  Lanthanum, yttrium, and cerium hydrides are the three most well-known
superconducting binary hydrides (La-H, Y-H, and Ce-H systems), which have
gained great attention in both theoretical and experimental studies. Recent
studies have shown that ternary hydrides composed of lanthanum and yttrium can
achieve high superconductivity around 253 K. In this study we employ the
evolutionary-algorithm-based crystal structure prediction (CSP) method and
first-principles calculations to investigate the stability and
superconductivity of ternary hydrides composed of (Y, Ce) and (La, Ce) under
high pressure. Our calculations show that there are multiple stable phases in
Y-Ce-H and La-Ce-H systems, among which $P4/mmm$-YCeH$_{8}$,
$P\bar{6}m2$-YCeH$_{18}$, $R\bar{3}m$-YCeH$_{20}$, $P4/mmm$-LaCeH$_{8}$, and
$R\bar{3}m$-LaCeH$_{20}$ possessing H$_{18}$, H$_{29}$ and H$_{32}$ clathrate
structures can maintain both the thermodynamic and lattice-dynamic stabilities.
In addition, we also find that these phases also maintain a strong resistance
to decomposition at high temperature. Electron-phonon coupling calculations
show that only three of these five phases can exhibit high-temperature
superconductivity. The superconducting transition temperatures ($T_\mathrm{c}$)
of $R\bar{3}m$-YCeH$_{20}$, $R\bar{3}m$-LaCeH$_{20}$, and
$P\bar{6}m2$-YCeH$_{18}$ are predicted using the Allen-Dynes-modified McMillan
formula to be 122 K at 300 GPa, 116 K at 250 GPa, and 173 K at 150 GPa,
respectively. Moreover, the pressure to stabilize $P\bar{6}m2$-YCeH$_{18}$ can
be lowered to 150 GPa, suggesting an accessible condition for its high-pressure
synthesis.
