Features of Two-Dimensional Bifurcations during Dissipative Electron Tunneling in Arrays of Au Nanoparticles
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RETICAL AND MATHEMATICAL PHYSICS
Features of Two-Dimensional Bifurcations during Dissipative Electron Tunneling in Arrays of Au Nanoparticles M. B. Semenova,*, V. D. Krevchika, D. O. Filatovb, A. V. Shorokhova,c,g,h, A. P. Shkurinovd, P. V. Krevchika, Y. H. Wange, T. R. Lie, A. K. Malik f, D. A. Antonovb, and I. M. Semenova a Penza
State University, Penza, 440026 Russia Lobachevsky Nizhny Novgorod State University, Nizhny Novgorod, 603950 Russia c University of Jyväskylä, Seminaarinkatu, Fl-40014 Finland d Institute of Problems of Laser and Information Technologies, Russian Academy of Sciences, Shatura, Moscow oblast, 140700 Russia e Key Laboratory for Special Function Materials, School of Physical Science and Technology, Lanzhou University, Lanzhou, 730000 China f Department of Physics, Multanimal Modi College Modinagar, 201204 Uttar Prasesh, India g Ogarev Institute of Physics and Chemistry, Mordovia State University, Saransk, 430005 Russia h International Research Center Mag Top, Institute of Physics, Polish Academy of Sciences, Warsaw, PL-02668 Poland *e-mail: [email protected] b
Received April 2, 2020; revised April 2, 2020; accepted April 2, 2020
Abstract—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. DOI: 10.1134/S1063784220110249
INTRODUCTION The effects of 2D tunneling bifurcations for quasione-dimensional and quasi-two-dimensional matrices of Au quantum dots (Au QDs) in thin dielectric films in an external electric field were theoretically and experimentally studied by tunneling (conductive) atomic force microscopy (CAFM). In the case of quasi-one-dimensional Au QD structures (with a QD size of about 5 nm) in a dielectric film, a single kink is observed on the tunneling current–voltage characteristic (CVC) at a positive bias po
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