Giant Grüneisen parameter in a superconducting quantum paraelectric

Superconductivity and ferroelectricity are typically incompatible because the former needs free carriers, but latter is usually suppressed by unless their concentration low. In case of strontium titanate with low carrier concentration, unconventional superconductivity were shown to be correlated. Here, we report theoretically experimentally evaluated Gr\"uneisen parameters whose divergence under tensile stress indicates that dominant phonon mode enhances superconducting order ferroelectric transverse soft-mode. This finding rules out all other modes as main contributors enhanced in strained titanate. methodology here can applied many quantum materials.