Coulomb blockade in two-island systems with highly conductive junctions

Abstract

We report measurements on single-electron pumps, consisting of two metallic islands formed by three tunnel junctions in series. We focus on the linear-response conductance as a function of gate voltage and temperature of three samples with varying system parameters. In all cases, strong quantum fluctuation phenomena are observed by a log (kBT /(2Eco)) reduction of the maximal conductance, where Eco measures the coupling strength between the islands. The samples display a rich phenomenology, culminating in a non-monotonic behavior of the maximal conductance as a function of temperature.PACS numbers: 73.23. Hk, 85.35.Gv, 73.40.Gk The transport properties of single electron devices are well described by the so called sequential tunneling model as long as the conductances of the underlying tunneling contacts are small compared to the conductance quantumIn most practical cases, however, one has to include higher-order corrections for a quantitative description due to quantum fluctuations of the charge number on the single electron islands. This has been demonstrated clearly for the single electron transistor (SET) [3,4,5,6,7]. Excellent agreement between experimental investigations and theoretical studies has been established at low conductances with the aid of perturbation expansion including the correct description of a logarithmic contribution to the linear-response conductance of the multichannel-Kondo type. At higher conductances however, perturbation theory breaks down. Nevertheless, by applying Monte-Carlo methods, the experimental results can be described with amazingly high accuracy [3,5,8]. The findings on the SET indicate that a close match between the model Hamiltonian and its experimental realization exists for single electron devices. It is not clear a priori whether the good agreement between perturbation expansion and experiment as well as Quantum-Monte-Carlo numerics found for the SET survives if more complex arrangements of single electron islands are investigated. E. g. the low temperature conductance of the SET involves finite occupation of only two states and the mapping onto the multichannel-Kondo model is based on identifying those two states with a pseudo spin. This procedure has no simple analogy in general arrangements. It is worthwhile to check the range of validity of perturbation theory in more general cases. Two island systems, readily accessible both by experiment and theory, serve as a good starting point.In this Letter we present an experimental study of the linear-response conductance of two single electron islands in series, an arrangement nicknamed single electron pump (SEP) [9,10,11] and sketched in Fig. 1. The linear-response conductance varies with the gate voltages and is bound between temperature dependent val- PSfrag replacementsSchematic representation of the single-electron pump. The three tunneling contacts T l , Tm, and Tr are laid out in a row forming two islands (each contact i ∈ {l, m, r} is characterized by its capacitance Ci and conductance Gi ≡ giGK ). n l and nr...

Transport in metallic multi-island Coulomb blockade systems: A systematic perturbative expansion in the junction transparency

“…Serial arrays of islands 13,14,15,16,17,18,19,20,21 have been put forward for metrological purposes: for primary thermometry 16 and, operated as electron pumps, as a standard for both current and capacitance. 17,18,19,20 For each cycle of periodically changing the gate voltages one electron is transfered through the system.…”

Transport Out of Locally Broken Detailed Balance

“…Thus energy-dependence of the barriers is not necessary. The involved technology is within nowadays reach [62,63,64,45,41,47] and could readily be tested in an experiment. This proposal contributes to the field of interaction-induced thermoelectric properties [59,60] and the control of thermal flows [71,72] in lowdimensional metallic conductors.…”

“…Consider an array of three tunnel junctions forming two islands [61,62,63,64], as sketched in Fig. 1.2.…”

Grand canonical partition function of a serial metallic island system

“…In this section, we focus on the two-metallic island system [18,28] and calculate average electron numbers of the system by the Monte Carlo method. Limbach et al [18] reported the experimental results of two-metallic island systems, usually called the single electron-pump (the SEP), which can be represented by the circuit diagram in Fig. 2.…”

“…In addition, one can apply the path integral Monte Carlo simulation [10,11,12,13] to study the systems as the SET without the restriction of coupling parameters and temperature as perturbation theory [14,15,16] and semiclassical approximation [8,17], respectively. However, since the complexity of the single-electron tunneling devices depends on the number of the island, it is still unclear whether the theoretical calculation would agree with more complex experiments than that of the SET, i.e., the systems consist of many islands [18,19,20].…”