Theoretical study of electrical conduction in finite metals and insulators

Abstract

A tight-binding model is presented which is suitable for numerical simulations of electrical conduction in finite multiband systems driven by a time-dependent vector potential. The systems studied are linear chains of static atoms with periodic boundary conditions. The time evolution of the electrons is followed by integrating numerically the equations of motion of the density matrix. Dimerized finite chains with one electron per atom, i.e., insulators, are found to exhibit undamped periodic current oscillations in a steady moderate electric field. These oscillations are interpreted in terms of the single-band acceleration theorem (SBAT) for finite insulators. At higher fields the SBAT breaks down and Zener tunneling is studied in different regimes. The effect of the presence of impurities on the electric currents in both insulating and metallic chains of atoms is also studied. The relationship between the present work and the London theory of ring currents in cyclic molecules in a magnetic field is discussed.