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Maxim Vavilov, PhD
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, University of Wisconsin (Madison)

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.
We also investigated the current through a nanoscale contact between a novel type of superconductor and a metal. Recently discovered iron--based pnictide superconductors are multiband electronic materials. We developed a theoretical description of differential conductance of point contact between pnictide superconductors and metals, based on a microscopic "circuit" theory that takes into account interactions in a superconducting channel and inter band scattering rate off impurities. We demonstrated that the inter band scattering off disorder is responsible for broadening of the of the differential conductance curve across the nanoscale contact between such superconductors and normal metals. This broadening provides a quantitative estimate for the inter band scattering rate. Our theory is in a quantitative agreement with experiments.
The main 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 photovoltaic elements and complicated electronic circuits.
We evaluated the low temperature and low bias behavior of the drag current and found that in this limit the Coulomb blockade between two nanoparticles is proportional to the second power of temperature and voltage. Therefore, at low voltage bias, the drag current between two nano particles is significantly suppressed when compared to one and two dimensional conductors. However, as bias increases, the electron-hole asymmetry increases and the drag current may be significantly enhanced at optimal value of voltage.
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 allowed us to investigate the statistical properties of the current using random matrix description of electron Hamiltonian in the devices. We developed a numerical method to model the distribution of the Coulomb drag current at arbitrary temperature and voltage. We are finalizing a manuscript where different aspects of the Coulomb drag effect between metallic nano particles will be discussed in detail.
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.