Non-Markovian phonon-driven transport of locally excited quasiparticles

Different regimes of quasiparticle transport can be observed in condensed matter. We have theoretically analyzed the transport properties of locally excited quasiparticles (for example, excitons) at an initial time in the vicinity of a one-dimensional interface formed by two different, atomically flat materials joined together by a heavy-tailed probability distribution of waiting times, accompanied by relaxation to the ground state. We have demonstrated that the microscopic origin of the heavy-tailed distribution of waiting times can be attributed to interactions with phonons. We showed that the non-Markovian nature of quasiparticle transport leads to a dependence of the mean squared displacement and diffusivity on the drift velocity. We also showed that negative diffusivity, which is measured experimentally for excitons using photoluminescence techniques, arises from the interplay of two effects. The first is the emergence of a subdiffusive regime with positive diffusivity. The second effect is a decrease in the number of excited quasiparticles that contribute to the photoluminescence signal.