Influence of the topological Lifshitz transition on the superconductivity of the high-pressure electride Li4Pd

High-pressure electride (HPE) superconductors often maintain structural symmetry over a wide pressure range, whereas their interstitial anion electrons (IAEs) undergo significant changes in topology and energy levels, potentially resulting in topological Lifshitz transitions in their Fermi surfaces. These Lifshitz transitions can play critical roles in influencing superconducting properties. However, their impact on the superconductivity of HPEs remains largely unexplored. To address this gap, we investigate a novel HPE, $\mathrm{L}{\mathrm{i}}_{4}\mathrm{Pd}$, which features distinct Fermi surfaces, including a hole ellipsoid and a warped electron rectangular cylinder. This combination satisfies the conditions for a Kohn anomaly, suggesting that $\mathrm{L}{\mathrm{i}}_{4}\mathrm{Pd}$ may be a potential HPE superconductor. Our theoretical calculations reveal that under high pressures, the Fermi surface of $\mathrm{L}{\mathrm{i}}_{4}\mathrm{Pd}$ undergoes a Lifshitz transition that affects the momentum distribution of electrons on the Fermi surface, leading to changes in the energy provided by phonons for forming Cooper pairs. Moreover, this transition modifies the phonon frequencies involved in electron-phonon coupling. The superconducting transition temperature of $\mathrm{L}{\mathrm{i}}_{4}\mathrm{Pd}$ is calculated to be 34.5 K at 250 GPa, which is comparable to that of $\mathrm{L}{\mathrm{i}}_{6}\mathrm{P}$ (39.3 K at 270 GPa). Our findings indicate that the formation of closed Fermi surfaces with extended spatial scales is a general feature that could be leveraged to design new classes of high-temperature superconductors among HPEs.