From Bloch oscillations to a steady-state current in strongly biased mesoscopic devices

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). These two observations naturally lead to the question: do BOs survive in some manner in mesoscopic devices in the presence of a constant electric field? To answer this question, we explore the interface between these two regimes in two-terminal devices and demonstrate theoretically that BOs can actually be observed in such apparatuses 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.