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The research work on the present project was devoted to understanding electron transport in nanostructres. Electron propagation on nanoscale distances exhibits quantum behavior, when electron state is characterized by quantum mechanical wave functions. However, the electronic states in nanoelectronic devices are not characterized by discrete energies because of electron interactions and escape to other components of nanoelectronic devices. As a result, electron energy spectrum is continuous, but varying irregularly.

One direction of the research work by the PI was aimed at theoretical description of multi photon processes in electron nanostructures. Electron multi photon scattering process may be suppressed or enhanced depending on the commensurability of variation of electron density of states and the photon energy. The theoretical work was applied to recent experiments performed with high-mobility electron quantum wells. In these experiments, electron system was exposed to high-power electro-magnetic radiation in the presence of strong electric and magnetic fields. The differential resistance shows a series of multiple maxima and minima all occurring in the close proximity to the cyclotron resonance and its harmonics. Furthermore, the period and the phase of these oscillations depend not only on photon frequency and strength of constant electric field but also on the radiation intensity. This characteristic sensitivity to radiation intensity sets apart this strongly non-linear phenomenon from all previously reported resistance oscillations phenomena.

To explain the experimental findings we proposed a theoretical model based on quantum kinetics which captures all important characteristics of the phenomenon. We showed that this unusual effect owes to the quantum oscillations in the density of states and a crucial role played by multi-photon processes. In the presence of radiation the electron states are split into Floquet subbands separated by the energy of photons of the electro-magnetic radiation. The electron scattering rate is then controlled by the overlap of such subbands leading to oscillatory behavior in the differential magneto resistance. Our model captures all important characteristics of the phenomenon. Namely, the period, the phase, and the amplitude of the oscillations are all in excellent agreement with experimental observations. Taken together, these results demonstrate the crucial role of the multi-photon processes near the cyclotron resonance and its harmonics in the presence of strong constant electric fields.

During the last eight months, the PI and a graduate student derived a general analytical expression for the electric current through a nanoscopic conductor. This expression contains the spectral components of the conductor (its Green's functions) and the polarization operator for the Coulomb field, describing the electron-electron interactions. This polarization operator characterizes the state of electromagnetic environment of the conductor. We also started the derivation for the current noise power in terms of the polarization operators and electron spectral functions.

The main current research effort of the PI and a graduate student focuses on development of a theoretical model of electron transport in adjacent nanoscale conductors. Electron flow in one conductor may drag electrons in other conductors because of electron-electron interaction between the conductors. This phenomenon is called the Coulomb drag.

The Coulomb drag can be evaluated by considering the non-equilibrium correction to the polarization operator due to the finite bias applied to conductors in the vicinity of the device in which the electrical current is measured. We evaluated the correction to the polarization operator due to the finite voltage beyond the linear response and at arbitrary temperatures. Quantitative analysis of the Coulomb blockade is important for understanding electronic transport in networks of nanoscale conductors in photo voltaic elements.

Another important property of the Coulomb drag in nanoscale electronic conductors originates from the randomness of electron wave functions. Even tiny deviations in device geometry significantly modify the structure of wave functions and result in large fluctuations of the Coulomb drag current from sample to sample. Our expression for the drag current allows us to investigate the statistical properties of the current using random matrix description of electron Hamiltonian in the devices.

The expression for the current and current noise in terms of the polarization operator may be also applied to analysis of effect of electrolytes on transport through nanodevices. In this case the polarization operator can be evaluated for a model of electron interaction with electric dipoles or free charges in the surrounding electrolyte. We are currently working on the microscopic formulation of this model.