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We study the possibility of superconductivity in a trilayer Ruddlesden-Popper nickelate La₄Ni₃O₁₀ under pressure both theoretically and experimentally, making comparison with the recently discovered high T₂ superconductor La₃Ni₂O₇, 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 calculations. The obtained results suggests that La₄Ni₃O₁₀ may also become superconducting under high pressure with T₂ comparable to some cuprates, although it is not as high as La₃Ni₂O₇. We also perform experimental studies using our polycrystalline samples of La₃Ni₂O₇. ₀₁ and La₄Ni₃O₉. ₉₉. The superconducting transition of La₃Ni₂O₇. ₀₁, with a maximum onset T₂ 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 also observed for La₄Ni₃O₉. ₉₉, where a drop in the resistance is observed at lower temperatures compared to La₃Ni₂O₇. 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 La₄Ni₃O₉. ₉₉. The temperature at which the resistance deviates from linear behavior, considered as the onset T₂, monotonically increases up to 23 K at 79. 2 GPa, which is opposite to the pressure dependence of T₂ in La₃Ni₂O₇. ₀₁.
Sakakibara et al. (Wed,) studied this question.