A not-so-steady state

Abstract

When roads are clear, traffic proceeds as a continuous flow of cars; if the road is blocked, everything comes to a standstill. However, anyone stuck in the office rush knows life is more complex—traffic tends to move in waves, often slowing down to an annoying stop-andgo. Traffic congestion also makes life difficult for electrons in nanodevices. We tend to think of charge carriers as experiencing a controlled flow, reaching steady state when the gates are opened and current is on. Now, in a study published in Physical Review Letters, a team of scientists from four European countries point to the subtle but significant deviations from steady-state behavior that appear if one looks at the time dependence of electrons traversing a nanoscale junction. Stefan Kurth at Universidad del Pais Vasco in San Sebastian, Spain, and colleagues in Italy, Sweden, and Germany predict that, on a femtosecond time scale, the current in a quantum dot junction is not in a steady state, as often assumed, but rather oscillates [1]. The amplitude of this oscillation depends on how fast the bias voltage across the dot is switched on, suggesting the importance of initial conditions in determining how a single-electron device will perform. Their paper recasts nanoscale transport as an intrinsically dynamic phenomenon, which has important practical implications for understanding and designing ultrafast nanoelectronic devices. The charge transport through a quantum dot under weak bias and weakly coupled (by tunneling barriers) to a left and right lead (Fig. 1) is dominated by Coulomb blockade, where an electron already present on the dot prevents further electrons from tunneling in, unless the bias is significantly increased to supply the necessary charging energy. The central region of this system, consisting of the dot and the tunneling barriers, has a capacitance C. The electrostatic energy of a charge Q sitting on the dot is given by Q2/2C. To bring in an extra electron, the Coulomb repulsion due to the charge already present needs to be overcome, and for this to happen, FIG. 1: Steady-state picture of Coulomb blockade in a nanoscale tunneling junction in which a quantum dot is weakly connected to two leads. Electrons can tunnel only if the bias voltage V is large enough to line up the chemical potential of the left lead (μL) and an empty level. Otherwise the access is blocked due to the Coulomb repulsion caused by the filled N-electron level. (Illustration: Alan Stonebraker)