattice tuning. Notably, temperature-dependent phonon splitting—indicative of RE 4f–phonon interactions—emerges for systems with partially filled f-shells (e.g., Nd), but is absent for Y and Pr, given the electronic configurations of these ions (Müllner et al., 2019).

2. Electronic Structure, Orbital Hybridization, and Dimensionality

Pr substitution induces a strong hybridization between Pr 4f and O 2p orbitals. In Pr-rich compounds, this hybridization modifies the electronic states at the Fermi level—an effect absent for other rare-earth substitutions. Resonant soft x-ray scattering (RSXS) and DFT+$U$ calculations reveal that Pr 4f$_{z(x^2-y^2)}$ states hybridize with the 2p$_{\pi}$ orbitals of planar oxygen, forming an antibonding band that crosses $E_F$ and bridges adjacent CuO$_2$ layers. This "orbital bridge" promotes interplanar electronic coherence and, at sufficient Pr content, stabilizes three-dimensional (3D) charge order (CO) with correlation lengths up to $\sim$364 Å, as evidenced by sharp diffraction peaks at integer L (out-of-plane) positions (Ruiz et al., 2022). In contrast, Dy substitution does not yield such 3D coherence; the analogous antibonding band resides far below $E_F$.

This interplanar orbital engineering underscores the role of dimensionality in the intertwining of superconductivity and CO. Enhanced interlayer coupling via Pr hybridization locks CO modulations across planes, driving the CO from quasi-2D toward fully 3D order.

3. Charge and Lattice Ordering: Identification via Site-Sensitive Spectroscopy

Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$ hosts at least two distinct translational symmetry–breaking orders with nearly identical in-plane modulation vectors, but physically different origins and atomic-site selectivity (Martinelli et al., 28 Jul 2025). Resonant elastic x-ray scattering (REXS) provides decisive discrimination:

• The first order, Q$_1$ ($\delta_1\approx0.337$), is quasi-commensurate, static, and resonates strongly at the Pr M and out-of-plane Cu L edges, indicating that it constitutes a superlattice structure driven by Pr substitution and associated lattice modulation. It persists up to high temperatures and possesses long-range correlations.
• The second order, Q$_2$ ($\delta_2\approx0.325$), resonates at the in-plane Cu L edge, is temperature dependent (diminishing above $\sim$250 K), and features short correlation lengths. It is characteristic of charge density wave (CDW) order in the CuO$_2$ planes, akin to that found in canonical YBa$_2$Cu$_3$O$_{6+y}$.

The table below summarizes ordering characteristics:

Order	Resonant Edge	Modulation Vector ($\delta$)	Temperature Dependence	Site Source
Q$_1$	Pr M, Cu L (ooplane)	$>1/3$ ($\sim$0.337)	Static	Pr sites
Q$_2$	Cu L (in-plane)	$<1/3$ ($\sim$0.325)	Suppressed $>$250 K	CuO$_2$ planes

Only site-selective techniques such as REXS can resolve these coexisting orders, revealing their subtle periodicity differences and distinct roles in the physics of the system.

4. Superconductivity, Charge Order, and Competing Phases

Pr substitution at the Y site in YBa$_2$Cu$_3$O$_{6+y}$ has a uniquely deleterious effect on superconductivity, rapidly suppressing $T_c$ even at low $x$. The emergence of the static Pr-driven superlattice modulation (Q$_1$) is specifically detrimental to superconducting pairing, as the broken symmetry at the Pr site interferes with the electronic states required for high-$T_c$ superconductivity (Martinelli et al., 28 Jul 2025). This effect is fundamentally different from the ubiquitous CDW order (Q$_2$), which competes with superconductivity but is not intrinsically incompatible.

In comparison, compositionally-complex cuprates alloyed on the Y site with multiple isovalent ions (including rare earths without strong 4f-O 2p hybridization) retain high $T_c$—within 1% of pure YBCO at optimal doping—demonstrating robust superconducting pairing when disorder is nonmagnetic and does not introduce strong local symmetry breaking (Raghavan et al., 2023). In contrast, Pr substitution, with its unique electronic and symmetry-breaking effects, suppresses superconductivity due to chemical and orbital effects rather than generic disorder.

In the broader class of underdoped cuprates, both CDW and spin/charge stripe order are found as universal competing phases. In YBa$_2$Cu$_3$O$_{6+y}$ and its relatives, CDW order is most prominent near $p\approx 0.12$, and its strength correlates inversely with $T_c$ (Ghiringhelli et al., 2012, Cyr-Choinière et al., 2015). In Pr-rich 123 systems, the enhanced robustness and dimensionality of the Pr-induced order further suppress $T_c$ beyond what would be expected from carrier localization alone.

5. Fermi Surface Reconstruction and Quantum Transport Phenomena

Substitution-induced changes to the Fermi surface topology are central to understanding electronic transport in Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$. In underdoped YBa$_2$Cu$_3$O$_{6+y}$, high magnetic field measurements of Seebeck ($S$) and Nernst ($\nu$) effects reveal signatures of Fermi surface reconstruction: as $T\rightarrow0$, $S/T$ and $\nu/T$ become large and negative, indicating the emergence of small electron-like pockets—a hallmark of density-wave-driven Fermi surface folding (0907.5039). This scenario is general across underdoped cuprates and is expected to manifest in Pr-substituted systems as well, with the additional possibility of Pr-driven orbital hybridization altering the shape and dimensionality of the reconstructed Fermi surface.

The negative Hall coefficient observed upon reduction or Pr incorporation, combined with pronounced $T^2$ resistivity (rather than the usual $T$-linear form) in Pr-based chain-dominated compounds, supports a model in which conduction shifts away from standard CuO$_2$-plane behavior to alternative, possibly 1D, channels (0707.2180). The possibility of Tomonaga–Luttinger liquid physics and strong electron correlations in these quasi-one-dimensional states is further reinforced by power-law transport and magnetotransport exponents ($\rho \propto T^\alpha$ with $0.08 < \alpha < 0.65$ depending on conditions) (0707.2180).

6. Pressure, Doping, and Phase Competition

The interplay of pressure, chemical doping, and disorder provides external control over the balance between superconductivity, CO, and other orders in Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$. In YBa$_2$Cu$_3$O$_{6+y}$, pressure suppresses CDW order and restores a smooth, higher superconducting dome, whereas magnetic field enhances CDW at the expense of superconductivity (Cyr-Choinière et al., 2015). In Pr-substituted systems, these effects may be more pronounced or complicated due to the robust static nature of Pr-induced symmetry breaking and enhanced three-dimensionality of charge order.

The pressure sensitivity of $T_c$ is given by:

$$\frac{\partial T_c}{\partial P} = \left(\frac{\partial p}{\partial P}\right) \left(\frac{\partial T_c}{\partial p}\right)_{\!P} + \left(\frac{\partial T_c}{\partial P}\right)_p,$$

capturing the interplay between pressure-induced hole doping and intrinsic modulation of superconductivity. In Pr-containing samples, a plausible implication is that the Pr-derived superlattice (Q$_1$) may impose a fundamental limit on how much superconductivity can be restored by pressure, in contrast to isovalent Y-site substitution.

7. Broader Context: Mechanisms, Materials Comparisons, and Outlook

The unique response of Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$ to Pr substitution sharply demarcates it from other rare earth–substituted 123 cuprates. Whereas most disorder (if isovalent and nonmagnetic) is tolerated robustly within the CuO$_2$ planes, leading to high $T_c$ with only minimal suppression (Raghavan et al., 2023), Pr exerts an outsize influence, creating both local symmetry-breaking superlattice order and direct changes in electronic structure. The correspondence between static symmetry breaking (at Q$_1$) and the absence or strong suppression of superconductivity in PrBa$_2$Cu$_3$O$_7$ is a central result (Martinelli et al., 28 Jul 2025).

Current research leverages site-sensitive spectroscopies and orbital-specific tuning (such as Pr-mediated hybridization) to engineer dimensionality and select among competing phases, demonstrating that spatially and chemically resolved order parameters are key to understanding the emergent phenomena in these highly correlated oxides (Ruiz et al., 2022). The ability to separate spin and lattice disorder by design, and to probe their individual effects on pairing, represents a promising direction for systematic investigation of high-$T_c$ physics in complex oxides.

In summary, Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$ serves as a paradigmatic system for unraveling the consequences of site-specific symmetry breaking, orbital hybridization, and interlayer coupling in correlated materials. Its paper reveals the delicate interplay between crystal chemistry, electronic and lattice ordering, and the emergence (or suppression) of high-temperature superconductivity.