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Prof. Lev Murokh

“ If I were again beginning my studies, I would follow the advice of Plato and start with mathematics. ”
- Galileo Galilei

During recent years, I (jointly with Dr. A. Yu. Smirnov) developed original approach to the theory of open quantum systems and successfully applied it to various problems of modern physics. This approach is based on the Heisenberg equations of motion with the interaction of the system of interest and its environment treated microscopically. It is valid for any nonlinear coupling as well as for strongly nonequilibrium situations. The only assumption been made is the Gaussian statistics of unperturbed heat bath variables (which is true for any bosonic heat bath), but even for non-Gaussian statistics this method can be employed if the coupling to heat bath is weak (which is true for most real physical situations). The derived Langevin-like equations contain the relaxation rate and fluctuation source having explicit expressions obtained microscopically to allow the calculation of correlation functions of any order. In the derivation the non-Markovian character of interaction is taken into account to incorporate intracollisional dynamics. This approach makes it possible to examine dynamics and fluctuations in open quantum systems, persistence of coherence and the effects of external fields on the decoherence processes in extraordinary limits far beyond the standard methods.
I have applied this method of Heisenberg-Langevin equations to analyze the electron transport in semiconductor nanostructures obtaining many very important results for electron transport and fluctuations in quantum wires, quantum rings, and superlattices. In the latter case, the analytical expressions for electron drift velocity and diffusion coefficient were obtained for the first time with better agreement with experimental data than other phenomenological and numerical results. Recently, this approach was combined with nonequilibrium Green’s function method, which leads to series of papers concerning transport and magnetic properties of double-quantum-dot and double-quantum-wire structures. The innovative two-step procedure was also proposed to examine spin relaxation in semiconductors. In this, the above-described approach was employed twice, for relaxation of spin degrees of freedom to orbital dynamics and, subsequently, for relaxation of orbital motion to environment.
During my years at the Brooklyn College of CUNY I provided theoretical support for the experimental group of Prof. Fred Pollak, participating in the projects related to photoreflectance and photoluminescence, as well as the thermoconductivity of semiconductor structures.
My current research interests include electron transport in quantum point contacts (QPCs), dynamics of nanoelectromechanical systems (NEMS), optical properties of colloidal quantum dots, and manifestations of nonlinear dynamics in semiconductor nanostructures.
QPCs are nanoscale electrical structures, consisting of a short and narrow constriction through which electrons move ballistically between two macroscopic reservoirs. The current flow associated with this motion is mediated by a small number of quantized one-dimensional (1D) subbands, the experimental signature of which is the quantization of the low-temperature conductance in integer units of 2e2/hGo). It has long been understood that this remarkable phenomenon can be well explained by a model of non-interacting transport, in which transmission of the 1D subbands is regulated by the self-consistent potential of the QPC. In spite of this, however, there has been much interest in recent years in the idea that many-body phenomena can lead to novel spin-dependent transport in these structures. The driving force for this work has been provided by experimental studies that have shown the presence of a non-integer conductance plateau at a value close to 0.7Go. There is a common understanding that this feature is associated with a spontaneous lifting of spin degeneracy and the local magnetic moment (LMM) formation that occurs as the electron density in the 1D channel vanishes in the region close to pinch-off. I work with the groups of Prof. J. Bird (University at Buffalo) and Prof. Y. Ochiai (Chiba University, Japan) on the understanding and interpretation of different kind of experiments which involves a measurement of the conductance of one QPC (the detector QPC) to detect LMM formation in another (the swept QPC). In such experiments, a resonant peak is observed in the conductance of the detector QPC when the swept QPC is near the pinch-off providing an independent support of the idea of the LMM formation. We believe that it may be possible to use the LMM in QPCs as an effective means to localize electron spins, to perform selective local operations on them, and to provide electrical readout of their resulting final state. Such capabilities would provide a significant contribution to attempts to implement spin-based quantum-information processing. In an independent project we with Prof. J. Bird have proposed to use the QPC as a terahertz detector. This idea was funded by NSF as a part of the project “Nanoscale Interdisciplinary Research Team: Nanostructure Components for Terahertz Spectroscopy on a Chip” in collaboration with Profs. A. Markelz (University at Buffalo), S. J. Allen (University at Santa Barbara), and G. Aizin (Kingsborough College of CUNY).
The rapid development of nanotechnology in recent years has ushered a new generation of devices, so-called nanoelectromechanical systems (NEMS), where nanoscale mechanical resonator (oscillator) is coupled to an electronic structure of comparable dimensions. Examples of these kinds of devices include small grains embedded in the elastic medium between the leads, single conducting molecules attached to metallic contacts or placed between them, carbon nanotubes, and man-made constructions, such as cantilevers (suspended beams clamped at one end), nanobridges (suspended beams clamped at both ends), nanopillars, and so on. The frequencies of these mechanical oscillations lie in the range from a few megahertz to about one gigahertz. Electron transport through the NEMS is usually achieved by electron tunneling to and from the nanooscillator. Tunnel matrix elements depend exponentially on the objects separation, so the mechanical motion affects the conductance of the system drastically. We (with Dr. A. Yu. Smirnov) analyzed two different systems, nanomechanical cantilever and quantum shuttle, and obtained their current-voltage characteristics for arbitrary values of applied bias voltage and temperature. The temperature dependencies of the current through such systems are shown to exhibit completely different behavior, from 1/T decay to exponential (not activation!) growth, depending on how deep the system is in the quantum regime, which allows to explain a wide variety of experimental data. In the present time, we are involved in the joint program with the theoretical group of Prof. A. O. Govorov (Ohio University) and the experimental group of Prof. R. Blick (University of Wisconsin-Madison) to analyze electron transport and possible coherent phonon emission in the suspended nanobridge with single or double-dot system embedded in it. An influence of the mechanical motion on the conductance of manganites is explored in collaboration with the experimental group of Prof. N. Noginova (Norfolk State University). Dynamics of NEMS is strongly nonlinear with exhibitions of irregular and chaotic behavior. To examine the feasibility of using this in actual electronic or mechanical devices, I establish collaboration with Profs. A. O. Govorov, R. Blick, J. Bird, H. Linke (University of Oregon), and G. M. Zaslavsky (New York University). In the other part of the same project, we are looking for manifestations of nonlinear dynamics behavior in electron billiard formed in ballistic semiconductor quantum dots.
Together with Profs. H. Matsui (Hunter College of CUNY) and I. Kuskovsky (Queens College of CUNY), we proposed a joint program of theoretical and experimental efforts which will examine the feasibility of exciton-based quantum computationand biomolecule sensorswith colloidal type-II core-shell quantum dots. These two quite different applications have the same fundamental process as their basis, the nonradiative energy transfer between the coupled dots (so-called Forster process). Type-II band alignment provides much longer exciton lifetimewhich is of crucial importance for both these quantum dot implementations.