Features of two-dimensional bifurcations during dissipative electron tunneling in arrays of Au nanoparticles

Within the 2D theory of dissipative tunneling in the semiclassical approximation (a rarefied gas of instanton–anti-instanton pairs) at a finite temperature in the presence of an external electric field, the features of tunneling transport in the planar structures with the quantum dots made of colloidal gold–which, presumably, possess the properties of a metamaterial–are investigated. It is shown experimentally that either a single effect or a double effect of 2D tunnel bifurcations (in the form of a kink or kinks on the tunneling current–voltage curve) is observed depending on the position of the cantilever tip of a combined atomic force and scanning tunneling microscope (AFM/STM), which can be either above a single quantum dot or between two adjacent quantum dots, respectively. As our theoretical model shows, such a regime of double bifurcation (a double smoothed kink on the tunneling current–voltage curve) that is associated with the manifestation of the properties of a metamaterial by the structure under study. A convincing qualitative agreement is obtained between the experimental current–voltage characteristics and the field dependence of the probability of 2D dissipative tunneling in the two investigated regimes with due regard for the observed quantum beats (oscillations) in the vicinity of 2D bifurcation points.