Theoretical analysis on the possibility of superconductivity in a trilayer Ruddlesden-Popper nickelate La_4Ni_3O_10 under pressure and its experimental examination: comparison with La_3Ni_2O_7

We study the possibility of superconductivity in a trilayer Ruddlesden-Popper nickelate La_4Ni_3O_10 under pressure both theoretically and experimentally, making comparison with the recently discovered high T_c superconductor La_3Ni_2O_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_4Ni_3O_10 may also become superconducting under high pressure with T_c comparable to some cuprates, although it is not as high as La_3Ni_2O_7. We also perform experimental studies using our polycrystalline samples of La_3Ni_2O_7.01 and La_4Ni_3O_9.99. The superconducting transition of La_3Ni_2O_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_4Ni_3O_9.99, where a drop in the resistance is observed at lower temperatures compared to La_3Ni_2O_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_4Ni_3O_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.