Observation of proton tunneling correlated with phonons and electrons in Pd | Science Advances

Quantum-mechanical properties substantially affect the dynamics of light particles, including hydrogen. The temperature dependence of the tunneling rate provides a clue to understanding the quantum effects. Important physics behind quantum tunneling involves the correlation with surrounding environment, such as phonons and electrons. However, this correlation is not yet well understood due to the difficulty of directly probing hydrogen hopping. Taking advantage of nuclear reaction analysis and resistance measurements, we successfully observed hydrogen hopping from tetrahedral to octahedral sites in palladium. The hydrogen hopping is observed even at low temperatures owing to the quantum tunneling. The tunneling rate reveals a slightly positive and negative temperature dependence above and below 20 kelvin, respectively. The former is explained by the phonon effects. The latter is attributed to the nonadiabatic effects of conduction electrons, whose coupling constant K was derived to be 0.41 ± 0.03 from its temperature ( T ) dependence described as T ^{2 K –1} .