Observation of resonant tunneling of proton from octahedral to tetrahedral sites in Pd

Abstract

Hydrogen (H), the lightest element, exhibits quantum nature. Because the quantum tunneling is almost independent of temperature, H diffusion shows a transition from thermal hopping to quantum tunneling at low temperature. The role of the nuclear quantum effects on H diffusion, however, has not been clarified around the crossover region. Hence, we elucidate the hopping mechanism at intermediate temperature by a combination of accurate experimental data on H hopping rates and theoretical calculations for quantum states of H. We derived H hopping rates in Pd from the resistance evolution due to the H ordering associated with the 50 K anomaly. A gradual transition from thermal hopping to quantum tunneling was observed around 65 K. Three-dimensional quantum-mechanical analysis for the H quantum states revealed that the gradual transition is attributed to the resonant tunneling between the discrete vibrational states in the octahedral site and the tetrahedral site via the thermal vibrational excitation. Based on the results at different H concentrations and deuterium, we demonstrated that the tunneling rate is tuned by energy level matching and the resonance nature is manifested as the abruptness of the transition from thermal to quantum hopping.