Title: Signature of superconductivity in pressurized La$_4$Ni$_3$O$_{10}$

Abstract: The discovery of high-temperature superconductivity near 80 K in bilayer nickelate La$_3$Ni$_2$O$_7$ under high pressures has renewed the exploration of superconducting nickelate in bulk materials. The extension of superconductivity in other nickelates in a broader family is also essential. Here, we report the experimental observation of superconducting signature in trilayer nickelate La$_4$Ni$_3$O$_{10}$ under high pressures. By using a modified sol-gel method and post-annealing treatment under high oxygen pressure, we successfully obtained polycrystalline La$_4$Ni$_3$O$_{10}$ samples with different transport behaviors at ambient pressure. Then we performed high-pressure electrical resistance measurements on these samples in a diamond-anvil-cell (DAC) apparatus. Surprisingly, the signature of possible superconducting transition with a maximum transition temperature ($T_\text{c}$) of about 20 K under high pressures is observed, as evidenced by a clear drop of resistance and the suppression of resistance drops under magnetic fields. Although the resistance drop is sample-dependent and relatively small, it appears in all of our measured samples. We argue that the observed superconducting signal is most likely to originate from the main phase of La$_4$Ni$_3$O$_{10}$. Our findings will motivate the exploration of superconductivity in a broader family of nickelates and shed light on the understanding of the underlying mechanisms of high-$T_\text{c}$ superconductivity in nickelates.