  Experimental quest for high-temperature and room-temperature
superconductivity (SC) at ambient pressure has been a long-standing research
theme in physics. It has also been desired to construct reliable microscopic
mechanisms that may achieve high-temperature SC. Here we systematically explore
SC in the Su-Schrieffer-Heeger (SSH) electron-phonon coupling models by
performing numerically-exact quantum Monte-Carlo simulations. Our results
reliably showed that superconducting $T_c$ of the SSH models is high,
remarkably higher than those in the Holstein models, particularly in strong
electron-phonon coupling regime. This is mainly because SSH phonons can not
only induce strong pairing between electrons but also help the phase coherence
of Cooper pairs, thus realizing higher $T_c$. As mechanism of higher-$T_c$ of
the SSH models could be potentially relevant to realistic materials, it paves a
promising way to find higher-temperature SC in the future.
