Emergence of Bloch oscillations in one-dimensional systems

Abstract

Electrons in periodic potentials exhibit oscillatory motion in presence of an electric field. Such oscillations are known as Bloch oscillations. In this article we theoretically investigate the emergence of Bloch oscillations for systems where the electric field is confined to a finite region, like in typical electronic devices. We use a one-dimensional tight-binding model within the single-band approximation to numerically study the dynamics of electrons after a sudden switching-on of the electric field. We find a transition from a regime with direct current to Bloch oscillations when increasing the system size or decreasing the field strength. We propose a pump-probe scheme to observe the oscillations by measuring the accumulated charge as a function of the pulse-length.

Characteristic length scales from entanglement dynamics in electric-field-driven tight-binding chains

“…We believe that the same experimental set-up, as put forward in Ref. 12 can be generalized for this purpose. Furthermore, time-dependent phenomena in a nonequilibrium set-up have mostly been studied with a small number of degrees of freedom (like a quantum dot for example).…”

“…These states are extended over a length called Bloch length. Hence, to observe Bloch oscillations, the system size must be greater than this length [12]. Also, the equispaced energy spectrum results in recurrence of any initial state.…”

Numerical Simulation of Non-Equilibrium Stationary Currents Through Nano-scale One-Dimensional Chains

“…where ∆V measures the bias applied to the contacts. A similar scheme was already used in computer simulations by Poppescu et al [12] on a different context. As referred in Sect.…”

Landauer transport as a quasisteady state on finite chains under unitary quantum dynamics

“…In more recent years, a significant effort was devoted to the study of time-dependent transport and transient dynamics in mesoscopic systems attached to infinite leads 11,[15][16][17][18][19][20] . In the work of Pal et al 21 , this assumption was relaxed and time-dependent transport through a quantum-dot connected to two systems with a quasicontinuum spectrum (discrete, but dense), which take the role of finite leads, was considered in the partitioned approach.…”