Superconductivity suppression and bilayer decoupling in Pr substituted YBa$_2$Cu$_3$O$_{7-δ}$

The mechanism behind superconductivity suppression induced by Pr substitutions in YBa$_2$Cu$3$O${7-δ}$ (YBCO) has been a mystery since its discovery: in spite of being isovalent to Y$^{3+}$ with a small magnetic moment, it is the only rare-earth element that has a dramatic impact on YBCO’s superconducting properties. Using angle-resolved photoemission spectroscopy (ARPES) and DFT+$U$ calculations, we uncover how Pr substitution modifies the low-energy electronic structure of YBCO. Contrary to the prevailing Fehrenbacher-Rice (FR) and Liechtenstein-Mazin (LM) models, the low energy electronic structure contains no signature of any $f$-electron hybridization or new states. Yet, strong electron doping is observed primarily on the antibonding Fermi surface. Meanwhile, we reveal major electronic structure modifications to Cu-derived states with increasing Pr substitution: a pronounced CuO$_2$ bilayer decoupling and an enhanced CuO chain hopping, implying indirect electron-release pathways beyond simple 4$f$ state ionization. Our results challenge the long-standing FR/LM mechanism and establish Pr substituted YBCO as a potential platform for exploring correlation-driven phenomena in coupled 1D-2D systems.

💡 Research Summary

The authors investigate why partial substitution of praseodymium (Pr) for yttrium in YBa₂Cu₃O₇₋δ (YBCO) dramatically suppresses superconductivity, a puzzle that has persisted for decades. Using angle‑resolved photoemission spectroscopy (ARPES), density‑functional theory with a Hubbard U correction (DFT+U), and non‑resonant inelastic X‑ray scattering (NRIXS), they map the low‑energy electronic structure of pristine YBCO and four Pr‑substituted samples with transition temperatures (Tc) of 91 K, 84 K, 63 K, and 53 K (Pr concentrations ranging from 5 % to 28 %).

The ARPES data reveal three bands crossing the Fermi level in all samples: a bonding (BB) and an antibonding (AB) CuO₂ bilayer band, and a quasi‑one‑dimensional CuO chain band. Contrary to the long‑standing Fehrenbacher‑Rice (FR) and Liechtenstein‑Mazin (LM) models, no Pr‑derived hole pocket appears at the Brillouin‑zone corner, and no low‑energy 4f‑related anti‑crossings are observed. Instead, systematic electron doping is evident, primarily on the AB sheet, as the hole pockets shrink with increasing Pr content. The electron doping is modest on the chain band but clearly present.

A striking observation is the reduction of the CuO₂ bilayer splitting energy by more than 30 % as Pr is added. This indicates a rapid electronic decoupling of the two CuO₂ planes, far exceeding the modest splitting reduction predicted by DFT for Pr occupying either the Y or Ba sites. The chain band, meanwhile, steepens and its effective mass increases, suggesting enhanced hopping along the chains and a possible secondary pathway for electron release.

NRIXS measurements of the Cu M₁ edge show a flattening of the Cu 3d_{z²} orbital intensity with heavy Pr doping, implying a lowered energy and reduced hole occupancy of this orbital. This orbital reshaping is consistent with a flattening of the CuO₅ pyramids, which reduces the crystal‑field splitting between d_{x²‑y²} and d_{z²} and contributes to the observed bilayer decoupling.

DFT+U calculations confirm that Pr 4f states lie well below the Fermi level and do not hybridize with Cu‑O bands. The calculations also explore two substitution scenarios: Pr on the Y site and Pr on the Ba site. Ba‑site substitution introduces an extra electron per Pr atom, providing a natural source of the observed electron doping, while Y‑site substitution mainly perturbs the CuO₂ planes. Both scenarios predict a modest bilayer splitting reduction, but the experimental effect is larger, indicating additional correlation‑driven mechanisms.

The authors therefore propose a new mechanism for Tc suppression: (1) Pr does not act through 4f‑O hybridization; instead it releases electrons directly into the CuO₂ planes, especially the antibonding sheet; (2) the CuO₂ bilayer becomes electronically decoupled, weakening the inter‑plane pairing interaction; (3) the CuO chains experience enhanced hopping and act as an auxiliary electron‑release channel; and (4) partial Pr substitution on Ba sites contributes extra electrons, further doping the system.

By plotting the ARPES‑derived surface hole concentration against Tc, they find that the Pr‑substituted samples follow the same dome‑shaped Tc versus hole‑doping curve as oxygen‑controlled YBCO, confirming that electron doping, not hole localization, dominates the suppression. Moreover, at ~30 % Pr substitution a three‑dimensional charge order emerges, comparable to the charge‑order doping level in under‑doped YBCO, linking the electronic reconstruction to the observed ordering phenomena.

In summary, this work overturns the FR/LM paradigm, demonstrates that Pr substitution primarily induces electron doping and bilayer decoupling, and positions Pr‑substituted YBCO as a versatile platform for studying correlated 1D‑2D electronic systems and the interplay between charge order, bilayer coupling, and high‑temperature superconductivity.