  For Y$_2$C$_3$ with a superconducting critical temperature (T$_c$) $\sim$18
K, zone-center imaginary optical phonon modes have been found for the
high-symmetry $I$-$43d$ structure due to C dimer wobbling motion and electronic
instability from a flat band near Fermi energy. After lattice distortion to the
more stable lowest symmetry $P1$ structure, these stabilized low-energy phonon
modes with mixed C and Y characters carry a strong electron-phonon coupling to
give arise to the observed sizable T$_c$. Our work shows that compounds with
the calculated dynamical instability should not be simply excluded in
high-throughput search for new phonon-mediated superconductors.

Superconductivity;Materials Science