Inelastic transport dynamics through attractive impurity in charge Kondo regime

Within the frame of quantum dissipation theory, we develop a new hierarchical equations of motion theory, combined with the small polaron transformation. We fully investigate the electron transport of a single attractive impurity system with the strong electron-phonon coupling in charge- Kondo regime. Numerical results demonstrate the following facts: (i) The density of states curve shows that the attraction mechanism results in not only the charge-Kondo resonance (i.e. elastic pair-transition resonance), but also the inelastic pair-transition resonances and inelastic cotunneling resonances. These signals are separated discernibly in asymmetric levels about Fermi level; (ii) The differential conductance spectrum shows the distinct peaks or wiggles and the abnormal split of pair-transition peaks under the asymmetric bias; (iii) The improvement of bath-temperature can enhance the phonon-emission (absorption)-assisted sequential tunneling and also strengthen the signals of inelastic pair-transition under the asymmetric bias; (iv) The inelastic dynamics driven by the ramp-up time-dependent voltage presents clear steps which can be tailored by the duration-time and bath-temperature; (v) The linear-response spectrum obtained from the linear-response theory in the Liouville space reveals the excitation signals of electrons' dynamical transition. Briefly, the physics caused by attraction mechanism stems from the double-occupancy or vacant-occupation of impurity system