Time-resolved detection of temporally correlated, single-charge tunnelling

Abstract: We report real-time detection of the single charges that constitute a small electrical current, as they flow through a nano-electronic device. This represents a direct demonstration of charge discreteness in an electrical current. In a chain of small metallic islands connected by tunnel junctions (allowing electrons to pass by quantum tunnelling), Coulomb repulsion imposes a spatial correlation between single electrons which occupy different islands. When a current I flows through this chain, these electrons move in concert, and tunnel in a temporally correlated way at the average frequency f_e=I/e, where e is the electronic charge. We have been able to detect this time-correlated, single-electron tunnelling by combining such a chain with an ultrasensitive charge detector, a radio-frequency single-electron transistor (RF-SET). Two different ways of connecting the chain to the SET were investigated. We ultimately measured currents in the range 5 fA-1 pA by counting the single electrons. We found that the line width of the spectral peak is nearly proportional to the frequency f_e of the oscillations, in good agreement between experimental data and numerical calculations. The tunnelling of the single electrons took place while the islands were in the superconducting state, but the inter-island Josephson coupling was low. Cooper pairs were also easily broken into quasiparticles as the magnetic field was relatively strong. Under these conditions, we have additionally observed a crossover to time-correlated, incoherent tunnelling of individual Cooper pairs as a function of decreased magnetic field and of current. Tunnelling dominated by Cooper pairs now produces a frequency f_2e=I/2e. We have found that the two types of tunnelling can coexist in an intermediate state, producing an average tunnelling frequency between f_e and f_2e. In a similar way, we have also attempted to directly observe Bloch oscillations in a one-dimensional array of small Josephson junctions, that is, the coherent, time-correlated tunnelling of Cooper pairs. This fundamentally new way to measure small currents has the advantage of being self-calibrated, since the only parameter involved is the natural constant e. In an optimised device with higher current and better accuracy, we see a possibility to use our electron counter in metrological applications.