Jahn-Teller distortion on strained La$_3$Ni$_2$O$_7$ thin films

Abstract: We present a systematic study of the electronic structure of strained La$3$Ni$_2$O$_7$ thin films. We show that biaxial compressive strain mainly elongates the outer apical Ni-O bond while leaving the inner apical Ni-O bond nearly unchanged. As a result, the Jahn-Teller splitting $Δ{JT}$ is strongly enhanced, whereas the interlayer $d_{z^2}$ hopping $t_\perp^z$ changes only weakly. Since superconductivity is widely believed to emerge only below a critical in-plane lattice constant, our results identify the strain-enhanced $Δ_{JT}$ as the relevant microscopic tuning parameter. Consistently, the calculated Fermi surfaces and Hall response for LaAlO$_3$ and SrLaAlO$_4$ substrates agree with ARPES and Hall measurements. Our results identify Jahn-Teller distortion as a key tuning parameter in strained La$_3$Ni$_2$O$_7$ and support its central role in optimizing superconductivity in bilayer nickelates.

• The paper demonstrates that substrate-induced strain selectively enhances Jahn-Teller splitting (ΔJT) by elongating the outer Ni-O bonds, which is critical for tuning superconductivity.
• It employs first-principles DFT, tight-binding modeling, and ICOHP analysis to quantitatively link strain effects with modifications in orbital energies and hopping parameters.
• The study reveals a clear connection between strain-tuned Fermi surface changes, Hall coefficient variations, and superconducting phase enhancements in La3Ni2O7 thin films.

Jahn-Teller Distortion as a Central Tuning Parameter in Strained La$_3$Ni$_2$O$_7$ Thin Films

Introduction

Recent reports of high-temperature superconductivity in bilayer nickelates, especially La$_3$Ni$_2$O$_7$, have sparked substantial interest in the interplay of structural, electronic, and orbital degrees of freedom in these systems. While the primary focus has been on the role of multi-orbital $e_g$ physics and interlayer $d_{z^2}$ hybridization, the influence of Jahn-Teller (JT) distortions—specifically, the splitting $\Delta_{JT}$ between $d_{x^2-y^2}$ and $_2$0 states—has remained comparatively underexplored. This study provides a detailed theoretical analysis, integrating density functional theory (DFT), tight-binding (TB) modeling, and experimental comparison, to elucidate how epitaxial strain in thin films selectively enhances JT splitting, establishing it as a decisive microscopic parameter for tuning superconductivity in bilayer nickelate platforms (2604.02191).

Structural Response to Epitaxial Strain

The bilayer structure of La$_2$1Ni$_2$2O$_2$3 introduces significant local symmetry reduction from $_2$4 to $_2$5, due to the inequivalence of inner ($_2$6) and outer ($_2$7) apical oxygen sites. Crucially, biaxial compressive strain in the $_2$8-plane elongates the Ni-O$_2$9 outer bonds, while the Ni-O$_7$0 inner bond remains almost unaffected.

Figure 1: The NiO$_7$1 octahedral network in strained La$_7$2Ni$_7$3O$_7$4 thin films, relevant orbital level diagram, and empirical relation of $_7$5 with in-plane and out-of-plane lattice constants.

This asymmetric structural response translates into highly selective modification of the local crystal field environment. With decreasing in-plane lattice constant, the octahedral elongation is dominated by an increase in the $_7$6 bond length, directly enhancing the JT splitting $_7$7. The interlayer hopping $_7$8, set by the inner oxygen $_7$9, shows minimal variation.

First-Principles Modeling and TB Parameter Extraction

Ab initio calculations were performed using meta-GGA functionals within VASP, targeting an infinitely thick film geometry to best represent the experimental situation. By fixing the in-plane parameter $_3$0 and letting $_3$1 relax (mimicking substrate control), the calculations reveal:

• $_3$2 increases significantly with decreasing $_3$3,
• $_3$4 is robust against strain,
• $_3$5 increases rapidly as $_3$6 decreases (linear slope $_3$7),
• $_3$8 remains almost unchanged (linear slope $_3$9 for $_2$0-axis changes).

Figure 2: Evolution of apical bond lengths, $_2$1, and $_2$2 under changing $_2$3; demonstration of strong selective strain sensitivity for JT splitting.

The ICOHP analysis confirms that the enhanced Ni-O$_2$4 bond weakening is responsible for the selective increase in $_2$5.

Electronic Structure, Fermiology, and Hall Coefficient

The TB models parameterized against DFT provide insight into substrate-tuned Fermiology. Two representative substrates—SLAO (strong compressive strain) and LAO (weaker)—show marked differences:

• SLAO: Two Fermi pockets ($_2$6—electronlike, $_2$7—holelike); experiment/theory agreement.
• LAO: Additional $_2$8 (holelike) pocket emerges due to weaker JT splitting.

Figure 3: Calculated Fermi surfaces for SLAO and LAO substrates, experimental ARPES comparison, Hall coefficient evolution, and local orbital configuration changes with strain/JT distortion.

These Fermi surface changes result in a pronounced modulation of the Hall coefficient $_2$9. The magnitude of $_7$0 is far more negative for SLAO, mirroring the carrier compensation imposed by the strain-enhanced JT splitting. Quantitative trends in $_7$1 are in qualitative agreement with recent experimental data.

Theoretical Implications for Superconductivity

The orbital-resolved evolution—with anti-symmetric $_7$2 descending relative to $_7$3 as $_7$4 grows—positions the system near an optimal regime for two-orbital molecular Mott physics. This regime, previously posited to stabilize high-$_7$5 superconductivity via superexchange-mediated pairing [2025Zhange], is maximally accessed when $_7$6 and $_7$7 are comparable but not too large or too small.

The substrate-dependent $_7$8 enhancement across the LAO→SLAO transition correlates with the theoretical $_7$9 shift, supporting the assertion that JT splitting, not the interlayer hopping, is the critical tuning knob for superconductivity in strained La$e_g$0Ni$e_g$1O$e_g$2 films.

Comparison With Bulk Hydrostatic Pressure

Distinct from thin-film strain, hydrostatic pressure in the bulk compresses both inner and outer apical bonds uniformly, causing both $e_g$3 and $e_g$4 to change simultaneously and comparably.

Figure 4: Response of apical bond lengths, $e_g$5, and $e_g$6 to bulk hydrostatic pressure—depicting the lack of selective JT enhancement compared to thin-film strain-tuning.

This differentiation elucidates why thin films offer a cleaner avenue for isolating the role of JT physics; pressure inevitably convolutes changes in orbital energies and interlayer coupling.

Implications and Future Prospects

This work shifts the focus from interlayer hopping as the principal superconductivity tuning parameter to Jahn-Teller splitting, as directly controlled by substrate strain. A practical implication is the prescription to target compressive epitaxial strain to maximize $e_g$7 for enhanced $e_g$8 in nickelate heterostructures. Theoretical models of unconventional superconductivity in this class must thus incorporate strain-driven orbital polarization and its influence on Mott physics and pairing channels.

From a materials engineering perspective, these findings suggest that substrate selection and interface design offer considerable leverage for tuning the phase diagram, Fermi surface topology, and correlated electronic responses. The approach and analysis can be generalized to related Ruddlesden-Popper nickelates, where symmetry breaking and differential bond responses may provide routes to customizable orbital splitting and, potentially, higher $e_g$9.

Conclusion

This systematic theoretical investigation establishes JT distortion, quantified by $d_{z^2}$0, as the dominant microscopic parameter determining the electronic structure and superconducting propensity of La$d_{z^2}$1Ni$d_{z^2}$2O$d_{z^2}$3 thin films under epitaxial strain. Selective elongation of the outer Ni-O bond enhances $d_{z^2}$4 with minimal change to $d_{z^2}$5, driving substrate-dependent changes in Fermiology and Hall responses in agreement with experiment. These results highlight the necessity of incorporating explicit JT physics in future models of nickelate superconductivity and underscore the utility of strain as a direct, spectroscopically verifiable tuning parameter in complex oxide electronics.