Dynamics of tilted superlattices with time-dependent impurity

The influence of time-dependent impurity on the electronic and transport properties of the tilted superlattices modeled by the tight-binding Hamiltonian is investigated. The quasienergies of the system are calculated in two methods: exact diagonalization and Floquet replica technique, the subtle effects of the impurity on the dynamics of the system are discussed in detail. Through a perturbative analysis in terms of the inverse of the time-dependent impurity frequency, we obtain the time-independent effective Hamiltonian, whose reliability and physical implication are discussed.