Superexchanges and Charge Transfer in the La$_3$Ni$_2$O$_7$ Thin Films

The recent discovery of ambient-pressure superconductivity with $T_c$ above 40 K in La$_3$Ni$2$O$7$ thin films represents a significant advance in the field of nickelate superconductor. Motivated by the experimental reports, here we study an 11-band $d-p$ Hubbard model with tight-binding parameters derived from \textit{ab initio} calculations, using large scale determinant quantum Monte Carlo and cellular dynamical mean-field theory. Our results reveal that the major superexchange couplings in La$3$Ni$2$O$7$ thin films can be substantially weaker than in the bulk material at 29.5 Gpa. Specifically, the out-of-plane antiferromagnetic correlation between Ni$-d{3z^2-r^2}$ orbitals is reduced by about 27% in film, while the in-plane magnetic correlations remain largely unaffected. We evaluate the corresponding antiferromagnetic coupling constants, $J{\perp}$ and $J{\parallel}$ using perturbation theory. With regard to charge transfer properties, we find that the biaxial compression in films reduces charge transfer gap. We also resolve the orbital distribution of doped holes and electrons among the in-plane (Ni$-d{x^2-y^2}$ and O$-p_x/p_y$) and the out-of-plane (Ni$-d{3z^2-r^2}$ and O$-p_z$) orbitals, uncovering a pronounced particle-hole asymmetry. Theses findings lay a groundwork for the study of low-energy $t-J$ model of La$_3$Ni$_2$O$_7$ films and provide key insights into the understanding of physical distinctions between the film and bulk bilayer nickelates.

💡 Research Summary

The paper investigates the microscopic origins of the recently reported ambient‑pressure superconductivity in La₃Ni₂O₇ (LNO) thin films, which exhibit transition temperatures above 40 K, by constructing and solving an 11‑band d‑p Hubbard model that explicitly includes the four Ni‑e_g (d_{x²‑y²} and d_{3z²‑r²}) orbitals and the seven most relevant O‑2p orbitals of the NiO₂ bilayer. Tight‑binding parameters (hopping integrals t₁–t₇ and on‑site energies ε) are taken from density‑functional calculations performed on a biaxially compressed film structure (grown on LaAlO₃ or SrLaAlO₄ substrates). Electron correlations are introduced via a Hubbard repulsion U (default 7 eV) applied only to Ni‑d orbitals and an Ising‑type Hund’s coupling J_H = 0.15 U; the double‑counting correction follows Held’s formula.

Two complementary many‑body techniques are employed. Determinant quantum Monte Carlo (DQMC) simulations are carried out on a 6 × 6 unit‑cell lattice (396 orbitals) at relatively high temperatures (lowest reachable T = 0.25 eV) with an average sign ⟨s⟩≈0.79. Cellular dynamical mean‑field theory (CDMFT) with a 2 × 2 cluster (44 orbitals) is used to access lower temperatures (T ≈ 0.08 eV) while maintaining a reasonable sign (⟨s⟩≈0.56). Both methods allow direct measurement of spin–spin correlation functions ⟨S_i·S_j⟩ and orbital‑resolved occupations, enabling an extraction of the effective superexchange couplings J⊥ (inter‑layer, involving d_{3z²‑r²}) and J∥ (intra‑layer, involving d_{x²‑y²}).

Perturbative second‑order analysis in the atomic limit yields J⊥≈0.135 eV and J∥≈0.084 eV for U = 7 eV, giving a ratio J∥/J⊥≈0.62. DQMC and CDMFT confirm these values qualitatively but reveal a substantial reduction of the inter‑layer antiferromagnetic (AFM) exchange in the thin film relative to bulk LNO. Specifically, the DQMC spin correlation ⟨S·S⟩ for the d_{3z²‑r²}–d_{3z²‑r²} pair drops by roughly 27 % (from –0.057 in bulk to –0.041 in the film). In contrast, the intra‑layer d_{x²‑y²}–d_{x²‑y²} AFM correlation remains essentially unchanged, so that in the film the two exchange pathways become comparable in strength. Temperature scans show that the suppression of J⊥ is more pronounced at low T, while J∥ varies only mildly, suggesting that the weakened vertical superexchange is a key factor behind the lower T_c observed in films compared with bulk (where J⊥ dominates).

Charge‑transfer properties are examined by plotting hole concentration n_h versus hole chemical potential μ_h (or equivalently electron chemical potential μ_e). An inflection near μ_h ≈ –1.55 signals the opening of a charge‑transfer gap at half‑filling; however, the gap in the film is less flat than in bulk, indicating a reduced gap magnitude (≈0.2 eV smaller). Doping studies reveal a pronounced particle‑hole asymmetry. Upon hole doping, added holes preferentially occupy O‑p_x/p_y orbitals and the Ni‑d_{x²‑y²} orbital, while the d_{3z²‑r²} orbital receives comparatively few holes. Electron doping, on the other hand, fills Ni‑d orbitals, with the d_{3z²‑r²} orbital acquiring roughly three times more electrons than d_{x²‑y²}. This orbital selectivity is interpreted within the Zaanen‑Sawatzky‑Allen framework and linked to the competition between Hund’s‑coupling‑driven pairing and e_g‑hybridization‑driven mechanisms; the occupation of d_{3z²‑r²} appears crucial for determining which route dominates in the thin film.

The authors conclude that biaxial compression in LNO thin films simultaneously weakens the vertical superexchange and narrows the charge‑transfer gap, thereby reshaping the low‑energy effective Hamiltonian. For theoretical modeling, the t‑J description must be revised to incorporate a reduced J⊥/J∥ ratio and a smaller charge‑transfer energy Δ. These adjustments are essential for capturing the distinct magnetic and electronic landscape of the film and for guiding future material‑design strategies aimed at optimizing superconductivity in nickelate heterostructures.