The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom
P. Pals and A.MacKinnon
28th September 1994
The Ohmic conductance and current through two quantum dots in series is investigated for the case of incoherent tunnelling. A generalised master equation is employed to include the discrete nature of the energy levels. Regions of negative differential conductance can occur in the I-V characteristics. Transport is dominated by matching energy levels, even when they do not occur at the charge degeneracy points.
72.10.D, 73.20.D
Due to the improvement of lithographical techniques on a nanometre scale in recent years it has become possible to study systems that were inaccessible to experimentation before. The most easily controlled mesoscopic systems are defined in the 2-dimensional electron gas of a semiconductor. By the application of gate electrodes [1, 2] it is possible to confine the electron gas effectively to produce quantum wires and dots. This allows charge quantisation to be observed in the form of the Coulomb blockade [3, 4]. Moreover, the importance of size quantisation has been shown by Reed et al. who discerned discrete states in small quantum dots [5].
The effect of the charge quantisation has been studied both for a single dot [6] and a double dot [7, 8]. In both cases the level spectrum could be considered continuous. The effect of level quantisation on the Ohmic conductance through a single dot has been studied in the limit of weak coupling to the reservoirs. Coherent [9] and incoherent methods [10] lead to the same result in this limit. There is still a proliferation of on-going research in this area [11].
Until recently, not much work had been done on the transport properties of a double dot with discrete energy levels. However, some useful experiments were performed recently by Van der Vaart et al.[12] in which the lineshape of the resonance peaks was determined in the coherent regime. Even though the remainder of this paper will focus attention on the incoherent regime, the above experiment is relevant in that it provides a feasible experimental set-up which allows interdot tunnelling between discrete levels to be observed in a straightforward manner. The limit of completely incoherent tunnelling is studied, where the phase-breaking rate is large and the tunnelling process is sequential. This justifies the use of a semi-classical method like the master equation. It must be noted that the phase-breaking time is still large compared to the time it takes for an electron to traverse the dot. This ensures that the energy levels are quantised, due to the coherence of the wavefunctions inside the dot.