Unconventional superconductivity without doping in infinite-layer nickelates under pressure

The study addresses whether isotropic pressure can enhance unconventional superconductivity in infinite-layer nickelates and, crucially, whether superconductivity can be realized without chemical doping (Sr substitution) by leveraging pressure-induced changes in electronic structure. Motivated by the similarities and differences between nickelates and cuprates and by prior theoretical predictions of nickelate superconductivity with a dome-like Tc(x), the authors investigate Sr- and pressure-dependent superconductivity in SrxPr1−xNiO2. Prior work showed that self-doping via rare-earth-derived electron pockets places nickelates close to a correlated-metal regime rather than an antiferromagnetic insulator, and models ranging from single-band to multiband have been proposed. A recent experiment reported a monotonic increase of Tc with pressure up to 12 GPa for x=0.18 without signs of saturation. The purpose here is to compute the full Tc phase diagram versus Sr doping x and pressure P, quantify the role of pressure on hopping t, interaction U, and effective self-doping δ of the Ni dx2−y2 band, and determine whether undoped PrNiO2 becomes superconducting under pressure.

• Foundational context: High-Tc superconductivity in cuprates established the paradigm of doping correlated parent compounds (Bednorz & Müller). Nickelate superconductivity in infinite-layer A1−xBxNiO2 (A=La, Nd, Pr; B=Sr, Ca) has been discovered, exhibiting a dome-like Tc vs doping relatively independent of A and B.
• Similarities/differences to cuprates: Nickelates share structural/electronic motifs with cuprates but have weaker O-2p/transition-metal 3d hybridization and additional rare-earth-derived bands that cross the Fermi level, forming electron pockets that self-dope the Ni dx2−y2 band by ~5% holes, preventing a Mott insulating parent.
• Theoretical status: Multiple models (single-band to multiband, GW+EDMFT, cluster DMFT) support unconventional (non-phonon) pairing in nickelates. Kitatani et al. predicted the superconducting dome quantitatively using a one-band Hubbard model for Ni dx2−y2 supplemented by electron reservoirs (pockets). Prior work suggested increasing Tc by reducing U/t.
• Pressure experiments and prior calculations: Wang et al. observed Tc increasing from 18 to 31 K at 12 GPa for Pr0.82Sr0.18NiO2 thin films on STO, with no saturation. Earlier electronic-structure calculations under pressure fixed in-plane lattice constants to ambient STO and relaxed c, while the current work simulates isotropic pressure more realistically via the substrate’s equation of state.
• Distinct systems: High Tc or resistive anomalies under pressure were also reported for La3Ni2O7 with a different mechanism (3d5, CDW fluctuations), distinct from the slightly doped 3d8 nickelates studied here.

• Structural treatment under pressure: Because superconducting films are grown on SrTiO3 (STO) substrates and measured under isotropic pressure in a diamond anvil cell, the STO equation of state was computed using DFT to obtain pressure-dependent in-plane lattice parameters. For each pressure, the nickelate in-plane a,b lattice parameters were fixed to those of STO, and the out-of-plane c was relaxed by minimizing enthalpy. Resulting lattice constants for P = 0, 12, 50, 100, 150 GPa were obtained.
• Electronic-structure calculations: DFT calculations were performed (VASP, PAW, PBESol functional; 500 eV plane-wave cutoff; Brillouin-zone grid spacing 0.25 Å−1 with Gaussian smearing 0.05 eV). Wannierization (wannier90) produced (i) a 10-band model including all Pr-d and Ni-d orbitals and (ii) a 1-band model for the Ni dx2−y2 orbital.
• Interaction parameters: Local Coulomb interactions were obtained from constrained random phase approximation (CRPA) in a Wannier basis for entangled bands using a full-potential LMTO framework. For the 10-band model: U(Ni 3d)=4.4 eV, J=0.65 eV; U(Pr 5d)=2.5 eV, J=0.25 eV (from prior work). For the 1-band model: U=3.4 eV, notably pressure-insensitive; the main pressure effect is via hopping parameters t, t′, t″ (from Wannier fits), with t increasing from −0.39 eV (0 GPa) to −0.62 eV (150 GPa).
• Many-body calculations: DMFT (w2dynamics) was performed for the 10-band model (T=300 K; ~30 iterations) to obtain renormalized spectral functions and to quantify the effective hole doping δ of the Ni dx2−y2 band (relative to half-filling) by accounting for electron-pocket occupation. A second set of DMFT calculations for the 1-band Hubbard model (variable T; ~70 iterations) used pressure-dependent hoppings and the δ determined from the 10-band DMFT.
• Superconductivity evaluation: The dynamical vertex approximation (ladder DIA/DfA) was employed. From the local irreducible particle-hole vertex (w2dynamics), non-local susceptibilities/vertices were computed using DGApy with a Moriya-λ correction. These were input to the particle-particle channel, solving the linearized Eliashberg equation (one parquet step without full self-consistency). The superconducting eigenvalue and Tc were mapped along four paths: Tc vs x at P=0 and 50 GPa; Tc vs P at fixed x=0.18; Tc vs P at x=0.
• Codes: VASP (DFT), wannier90 (Wannierization), w2dynamics (DMFT), DGApy (non-local ladders). Data and inputs available via the TU Wien and NOMAD repositories.

• Pressure-driven changes in electronic parameters:
  • Hopping amplitude t for Ni dx2−y2 nearly doubles from |t|=0.39 eV (0 GPa) to 0.62 eV (150 GPa), widening the bandwidth. U remains essentially unchanged with pressure, reducing U/t at higher P.
  • Electron pockets deepen and enlarge with pressure, increasing the effective hole doping δ of the Ni dx2−y2 band by ~0.06 from 0 to 100 GPa.
• Tc vs doping x at fixed pressure:
  • At ambient pressure (0 GPa), results reproduce prior nickelate domes; at 50 GPa, the maximum Tc roughly doubles and shifts to lower x (peak near x≈0.10). Even at x=0 (undoped), superconductivity appears at 50 GPa due to enhanced self-doping.
• Tc vs pressure P:
  • For x=0.18, Tc increases at a rate of 0.81 K/GPa up to 12 GPa, matching the experimental rate 0.96 K/GPa. Theoretical Tc at 0 GPa is ~30 K (experiment ~18 K). Tc continues to increase with P, peaking at ~49 K near 50 GPa, then decreases at higher P.
  • For x=0 (PrNiO2), superconductivity onsets below 50 GPa and peaks near ~100 K around 100 GPa, enabled solely by pressure-enhanced self-doping and bandwidth.
• Mechanism:
  • Two key pressure effects explain the trends: (1) increased t lowers U/t toward and past an optimal regime, raising then reducing Tc as P grows; (2) increased δ from larger electron pockets moves x=0.18 toward overdoping with P (reducing Tc beyond 50 GPa) while moving x=0 from underdoped to optimal (maximizing Tc between 50–100 GPa).

The findings address whether pressure can enhance superconductivity and induce it without chemical doping in infinite-layer nickelates. Pressure increases the bandwidth (larger t) while leaving U nearly unchanged, thereby reducing U/t toward an optimal regime for d-wave superconductivity. Concurrently, pressure enlarges rare-earth electron pockets, increasing the effective hole doping δ of the Ni dx2−y2 band. For x=0.18, pressure drives the system from near-optimal doping into overdoping, explaining the rise of Tc up to ~50 GPa followed by a decrease at higher pressures. For the undoped parent (x=0), pressure moves the system from underdoped to optimal δ and favorable U/t between 50–100 GPa, yielding a predicted Tc approaching 100 K. Thus, the pressure phase diagram features an enhanced and broadened superconducting dome, with its maximum shifted to lower Sr content under 50–100 GPa. Experimentally, the computed Tc(P) slope up to 12 GPa closely matches measurements, supporting the proposed mechanism. The results imply that nickelates have not yet reached their intrinsic Tc ceiling and could approach cuprate-like Tc via pressure or epitaxial strain strategies.

This work maps the superconducting phase diagram of SrxPr1−xNiO2 under pressure using DFT+DMFT combined with ladder DIA. It reproduces the experimentally observed rise of Tc with pressure for x=0.18 and predicts further enhancements: a peak Tc ≈ 49 K at ~50 GPa for x=0.18 and, most notably, superconductivity without Sr doping with a maximum Tc near 100 K at ~100 GPa in PrNiO2. The underlying mechanism is the dual pressure effect of increased hopping (lower U/t) and enhanced self-doping δ from enlarged electron pockets. These results place nickelates nearly on par with cuprates in achievable Tc and suggest that optimal performance may occur at lower Sr content under substantial pressure. Future directions include experimental verification of high-pressure superconductivity in undoped PrNiO2, exploration of alternative substrates to mimic in-plane compression (potentially requiring ≥10% doping due to reduced self-doping), and methodological advances toward fully self-consistent parquet treatments.

• The superconductivity analysis uses ladder DIA with a single parquet step and Moriya-λ correction, without full parquet self-consistency.
• DMFT and DFT were not run in a fully self-consistent feedback loop.
• 10-band DMFT calculations were performed at 300 K, and antiferromagnetism may compete at low δ; regions dominated by AFM are not mapped by superconducting eigenvalues.
• Modeling of pressure in thin films relies on fixing in-plane parameters to pressure-dependent STO substrate values and relaxing c; real experimental conditions and defects/inhomogeneities may introduce deviations.
• The theoretical Tc at 0 GPa for x=0.18 exceeds the reported experimental value, indicating possible materials-specific effects (defects, stoichiometry, disorder) not captured in the model.