Time-dependent current in a one-dimensional conductive ring under periodic Peierls phase modulation

Abstract The temporal variation of the electric current induced by an oscillating Peierls phase in a ring-shaped system is studied using a tight-binding model with the Peierls substitution. For a single electron current, when the initial wavefunction is a traveling wave with a constant wave number, the time-averaged current does not depend on the oscillation frequency of Peierls phase, in contrast to conventional electrical induction. However, when the initial state is a superposition of degenerate eigenstates, the mean square current between nearest-neighbor sites depends on both the initial amplitudes of the clockwise and counterclockwise traveling waves and the oscillation frequency. Moreover, the total current, defined as the sum of currents between nearest-neighbor sites and determines the induced magnetic field, depends on the amplitudes of the superposition but remains independent of the oscillation frequency.