Imaginary phonon modes and phonon-mediated superconductivity in Y2C3

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 a mixed C and Y character 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. Moreover, we have studied the phase stability of the $I$-$43d$ structure by calculating the enthalpy of different structural motifs of binary compounds containing group IV elements at the 2:3 composition and also exploring the energy landscapes via $ab$ $initio$ molecular dynamics near and out of the $I$-$43d$ structure. Our results show that the $I$-$43d$ type structures with C dimers are preferred in the low to medium pressure range. Because of the wobbling motion of the C dimers, there are many local energy minimums with degenerated energies. Thus, the ensemble average of many $I$-$43d$-distorted structures with C dimer wobbling motion at finite temperature still gives an overall $I$-$43d$ structure.