The influence of time-dependent electric and magnetic fields on the dynamic localization of lattice electrons

Abstract

In this paper we deal with the derivation of dynamic localization conditions for electrons on the one-dimensional (1D) lattice under the influence of ac electric and magnetic fields of the same frequency. We resort, for convenience, to a tight-binding single-band Hamiltonian. Our emphasis is on a more fundamental theoretical understanding by investigating interplays between such fields and the nearest-neighbor hopping interactions characterizing the Hamiltonian. In general, such conditions get expressed in terms of infinite sums of binary products of Bessel functions of the first kind. These sums are hardly tractable, but we found that selecting in a suitable manner the phases of time-dependent modulations leads to controllable frequency-mixing effects providing appreciable simplifications. Such mixings concern competitions between the number of flux quanta and the quotients of field amplitudes and field frequencies. More exactly, tuning one of the mixed frequencies to zero opens the way to establishing the simplified dynamic localization conditions. By resorting again to the zeros of the Bessel function of zeroth order. This results in quickly tractable relationships between the amplitudes of electric and magnetic fields, the field frequency, and the zeros referred to just above. Pure field limits and superpositions between uniform electric and time-dependent magnetic fields are also discussed. Comments concerning the role of disorder and of the Coulomb interaction are also made.