Proton Collective Quantum Tunneling Induces Anomalous Thermal Conductivity of Ice under Pressure

Proton tunneling is believed to be non-local in ice but has never been shown experimentally. Here we measured thermal conductivity of ice under pressure up to 50 GPa and found it to increase with pressure until 20 GPa but decrease at higher pressures. We attribute this anomalous drop of thermal conductivity to the collective tunneling of protons at high pressures, supported by large-scale quantum molecular dynamics simulations. The collective tunneling loops span several picoseconds in time and are as large as nanometers in space, which match the phonon periods and wavelengths, leading to strong phonon scattering at high pressures. Our results show direct evidence of collective quantum motion existing in high-pressure ice and provide a new perspective to understanding the coupling between phonon propagation and atomic tunneling.