The modern physics of condensed matter, chemistry, and biology deal with quite a large number of systems that are modeled by 1D and 2D oscillatory double-well potentials of variable topology, the parameters of which can change in an external electric field. In solving quantum problems, an exact analytical solution of the Schrödinger equation can only be obtained for a limited number of models (a well with infinite walls, a quantum oscillator, a hydrogen atom, a cubic parabola potential, a double-well oscillator, and some others). When studying a double-well oscillator potential, which simulates the low-temperature chemical kinetics, tunneling transport in structures with quantum dots (QDs) and quantum molecules and another analytical solution to the Schrödinger equation can only be found under the zero temperature condition and the assumption of the absent interaction of tunneling particles with a medium‒thermostat matrix. If these parameters are taken into account, the Schrödinger equation cannot be solved analytically within the conventional quantum-mechanical approach. In the semiclassical approximation (when the de Broglie wavelength of a tunneling particle is significantly shorter than the subbarrier length), using the instanton method, one can analytically determine the tunneling probability. This was first done by the pioneers of the science of quantum tunneling with dissipation: Acad. of the Russian Academy of Sciences A.I. Larkin, Prof. Yu.N. Ovchinnikov (Landau Institute for Theoretical Physics, Russian Academy of Sciences), and winner of the Nobel Prize in Physics (2003) Prof. A.J. Leggett et al. when modeling Josephson contacts with a cubic parabola potential [1, 2, 11]. A.A. Ovchinnikov, Yu.I. Dakhnovsky, and M.B. Semenov [11] were the first to obtain an analytical solution for a 1D double-well oscillatory potential within this theory when modeling low-temperature chemical reactions as tunnel systems with dissipation.

We report the results of experimental studies of the photoelectric properties of a p–i–n GaAs photodiode with InAs/GaAs(001) double asymmetric quantum dots (DAQDs) grown by self-assembling in the metal–organic vapor-phase epitaxy process. Three peaks were observed in the dependence of the photocurrent on the reverse bias measured at monochromatic photoexcitation of the DAQDs at the wavelength corresponding to the energy of interband optical transitions between the ground hole and electron states in the larger quantum dots (QDs). These peaks were related to the tunneling of the photoexcited electrons between the QDs, including a dissipative one (with emission and absorption of optical phonons). The experimental results agree qualitatively with the theoretical field dependence of the probability of 1D dissipative tunneling between QDs.

We report on the results of experimental studies of the photoelectric properties of a GaAs p-i-n photodiode with InAs/GaAs(001) double asymmetric quantum dots (DAQDs) grown by self-assembling in Metal Organic Vapor Phase Epitaxy (MOVPE) process. Three peaks were observed in the dependence of the photocurrent on the reverse bias measured at monochromatic photoexcitation of the DAQDs at the wavelength corresponding to the energy of interband optical transitions between the ground hole and electron states in the bigger QDs. These peaks were related to the tunneling of the photoexcited electrons between the QDs including the dissipative one (with emission and absorption of the optical phonons). The experimental results agree qualitatively with the theoretical field dependence of the 1D dissipative tunneling probability between the QDs.

We report on the results of experimental studies of the photocurrent (PC) of photodiodes based on GaAs p-i-n structures with InAs/GaAs(001) double asymmetric quantum dot (DAQD) arrays obtained by self-assembling in the process of low-pressure metal-organic vapor phase epitaxy (LP-MOVPE). Three peaks were observed in the dependence of the PC on the reverse bias, measured under photoexcitation with a photon energy equal to the energy of the interband ground state transition in larger InAs QDs. These peaks were attributed to photoexcitation of electrons from the ground hole states in larger QDs into the ground electron states followed by resonant dissipative (with absorption or emission of optical phonons) and conservative tunneling into the GaAs conduction band via the ground electron states in smaller QDs. The PC dependence on the bias voltage agrees qualitatively with the theoretical field dependence of the probability of 1D dissipative tunneling between the QDs.

Abstract. In framework of the 2D - dissipative tunneling theory in approximation of a rarefied gas of the «instanton - antiinstanton pairs» at a finite temperature under the conditions of an external electric field, the features of tunneling transport for planar structures with quantum dots (QDs) from colloidal gold, that have metamaterial properties, have been studied. It was experimentally shown that, depending on the positioning of the cantilever needle of a combined atomic force and scanning tunneling microscope (AFM / STM), either above a single quantum dot or between two neighboring quantum dots, either a single or double effect of 2D tunneling bifurcations have been observed, respectively. It is such a double bifurcation regime, as our theoretical model has shown, that is associated with the manifestation of the metamaterial properties by the structure under study. A convincing qualitative agreement between the experimental I – V characteristics and the field dependence of the 2D - dissipative tunneling probability in the two studied modes, taking into account the observed quantum beats in the vicinity of the 2D bifurcation points, has been obtained.

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.

A brief review of articles developing the quantum tunneling with dissipation theory, as well as its applications to various problems in condensed matter physics, in particular, quantum mesoscopy of nanostructures, has been presented. A generalization of the instanton method to the case of impurity quasistationary states in quantum molecules described in the model of a double-well oscillatory potential has been also considered. The flexibility of the instanton method is demonstrated, which allows, in combination with the physics of low-dimensional systems, to obtain the solution of problems on the optical and transport properties of quantum molecules with impurity quasistationary states in an analytical form, as well as to take into account the effect of external fields. Part I of the article is presented in № 1 for 2017.

Temperature effects of lD-dissipative tunneling for the two-well oscillator potential model within the strong dissipation limit for the case of semiconductor QDs of InAs, were analyzed using a combined atomic force and scanning tunneling microscope. The effect of thermal control for the amplitude of single peaks on the field dependence of the one-dimensional dissipative tunneling probability in the model under consideration was theoretically revealed. A qualitative comparison of the calculated field dependences of the lD-dissipative tunneling probability at a finite temperature within a strong coupling limit (with allowance for the influence of two local phonon modes) with experimental tunnel CVC was obtained. A fairly convincing agreement of theoretical and experimental curves was demonstrated. It is shown that in addition to temperature and external electric field, another important controlling parameter of dissipative tunneling is the type of thermostat matrix in which QDs have been synthesized, taking into account the number of local phonon modes involved in the tunneling process.

M. B. Semenov, V. D. Krevchik, O. N. Gorshkov, D. O. Filatov, Y. Dakhnovsky, A. V. Nikolaev, A. P. Shkurinov, V. Yu. Timoshenko, P. V. Krevchik, A. K. Malik, Y. H. Wang, T. R. Li, Y. Zhu, S. Zhuang, R. V. Zaytsev, I. S. Antonov, I. M. Semenov, A. K. Aringazin, A. V. Shorokhov Department of Physics, Penza State University, Penza 440026, Russia Department of Physics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia 3 Department of Physics and Astronomy, University of Wyoming, WY 82071 Laramie, USA Moscow State University, Moscow 119991, Russia Department of Physics, Multanimal Modi College Modinagar, Uttar Prasesh 201204, India 6 Institute of Functional and Environmental Materials, Lanzhou University, Lanzhou, China University of Shanghai for Science and Technology, Shanghai 200093, China 8 Institute for Basic Research, Eurasian National University, Astana 010008, Kazakhstan Institute of Physics and Chemistry, National Research Mordovia State University, Saransk 430005, Russia misha29.02@gmail.com, alex.shorokhov@mail.ru

In this project the tunnel volt-ampere characteristics of colloidal gold quantum dots in a system of combined tunnel and atomic force microscopes were experimentally measured. It is assumed that ionic conductivity contributes for tunnel current the most. A qualitative comparison was made for tunnel volt-ampere characteristics and the theoretical probability curve of 2D-dissipative tunneling under influence of two local wide-band phonon modes. A qualitative agreement was found for theoretical and experimental curves, which indicates the possible contribution of the dissipative tunneling in the current through a quantum dot at the tip of a cantilever, which can be amplified in clusters ranging in size from 1 to 5 nm in thinner films.

The field and temperature dependence of the probability of two-dimensional dissipative tunneling is studied in the framework of one-instanton approximation for a model double-well oscillator potential in an external electric field at finite temperature with account for the influence of two local phonon modes for quantum dots in a system of a combined atomic force and a scanning tunneling microscope. It is demonstrated that in the mode of synchronous parallel transfer of tunneling particles from the cantilever tip to the quantum dot the two local phonon modes result in the occurrence of two stable peaks in the curve of the 2D dissipative tunneling probability as a function of the field. Qualitative comparison of the theoretical curve in the limit of weak dissociation and the experimental current–voltage characteristic for quantum dots that grow from colloidal gold under a cantilever tip at the initial stage of quantum-dot formation when the quantum dot size does not exceed 10 nm is performed. It is established that one of the two stable peaks that correspond to interaction of tunneling particles with two local phonon modes in the temperature dependence of the 2D dissipative tunneling probability can be split in two, which corresponds to the tunneling channel interference mechanism. It is found that the theoretically predicted and experimentally observed mode of quantum beats occurs near the bifurcation point.

We observe a series of sharp resonant features in the tunneling differential conductance of InAs quantum dots. We found that dissipative quantum tunneling has a strong influence on the operation of nanodevices. Because of such tunneling the current–voltage characteristics of tunnel contact created between atomic force microscope tip and a surface of InAs/GaAs quantum dots display many interesting peaks. We found that the number, position, and heights of these peaks are associated with the phonon modes involved. To describe the found effect we use a quasi-classical approximation. There the tunneling current is related to a creation of a dilute instanton–anti-instanton gas. Our experimental data are well described with exactly solvable model where one charged particle is weakly interacting with two promoting phonon modes associated with external medium. We conclude that the characteristics of the tunnel nanoelectronic devices can thus be controlled by a proper choice of phonons existing in materials, which are involved.

The problem of controllability for 2D-tunnel bifurcations in systems with quantum molecules in a dielectric matrix of a metamaterial in the external electric field at finite temperature has been investigated. Usage of the theory of quantum tunneling with dissipation to study the interaction of quantum molecules (QM) with contact medium is productive, because, in spite of usage of the instanton approach, it is possible to get the main results in an analytical form with account of the environment effects on the tunneling process, which it is not possible in other often used approaches. A theoretical study of the electric field influence on the 2D-quantum tunneling for quantum molecules in the matrix of a metama-terial (with negative effective permittivity) at finite temperature has been fulfilled in the instanton approximation. It is shown that a stable regime of 2D-bifurcations in such matrix can take place in a narrower range of parameters than in the case of usual dielectric matrix. An important problem in this case is to identify the range of experimentally realizable values of the relative dielectric permittivity (including negative values) for the matrix environment that allows realization of the 2D-bifurcations regime. A range of the control parameters (electric field, temperature, and the relative permittivity of the meta-material matrix), in which the regime of stable 2D-bifurcations in the system of quantum molecules, as well as in the system “AFM/STM cantilever - quantum dot or quantum molecule”, can take place, has been theoretically investigated. The “phase diagram” for the stable 2D-bifurcations regime for tunnel current in the matrix of a metamaterial in dependence on controllable parameters (the inverse temperature, electric field intensity and values of the negative relative permittivity for the heat bath environmental matrix), has been presented. It is shown that in contrast to usual dielectric matrices, in the case of the metamaterial matrix the region of stable 2D-bifurcation is significantly narrowed, which is probably due to inversion of the sign of the tunneling particles interaction.

One-dimensional dissipative quantum tunneling model has been proposed to interpret the recent experimental data on current-voltage characteristics of tunnel contact between atomic force microscope probe and surface of InAs/GaAs quantum dots. Our conductive atomic force microscope experiment provided measurements of their local density of states. In a quasiclassical, dilute instanton - antiinstanton gas approximation, we obtain exact analytical result for the tunneling probability rate for one charged particle weakly interacting with two promoting phonon modes in the wide-band matrix, which characterizes medium. The agreement between the number, position, and heights of the peaks in the obtained current-voltage characteristics and that given by the theoretical result for the oscillatory case is strikingly better than in our preliminary result with only one local phonon mode taken into account. One of the practical implications of the obtained result is that the current-voltage characteristics of the semiconductor tunnel nanoelectronic devices can thus be controlled to certain extent by modulations of the wide-band matrix parameters.

We have obtained tunneling current - voltage characteristics for growing quantum dots of colloidal gold in the combined atomic - force and scanning tunneling microscope. It is assumed that the main contribution to current gives the ionic conductivity. A qualitative comparison of the tunneling current voltage characteristics with the theoretical curve for field dependence of the probability of 2D - dissipative tunneling with the influence of two local phonon modes in wide - band matrix has been fulfilled. A qualitative agreement of the experimental and theoretical curves, suggesting a possible contribution of the dissipative tunneling in the tunnel current through a growing quantum dot under the needle of the cantilever, which can be amplified in clusters ranging in size from 1 to 5 nm in thinner films, has been also established.