From Bloch Oscillations to a Steady-State Current in Strongly Biased Mesoscopic Devices

TL;DR

This paper demonstrates that Bloch Oscillations can be observed as a transient in biased mesoscopic devices before relaxing into a steady-state current, reconciling two seemingly conflicting quantum phenomena.

Contribution

It provides a theoretical framework showing how Bloch Oscillations transition into steady-state current in biased mesoscopic systems, combining analytical and numerical methods.

Findings

BOs are observable as a transient phenomenon in biased devices

Steady-state current aligns with the Landauer formula after BO decay

Decay times of BOs depend on system parameters

Abstract

It has long been known that quantum particles moving in a periodic lattice and subject to a constant force field undergo an oscillatory motion that is referred to as Bloch Oscillations (BOs). However, it is also known that, under quite general conditions, a biased mesoscopic system connected to leads should settle in a steady-state regime characterized by a constant electric current (described by the Landauer formula). Since both effects are driven by a constant field, these two quantum transport phenomena appear to be at odds with each other. Here, we solve this apparent contradiction by theoretically demonstrating that BOs can actually be observed in biased two-terminal mesoscopic devices as a transient phenomenon, which relaxes for long times to a steady-state current that agrees with the Landauer formula. Furthermore, we also combine analytical and numerical time-evolution results for a one-dimensional tight-binding model of a biased two-terminal mesoscopic system, in order to characterize the decay times of the transient BOs and establish the conditions under which they can occur.