Electronic structure trends in La₂RNi₂O₇ (R= Pr, Nd, Sm) from first-principles

Summary

Using first-principles DFT+U calculations, this work investigates the trends in crystal structure and electronic properties of La₃Ni₂O₇ doped with different rare-earth elements (Pr, Nd, Sm). The results show that dopant atoms preferentially occupy La sites in the rock-salt layer; as the ionic radius decreases from Pr to Sm, the chemical pressure effect leads to a monotonic reduction in unit-cell volume and a successive increase in the monoclinic-to-tetragonal structural transition pressure, with this transition largely coinciding with the emergence of superconductivity, in agreement with experimental observations. In the high-pressure tetragonal phase, the dz² band flattens and crosses the Fermi level, producing a characteristic hole-type Fermi surface that is regarded as a key electronic hallmark of superconductivity. With decreasing rare-earth ion size, the in-plane hopping integral is enhanced, whereas the out-of-plane hopping integral is weakened due to the shortening of the apical Ni–O bond. These findings offer microscopic mechanistic insights into how rare-earth doping influences the electronic structure of bilayer Ruddlesden-Popper nickelates and its connection to the superconducting transition temperature.

Materials

• La₃Ni₂O₇
• La₂PrNi₂O₇
• La₂NdNi₂O₇
• La₂SmNi₂O₇

Methods

• DFT
• DFT+U (GGA+U)
• Wannier function analysis
• first-principles structural optimization
• enthalpy comparison

Keywords

• chemical pressure
• monoclinic to tetragonal structural transition
• flat dz2 band
• hole pocket
• in plane hopping
• out of plane hopping
• apical ni o bond length

Highlights

• The doped atoms preferentially occupy the La sites in the rocksalt layer, confirmed by enthalpy comparison.
• Despite c-axis lattice constant compression, out-of-plane hopping decreases due to a reduction in the apical Ni-O bond length in the rocksalt layer, challenging the expectation of enhanced interlayer coupling.
• The emergence of flat dz2 bands at the Fermi level and corresponding hole pockets is a universal electronic signature of the superconducting phase across all compounds.
• The increase of T_c with chemical pressure correlates with enhanced in-plane hopping and hybridization rather than increased interlayer coupling.

Conclusions

• All compounds undergo a pressure-driven structural transition from monoclinic to tetragonal phase, with the critical pressure increasing as the rare-earth size decreases.
• At high pressure, flat dz2 bands of character emerge at the Fermi level, similar to hydrostatic pressure.
• The dominant out-of-plane hopping decreases upon chemical pressure, associated with a decrease in the apical Ni-O bond length to the rocksalt layer.
• The dominant planar hopping increases upon chemical pressure.
• The results emphasize the importance of hybridization effects between out-of-plane dz2 orbitals and itinerant planar dx2-y2 states for superconductivity in this family.

Main claims

• Substitution of rare-earth elements (Pr, Nd, Sm) into La₃Ni₂O₇ occurs preferentially at the rock-salt layer La sites.
  • Evidence: Enthalpy comparison (Appendix A) shows rock-salt substitution energetically favorable,Agrees with experimental X-ray diffraction data (Refs [44,24])
• The pressure-induced structural transition from monoclinic to tetragonal phase coincides with the emergence of superconductivity, and the transition pressure increases with decreasing R ionic radius.
  • Evidence: Fig. 1(b) enthalpy vs pressure curves: transition pressures increase from 9.5 to 20.5 GPa,Qualitative agreement with experimental pressures (Pr: 11 GPa, Nd: 13 GPa, Sm: 18 GPa),All compounds become tetragonal around the superconducting pressure range
• At high pressure, flat dz2 bands cross the Fermi level forming extra hole pockets, a key electronic signature for superconductivity; chemical pressure enhances in-plane hopping and hybridization while reducing out-of-plane hopping.
  • Evidence: Fig. 3(c,d): band structures at 21 GPa show flat dz2 bonding band at E_F,Fermi surfaces (Fig. 3 lower panels) show five pockets including dz2 hole pockets,Fig. 4(a,b): t_perp decreases, t_planar and hybridization increase with smaller R,Apical Ni-O_rocksalt bond length decreases (Appendix D)
• The enhancement of T_c in Sm-doped La₃Ni₂O₇ is likely driven by increased planar hybridization and hopping rather than out-of-plane coupling.
  • Evidence: T_c increases from ≈80 K (undoped) to 96 K (Sm-doped) experimentally,Calculated t_perp decreases while t_planar and hybridization increase with decreasing R size,Hybridization between dz2 and dx2-y2 states is argued to be important for superconductivity

Workflow

• Structural optimization and phase transition analysis — Chemical pressure from smaller R ions increases the monoclinic-to-tetragonal transition pressure, aligning with the onset of superconductivity.
  • Materials: QUANTUM-ESPRESSO; GGA+U (U=8 eV); Experimental crystal structures (P₂₁/n, I₄/mmm); Plane-wave basis (80R_y cutoff)
  • Methods: Enthalpy difference comparison for substitution site preference; Full geometry optimization (forces < 10-4Ry/Bohr); Enthalpy vs pressure calculations to determine transition pressure
  • Observations: Dopants prefer rock-salt-layer La sites (energetically favorable); Transition pressures: 9.5 GPa (La), 14 GPa (Pr), 17 GPa (Nd), 20.5 GPa (Sm); c-axis and volume decrease with smaller R; apical Ni-O-Ni bond angle decreases
• Electronic band structure and Fermi surface calculations — The emergence of flat dz2 hole pockets at high pressure is a robust electronic hallmark of superconductivity across all compounds.
  • Materials: DFT with same setup; FermiSurfer for visualization
  • Methods: Nonmagnetic band structure calculation; Orbital-resolved Fermi surface analysis
  • Observations: At ambient: Ni-dx2-y2 and dz2 bands near E_F, two Fermi sheets (electron α, hole β); At₂₁ GPa: flat dz2 bonding band crosses E_F, five Fermi pockets including extra hole pockets γ,δ of dz2 character; Subtle band shifts and pocket size changes with R size
• Wannier function analysis and interpretation — The enhancement of T_c upon rare-earth doping is correlated with increased planar hopping and hybridization, emphasizing the role of dz2–dx2-y2 hybridization in superconductivity.
  • Materials: Wannier90; Projection onto Ni-3d orbitals
  • Methods: Construction of maximally localized Wannier functions to extract hopping integrals; Correlation of hopping trends with bond lengths
  • Observations: Out-of-plane hopping t_perp decreases (from La to Sm) due to shortening of apical Ni-O_rocksalt bond; In-plane hopping t_planar increases; Hybridization between dz2 and dx2-y2 increases