Small normal-metal tunnel junctions in electromagnetic environment

Abstract

The effect of the electromagnetic environment on single junctions and on one- and two-dimensional arrays of junctions has been studied theoretically. The phase-correlation theory [or the P(E) theory], originally developed for the weak tunneling regime, its extension to the regime of strong tunneling, and the quasiclassical Langevin equation model have been investigated in more detail. The path-integral method and the voltage fluctuations model are shortly introduced. Limitations of each model along with its domain of applicability have also been discussed. The main results of the phase-correlation theory in the high temperature limit, i. e. for junctions with the Coulomb gap smaller than the thermal energy kBT, are reviewed. While doing this, emphasis has been put on the Coulomb blockade thermometry (CBT) applications. Results have been earlier obtained for the case of negligible environmental impedance. Here, the effect of the electromagnetic environment is investigated both theoretically and experimentally. This is done first for the single tunnel junctions, then for the one-dimensional (1D) and finally for two-dimensional (2D) arrays of tunnel junctions. It is shown that the effect of the electromagnetic environment is most pronounced for solitary tunnel junctions and, as another important example for two-junction arrays, and becomes negligible by increasing the number of junctions in an array. Furthermore, the strong tunneling corrections to the basic phase-correlation theory improve the agreement between the theory and our measurements in the case of solitary tunnel junctions with resistances much smaller than the quantum resistance RK ≈ 25.8 kΩ. Performing the Monte-Carlo simulations for arrays of tunnel junctions with N ≥ 2, we show that there is a value of external electromagnetic impedance, typically ~ 0.5 kΩ, at which the half-width of the conductance curve around zero bias voltage, V1/2, shows a maximum. This observation is further confirmed by the measured data, although the quantitative agreement is only fair. Introducing a relatively simple theory for the high-conductance 1D arrays, i.e. for arrays in the strong tunneling regime, the measured data for these structures together with their comparison to the theoretical predictions are presented. This is done with an eye on CBT applications. The desired strong tunneling correction to the simple linear relation used in the thermometry, V1/2,0 = 5.439NkBT/e, is given. The effect of non-homogeneity of tunnel junctions on the tunneling in the arrays has been discussed, as well. In the last part, assuming that the tunneling regime is sequential, the P(E) theory has been applied to the topologically simple two-dimensional structures. The results have been compared to the measured data, and it has been shown that, as thermometers, 1D arrays are superior to their 2D counterparts.