Optically stimulated proton hopping in oxides at low temperatures

This communication is inspired by recent results on the observation of “giant” rates for proton transfer in rutile TiO2 at low temperatures in pump-probe experiments. An important point is that this is not a tunneling effect. We show that this classical looking effect has a quantum mechanical origin and may be called lattice-assisted hopping. To explore the possibility of formulating transport properties in terms of mode vibrations, we use a “quantum” fluctuation–dissipation theorem, thus providing a concept of dynamic activation energy for ion hopping, which had been used in the above experimental study, rather heuristically, to fit the low-temperature “over the barrier” motion data. The resulting expression of hopping activation energy is more general than the standard one defined in units of k B T and is able to describe the crossover from the high to low-temperature regime of proton jumps.