From Bloch oscillations to a steady-state current in strongly biased mesoscopic devices
J. M. Alendouro Pinho, J. P. Santos Pires, Simão M. João, Bruno Amorim, J. M. Viana Parente Lopes
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). 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.