Nickelate Superconductivity

• Nickelate superconductivity is a phenomenon exhibiting zero electrical resistance in layered nickel oxide compounds characterized by 2D NiO₂ planes coupled to 3D rare-earth 5d metallic spacer layers.
• It features an unconventional pairing mechanism, likely d-wave in nature, driven by strong antiferromagnetic superexchange, and shows a dome-shaped Tc ranging from below 20 K to over 90 K under pressure.
• Optimal superconductivity relies on precise synthesis methods, strain and pressure tuning, and chemical control via rare-earth substitution to modulate electronic correlations and band hybridization.

Nickelate superconductivity refers to the phenomenon of zero electrical resistance and expulsion of magnetic flux in layered nickel oxide compounds, structurally and electronically analogous to the high-Tc cuprate superconductors but displaying key distinctions in electronic structure, synthesis, and pairing mechanisms. The field has rapidly expanded since the 2019 discovery of superconductivity in hole-doped infinite-layer nickelates, now encompassing single- and multi-layered Ruddlesden-Popper phases, thin films, and pressurized bulk crystals, with transition temperatures (Tc) ranging from below 20 K to above 90 K in select bilayer systems.

1. Electronic Structure and Minimal Hamiltonians

The electronic structure of superconducting nickelates is governed by a dual character comprising strongly correlated, quasi–two-dimensional (2D) NiO₂ layers and weakly correlated, three-dimensional (3D) rare-earth (R) 5d metallic spacer layers. The Ni site is typically in a $d^9$ or $d^{8.8}$ configuration, with the $3d_{x^2-y^2}$ orbital forming the principal low-energy band. In contrast to cuprates—where the charge-transfer insulator scenario is paradigmatic—rare-earth nickelates feature an “oxide-intermetallic” state, as insulating spacer layers are replaced by 3D metallic R 5d bands (Hepting et al., 2019, Singh, 2019, Kitatani et al., 2020).

A representative effective Hamiltonian is: $$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$ with $c_k^\dagger$ ($d_k^\dagger$) creating an electron in the rare-earth 5d (Ni $3d_{x^2-y^2}$) band, and $V_k$ representing weak interband hybridization.

This leads to a Kondo- or Anderson-lattice–like description, but with a 2D correlated Ni layer coupled to a 3D metallic fluid, rather than the 4f/5d system typical of heavy fermions.

2. Phases, Superconducting Pairing, and Contrasts with Cuprates

Nickelate superconductors display several critical differences and similarities with cuprates:

• Cuprates: Exhibit a Mott or charge-transfer insulating parent phase with insulating spacer layers. Superconductivity arises via hole doping that disrupts robust antiferromagnetism.
• Nickelates: The parent state is metallic due to rare-earth 5d conduction. The NiO₂ planes are close in structure to CuO₂ planes, and the $3d_{x^2-y^2}$ orbital is half-filled, but the system is not a true Mott insulator. The rare-earth spacer hybridizes weakly with Ni 3d, generating small 3D Fermi surface pockets (Hepting et al., 2019, Wang et al., 10 Sep 2025).

Pairing is believed to be unconventional—governed by strong repulsive interactions—leading to a sign-changing (likely $d$-wave) order parameter, though alternative or coexisting $d^{8.8}$0 and $d^{8.8}$1 pairings may emerge in multiorbital models depending on hybridization and Coulomb terms (Luo et al., 2023). In pressurized and multilayer nickelates (e.g., Ruddlesden-Popper phases), antiferromagnetic superexchange between $d^{8.8}$2 and $d^{8.8}$3 orbitals (enhanced by interlayer hopping and Hund's coupling) is implicated as the primary pairing interaction (Zhang et al., 2023, Nica et al., 2020).

3. Material Families, Phase Diagrams, and Tc Range

Nickelate superconductors now span several crystallographic series:

• Infinite-layer (112) series: $d^{8.8}$4NiO$d^{8.8}$5 (R = La, Pr, Nd) and their doped derivatives. Ca- and Sr-doped films (e.g., $d^{8.8}$6, $d^{8.8}$7) exhibit superconducting domes with $d^{8.8}$8 ranging 10–20 K, but onset above 50 K has been reported in optimized thin films (Zeng et al., 2021, Eyal et al., 25 Feb 2025).
• Bilayer (327) series: $d^{8.8}$9 and Sm-substituted variants, showing bulk superconductivity at $3d_{x^2-y^2}$0 up to 92 K (onset) and 73 K (zero resistance) under pressures of 20 GPa (Li et al., 24 Jan 2025). High-pressure tuning and chemical "pressure" (via rare-earth substitution) are essential for stabilizing the high-Tc phase and optimizing the Ni–O–Ni bond geometry.
• Trilayer (4310) series: $3d_{x^2-y^2}$1 and $3d_{x^2-y^2}$2 demonstrate bulks superconducting transitions at 25–40 K under high pressure, with Pr substitution raising $3d_{x^2-y^2}$3 higher than La due to internal chemical pressure (Zhang et al., 29 Jan 2025).
• Multilayer and hybrid phases: Quintuple-layer compounds (e.g., $3d_{x^2-y^2}$4) achieve a cuprate-like $3d_{x^2-y^2}$5 filling and show superconductivity near 13–15 K without chemical doping (Pan et al., 2021). Other hybrid phases with various layer stacking and oxygen stoichiometry have also been explored.

A universal feature across all families is a dome-shaped $3d_{x^2-y^2}$6 vs. doping or pressure phase diagram, reminiscent of cuprates. High-pressure or strain engineering of the lattice drives structural transitions (often monoclinic to tetragonal) that flatten NiO$3d_{x^2-y^2}$7 planes and tune the electronic structure for optimal superconductivity (Li et al., 24 Jan 2025, Huang et al., 2024).

4. Normal State, Transport Properties, and Multiband Effects

Nickelate superconductors show a correlated normal-state regime analogous to cuprates but with unique features:

• In the underdoped regime, $3d_{x^2-y^2}$8 exhibits a low-temperature upturn (logarithmic or insulating), linked to strong correlations and possible Kondo-like scattering between Ni $3d_{x^2-y^2}$9 local moments and rare-earth $$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$0 conduction electrons (Singh, 2019, Lee et al., 2022).
• At optimal doping/pressure, strange-metal, linear-in-$$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$1 resistivity is universally observed, with slope ($$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$211 m$$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$3·cm/K) comparable to cuprates (Lee et al., 2022).
• In the overdoped or highly pressurized regime, resistivity exhibits conventional Fermi-liquid T$$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$4 behavior.

Multiband effects are crucial: both the $$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$5 and the rare-earth $$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$6 bands cross the Fermi level, though weakly hybridized. The Hall coefficient $$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$7 displays nontrivial doping and temperature dependences, often undergoing sign-changing transitions at low temperatures linked to multiband carrier dynamics. In La-based nickelates, the Hall sign-change temperature is pinned near 35 K, while in Nd-/Pr-based systems it shifts with doping (Zeng et al., 2021).

5. Synthesis, Structural Control, and Challenges

Synthesis of high-quality nickelate superconductors is a principal technical bottleneck. Critical strategies include:

• Topotactic reduction of a perovskite precursor using a reducing agent (commonly CaH$$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$8) to obtain the infinite-layer phase.
• Flux growth, enabling ambient-pressure synthesis of high-purity bilayer nickelate single crystals with sizes up to 220 μm and excellent compositional homogeneity (Li et al., 24 Jan 2025).
• Strain/pressure tuning through both bulk high-pressure apparatus and thin-film epitaxy on lattice-mismatched substrates.
• Chemical pressure via systematic rare-earth substitution, effectively compressing the Ni–O bond network and modifying interlayer distances (Li et al., 24 Jan 2025, Zhang et al., 29 Jan 2025).

Disorder and oxygen vacancies have complex roles. Oxygen vacancies (especially apical O) can drastically reconstruct the band structure, diminishing the Ni $$H = \sum_k \left( \varepsilon_k^R c_k^\dagger c_k + \varepsilon_k^{Ni} d_k^\dagger d_k \right) + U \sum_i n_{i,\uparrow}^{Ni} n_{i,\downarrow}^{Ni} + \sum_k \left( V_k c_k^\dagger d_k + \text{h.c.} \right)$$9 involvement at $c_k^\dagger$0 and suppressing superconductivity, as shown for $c_k^\dagger$1; Ce-based analogs with higher oxygen vacancy formation energies may better avoid this problem (Sui et al., 2023).

Persistent challenges include stabilizing the elusive Ni$c_k^\dagger$2 oxidation state, minimizing structural defects (e.g., Ruddlesden-Popper faults), achieving uniform stoichiometry, and suppressing competing density-wave states.

6. Theoretical Models and Mechanisms

Several theoretical approaches address nickelate superconductivity:

• Single-band Hubbard model: Appropriate for infinite-layer nickelates near optimal doping, once the weakly hybridized rare-earth $c_k^\dagger$3 bands are treated as a carrier reservoir. Dynamical vertex approximation and DMFT yield $c_k^\dagger$4 domes and phase diagrams consistent with experiment (Kitatani et al., 2020, Kitatani et al., 2022).
• Multiorbital/bilayer/t–J models: Required for multilayer nickelates and systems with significant $c_k^\dagger$5 admixture. In trilayer phases, strong superexchange between $c_k^\dagger$6 and $c_k^\dagger$7 orbitals is crucial, with pairing gaps and $c_k^\dagger$8 values greatly enhanced compared to single-layer systems (Nica et al., 2020, Zhang et al., 2023).
• Competing order analysis: Pressure suppresses density wave order, especially in $c_k^\dagger$9, and induces superconductivity—a feature paralleling but also departing from cuprate trends (Zhang et al., 2023).

Multiorbital calculations reveal $d_k^\dagger$0 pairing is robust at low hybridization but may be suppressed by strong $d_k^\dagger$1–$d_k^\dagger$2 hybridization, giving rise to $d_k^\dagger$3 or $d_k^\dagger$4 states under specific conditions (Luo et al., 2023). The primary pairing “glue” is identified as antiferromagnetic superexchange, though Anderson/Kondo-lattice physics arising from hybridization with metallic rare-earth layers alters the mechanism relative to the cuprates (Hepting et al., 2019).

7. Outlook and Open Problems

Recent advances have demonstrated $d_k^\dagger$5 values surpassing the boiling point of liquid nitrogen in bilayer nickelates under pressure (onset >90 K) (Li et al., 24 Jan 2025), diode and paramagnetic-Meissner phenomena in thin films (Eyal et al., 25 Feb 2025), and bulk superconductivity with robust volume fractions in trilayer systems (Zhang et al., 29 Jan 2025). However, there remain outstanding questions:

• The true pairing symmetry is debated, complicated by possible multiband and multi-gap states. Experimental confirmation via phase-sensitive probes is needed.
• The influence of disorder, especially oxygen non-stoichiometry and apical O vacancy formation, is determinative yet still not fully controlled or understood.
• The relationship to cuprate superconductivity is subtle: while key features (optimum $d_k^\dagger$6 filling, $d_k^\dagger$7 dome, strange-metal transport) are echoed, the electronic starting points and pairing mechanisms exhibit both overlap and distinction—especially due to the persistent involvement of rare-earth 5d states and multiorbital physics.
• Implementation of advanced synthesis (direct low-T routes avoiding reduction disorder), targeted chemical substitutions (including 4d/5d analogs), and improved structural control are poised to further clarify the role of electronic structure, dimensionality, and disorder.

A plausible implication is that the field is converging toward a unifying framework encompassing both cuprates and nickelates in the wider context of correlated oxide superconductivity, centering on the optimization of $d_k^\dagger$8 states via layer and chemical control—while also recognizing essential multi-orbital and hybridization-induced distinctions that will inform future materials design and theoretical models (Huang et al., 2024, Wang et al., 10 Sep 2025).