[Paper Review] Theoretical analysis on the possibility of superconductivity in a trilayer Ruddlesden-Popper nickelate La$_4$Ni$_3$O$_{10}$ under pressure and its experimental examination: comparison with La$_3$Ni$_2$O$_7$

Hirofumi Sakakibara, Masayuki Ochi+10 more|arXiv (Cornell University)|Sep 18, 2023

Magnetic and transport properties of perovskites and related materials92 references11 citations

TL;DR

The paper theoretically analyzes whether La4Ni3O10 can become superconducting under high pressure using DFT-derived models with FLEX and Eliashberg formalism, and complements this with high-pressure transport experiments on related nickelates to compare with La3Ni2O7.

ABSTRACT

We study the possibility of superconductivity in a trilayer Ruddlesden-Popper nickelate La$_4$Ni$_3$O$_{10}$ under pressure both theoretically and experimentally, making comparison with the recently discovered high $T_c$ superconductor La$_3$Ni$_2$O$_7$, a bilayer nickelate. Through DFT calculations, we find that a structural phase transition from monoclinic to tetragonal takes place around 10 - 15 GPa. Using the tetragonal crystal structure, we theoretically investigate the possibility of superconductivity, where a combination of fluctuation exchange approximation and linearized Eliashberg equation is applied to a six-orbital model constructed from first principles band calculation. The obtained results suggests that La$_4$Ni$_3$O$_{10}$ may also become superconducting under high pressure with $T_c$ comparable to some cuprates, although it is not as high as La$_3$Ni$_2$O$_7$. We also perform experimental studies using our polycrystalline samples of La$_3$Ni$_2$O$_{7.01}$ and La$_4$Ni$_3$O$_{9.99}$. The superconducting transition of La$_3$Ni$_2$O$_{7.01}$, with a maximum onset $T_c$ of 67.0 K at a pressure of 26.5 GPa, is confirmed by a drop in the electrical resistance, as well as the magnetic field dependence of the resistance. Quite interestingly, similar temperature and magnetic field dependencies of the resistance are observed also for La$_4$Ni$_3$O$_{9.99}$, where a drop in the resistance is observed at lower temperatures compared to La$_3$Ni$_2$O$_{7.01}$, under pressures of 32.8 GPa and above. Given the theoretical expectation, the reduction in the resistance can most likely be attributed to the occurrence of superconductivity in La$_4$Ni$_3$O$_{9.99}$. The temperature at which the resistance deviates from a linear behavior, considered as the onset $T_c$, monotonically increases up to 23 K at 79.2 GPa, which is opposite to the pressure dependence of $T_c$ in La3Ni2O7.01.

Motivation & Objective

• Motivate the search for superconductivity in trilayer nickelates under pressure and understand how dimensionality and orbital physics influence pairing.
• Develop a first-principles-based six-orbital model for La4Ni3O10 under high pressure and assess superconductivity via spin-fluctuation-mediated pairing.
• Compare theoretical expectations with high-pressure resistivity measurements on La3Ni2O7.12 and La4Ni3O9.99 to identify signatures of superconductivity.
• Investigate structural phase transitions under pressure and identify the tetragonal phase as the relevant regime for potential superconductivity.

Proposed method

• Perform DFT calculations with PBEsol and PAW in VASP to optimize structures under pressure.
• Identify a monoclinic-to-tetragonal transition around 20 GPa and verify the tetragonal phase with phonon calculations (no imaginary modes).
• Construct a six-orbital (three Ni layers × two Ni–orbitals) tight-binding model using Wannier90 based on the tetragonal structure at 40 GPa.
• Apply FLEX with on-site interactions (U, U', J, J') and solve the linearized Eliashberg equation to obtain the superconducting eigenvalue λ as a proxy for Tc.
• Analyze the superconducting gap functions across bonding, anti-bonding, and non-bonding d3z2−r2 bands and their doping dependence.
• Compare the theoretical findings for La4Ni3O10 with previously studied La3Ni2O7 to assess relative Tc expectations.

Experimental results

Research questions

• RQ1 Can La4Ni3O10 become superconducting under high pressure in its tetragonal phase?
• RQ2 How do the Fe-based-like spin fluctuations and multi-orbital bands in La4Ni3O10 influence superconducting pairing compared to La3Ni2O7?
• RQ3 What is the influence of band filling and the presence of a non-bonding d3z^2−r^2 band on the superconducting eigenvalue λ?
• RQ4 Does the experimentally observed high-pressure resistive behavior in related nickelates align with a superconducting interpretation?

Key findings

• DFT predicts a monoclinic to tetragonal transition around 20 GPa, with a stable tetragonal I4/mmm structure at higher pressures.
• For La4Ni3O10 under 40 GPa, the six-orbital model yields a superconducting eigenvalue λ that is reduced relative to La3Ni2O7 but remains sizable (around the range observed in some cuprates).
• λ for La4Ni3O10 is locally maximized near stoichiometry, as all three d3z^2−r^2 bands contribute to superconductivity in this regime.
• The superconducting gap function analyzes show sign changes between bonding/antibonding and non-bonding bands, indicating multi-band interlayer pairing tendencies.
• Experimentally, La3Ni2O7.12 shows a Tc onset around 78 K at 26.1 GPa, while La4Ni3O9.99 shows resistance drops at higher pressures with increasing onset temperature up to ~23 K by 79.2 GPa, suggesting possible superconductivity in the trilayer sample under pressure.