Theoretical analysis on the possibility of superconductivity in the trilayer Ruddlesden-Popper nickelate ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{10}$ under pressure and its experimental examination: Comparison with ${\mathrm{La}}_3{\mathrm{Ni}}_2{O}_7$

We study the possibility of superconductivity in a trilayer Ruddlesden-Popper nickelate ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{10}$ under pressure both theoretically and experimentally, making comparison with the recently discovered high $T_c$ superconductor ${\mathrm{La}}_3{\mathrm{Ni}}_2{O}_7$, 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 calculations. The obtained results suggests that ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{10}$ may also become superconducting under high pressure with $T_c$ comparable to some cuprates, although it is not as high as ${\mathrm{La}}_3{\mathrm{Ni}}_2{O}_7$. We also perform experimental studies using our polycrystalline samples of ${\mathrm{La}}_3{\mathrm{Ni}}_2{O}_{7.01}$ and ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{9.99}$. The superconducting transition of ${\mathrm{La}}_3{\mathrm{Ni}}_2{O}_{7.01}$, 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 also observed for ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{9.99}$, where a drop in the resistance is observed at lower temperatures compared to ${\mathrm{La}}_3{\mathrm{Ni}}_2{O}_{7.01}$, 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 ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{9.99}$. The temperature at which the resistance deviates from 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 ${\mathrm{La}}_3{\mathrm{Ni}}_2{O}_{7.01}$.