“ The roots of education are bitter, but the fruit is sweet. ”

Lev G. Murokh, Associate Professor
## Quantum Theory of Nanostructures

Contact:

el.vumorhkq@.cucyne.ud

(718) 997-4893, SB B218

(718) 997-4893, SB B218

Education:

1996 - Ph. D. in Physics, N. Lobachevsky State University (Nizhny Novgorod, Russia), Department of Physics

1991 - M. Sc. in Radiophysics and Electronics, N. Lobachevsky State University (Nizhny Novgorod, Russia), Department of Radiophysics

1991 - M. Sc. in Radiophysics and Electronics, N. Lobachevsky State University (Nizhny Novgorod, Russia), Department of Radiophysics

Teaching:

PH 311 - Electromagnetism 2

PH 615.2 - Electromagnetic Theory II

PH 615.2 - Electromagnetic Theory II

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 2*e*2/*h* (º *Go*). 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 0.7*Go*. 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

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

Together with

- A. Yu. Smirnov, G. F. Efremov, L. G. Mourokh, and S. N. Zheltov,
*"Problems in Quantum Mechanics with Solutions"*, N. Lobachevsky State University Press, Nizhny Novgorod, 1997 [in Russian].

- L. G. Mourokh and A. Yu. Smirnov,
*"Nanoelectromechanical Oscillator as an Open Quantum System"*, in:*Handbook on Nano- and Molecular Electronics*, Ed. Sergey Lyshevsky, Taylor and Francis, 2007, Ch.22.

- L. Mourokh and S. Lloyd,
*Optimal rates for electron transfer in Marcus theory*, Phys. Rev. E**88**, 042819 (2013). - S. Xiao, S. Xiang, Y. Yoon, M.-G. Kang, M. Kida, N.Aoki, J. L. Reno, Y. Ochiai, L. Mourokh, J. Fransson, and J. P. Bird,
*Talking through the continuum: New manifestations of Fano-resonance phenomenology realized with mesoscopic nanostructures*, Progr. Phys.**61**, 348 (2013). - S. Ishmail, P.Ivanushkin, and L Mourokh,
*Proton transport through D- and H-channels in the bovine heart cytochrome c oxidase*, Phys. Scr.**T151**, 014069 (2012). - L. Mourokh, P. Ivanushkin, Y. Yoon, N. Aoki, Y. Ochiai, and J. P. Bird,
*Multi-continuum Fano resonance in coupled quantum point contacts: A manifestation of the “integral” Fano formula*, J. Appl. Phys.**112**, 103704 (2012). - Y. Yoon, M.-G. Kang, T. Morimoto, M. Kida, N. Aoki, J. L. Reno, Y. Ochiai, L. Mourokh, J. Fransson, and J. P. Bird,
*Coupling quantum states through the continuum: a mesoscopic multi-state Fano resonance*, Phys. Rev. X**2**, 021003 (2012). - J. Yu. Romanova, E. V. Demidov, L. G. Mourokh, and Yu. A. Romanov,
*Zener tunneling in semiconductor superlattices*, J. Phys.: Cond. Matt.**23**, 305801 (2011). - A. Yu. Smirnov, L. G. Mourokh, and F. Nori,
*Electrostatic models of electron-driven proton transfer across a lipid membrane*, J. Phys.: Cond. Matt.**23**, 234101 (2011). - L. Mourokh, P. Ivanushkin, and J. Bird,
*Localized State in Quantum Point Contacts: Possible Qubit Implementation?*J. Comput. Theor. Nanosci. 8, 391 (2011). - A. Yu. Smirnov, L. G. Mourokh, P. K. Ghosh, and F. Nori,
*High-Efficiency Energy Conversion in a Molecular Triad Connected to Conducting Leads*, J. Phys. Chem. C**113**, 21218 (2009). - J. P. Bird and L. G. Mourokh,
*Localizing and detecting single spins in semiconductor nanostructures*, Nanotechnology Perceptions**5**, 61 (2009). - Y. Yoon, M.-G. Kang, P. Ivanushkin, L. Mourokh, T. Morimoto, N. Aoki, J. L. Reno, Y. Ochiai, and J. P. Bird,
*Non-local bias spectroscopy of the self-consistent bound state in quantum point contacts near pinch-off*, Appl. Phys. Lett.**94**, 213103 (2009). - A. Yu. Smirnov, L. G. Mourokh, and F. Nori,
*Kinetics of proton pumping in cytochrome c oxidase*, J. Chem. Phys.**130**, 235105 (2009). - A. Yu. Smirnov, L. G. Mourokh, S. Savel'ev, and F. Nori,
*Bio-mimicking rotary nanomotors*, Proc. of SPIE**7364**, 73640D (2009). - Yu. A. Romanov, J. Yu. Romanova, and L. G. Mourokh,
*Electron Bloch oscillations and electromagnetic transparency of semiconductor superlattices in multi-frequency electric fields*, Phys. Rev. B**79**, 245320 (2009). - Y. Yoon, M.-G. Kang, T. Morimoto, L. Mourokh, N. Aoki, J. L. Reno, J. P. Bird, and Y. Ochiai,
*Detector backaction on the self-consistent bound state in quantum point contacts*, Phys. Rev. B**79**, 121304(R) (2009). - A. Yu. Smirnov, S. Savel'ev, L. G. Mourokh, and F. Nori,
*Proton transport and torque generation in rotary biomotors*, Phys. Rev. E**78**, 031921 (2008) - J. W. Song, N. A. Kabir, Y. Kawano, K. Ishibashi, G. Aizin, L. G. Mourokh, J. L. Reno, A. G. Markelz, and J. P. Bird,
*Terahertz response in quantum point contacts*, Appl. Phys. Lett.**92**, 223115 (2008) - A. Ramamoorthy, L. Mourokh, J. P. Bird, and J. L. Reno,
*Tunneling spectroscopy of a ballistic quantum wire*, Phys. Rev. B**78**, 035335 (2008). - Y. Yoon, T. Morimoto, L. Mourokh, N. Aoki, Y. Ochiai, J. L. Reno, and J. P. Bird,
*Detecting Bound Spins Using Coupled Quantum Point Contacts*, J. Phys.: Cond. Matter**20**, 164216 (2008), invited paper for the special issue on “0.7 anomaly”. - J. R. Johansson, L. G. Mourokh, A. Yu. Smirnov, and F. Nori,
*Enhancing the Conductance of a Two-Electron Quantum Shuttle*, Phys. Rev. B**77**, 035428 (2008). - A. Yu. Smirnov, L. G. Mourokh, and F. Nori,
*Förster mechanism of electron-driven proton pumps*, Phys. Rev. E**77**, 011919 (2008). - A. Yu. Smirnov, L. G. Mourokh, and F. Nori,
*Resonant energy transfer in electron-driven proton pumps*, Phys. stat. sol. (c)**5**, 398 (2008). - A. Yu. Smirnov, S. Savel'ev, L. G. Mourokh, and F. Nori,
*Modeling chemical reactions using semiconductor quantum dots*, Europhys. Lett.**80**, 67008 (2007). - Y. Yoon, L. Mourokh, T. Morimoto, N. Aoki, Y. Ochiai, J. L. Reno, and J. P. Bird,
*Probing the microscopic structure of bound states in quantum point contacts*, Phys. Rev. Lett.**99**, 136805 (2007). - I. L. Kuskovsky, W. MacDonald, A. O. Govorov, L. G. Mourokh, X. Wei, M. C. Tamargo, M. Tadic, and F. M. Peeters,
*Optical Signature of Aharonov-Bohm Phase in Multilayer Structures with Type II Quantum Dots*, Phys. Rev. B**76**, 035342 (2007). - L. Mourokh, A. Smirnov, J. Bird, and M. Stopa,
*Fano resonances in the system of coupled quantum point contatcs*, J. Comp.-Aided Mat. Design**14**, 97 (2007). - L. G. Mourokh, A. Yu. Smirnov, and S. F. Fischer,
*Vertically-coupled quantum wires in a longitudinal magnetic field*, Appl. Phys. Lett.**90**, 132108 (2007). - Yu. A. Romanov, J. Yu. Romanova, and L. G. Mourokh, S
*emiconductor superlattice in a biharmonic field: Absolute negative conductivity and static electric field generation*, J. Appl. Phys.**99**, 013707 (2006). - L. G. Mourokh, V. I. Puller, A. Yu. Smirnov, and J. P. Bird,
*Implementation of Fano resonance in the quantum point contact for the single-spin readout*, Appl. Phys. Lett.**87**, 192501 (2005). - V. I. Puller, L. G. Mourokh, J. P. Bird, and Y. Ochiai,
*Influence of Magnetic Moment Formation on the Conductance of Coupled Quantum Wires*, J. Phys.: Cond. Matt.**17**, 5269 (2005). - L. G. Mourokh and A. Yu. Smirnov,
*Negative differential conductivity and population inversion in the double-dot system connected to three terminals*, Phys. Rev. B**72**, 033310 (2005). - A. Yu. Smirnov and L. G. Mourokh,
*Optically induced spin polarization of an electric current through a quantum dot*, Phys. Rev. B**71**, 161305(R) (2005). - L. G. Mourokh and A. Yu. Smirnov,
*Relaxation of a Nuclear Spin Placed on a Biased Nanomechanical Oscillator*, IEEE Trans. on Nanotechnology**4**, 96 (2005). - V. I. Puller, L. G. Mourokh, A. Shailos, and J. P. Bird,
*Electron Dynamics in a Coupled Quantum Point Contact Structure with Local Magnetic Moment*, IEEE Trans. on Nanotechnology**4**, 21 (2005). - G. R. Aizin, N. J. M. Horing, L. G. Mourokh, and V. M. Kovalev,
*Current driven electromagnetic wave amplification by a double quantum wire superlattice*, J. Appl. Phys.**96**, 4225 (2004). - A. Yu. Smirnov, L. G. Mourokh, and N. J. M. Horing,
*Temperature dependence of electron transport through a quantum shuttle*, Phys. Rev. B**69**, 155310 (2004). - L. G. Mourokh, V. M. Kovalev, and N. J. M. Horing,
*Control of Bond Formation, Electron Transport, and Interference in a Biased Asymmetric Parallel Double-Dot System*, J. Appl. Phys**95**, 3557 (2004). - V. I. Puller, L. G. Mourokh, A. Shailos, and J. P. Bird,
*Detection of local-moment formation using the resonant interaction between coupled quantum wires*, Phys. Rev. Lett.**92**, 096802 (2004). - L. Malikova, F. H. Pollak, R. A. Masut, P. Desjardins, and L. G. Mourokh,
*Temperature dependent contactless electroreflectance study of intersubband transitions in a self-assembled InAs/InP (001) quantum dot structure*, J. Appl. Phys.**94**, 4995 (2003). - A. Yu. Smirnov, L. G. Mourokh, and N. J. M. Horing,
*Equilibrium and nonequilibrium fluctuations of nanomechanical oscillator coupled to a tunnel junction*, Physica E,**19**, 58 (2003). - Yu. A. Romanov, L. G. Mourokh, and N. J. M. Horing,
*Negative high-frequency differential conductivity in semiconductor superlattices,*J. Appl. Phys.**93**, 4596 (2003). - V. I. Puller, L. G. Mourokh, N. J. M. Horing, and A. Yu. Smirnov,
*Electron Spin Relaxation in a Semiconductor Quantum Well*, Phys. Rev. B**67**, 155309 (2003). - A. Yu. Smirnov, L. G. Mourokh, and N. J. M. Horing,
*Nonequilibrium Fluctuations and Decoherence in Nanomechanical Devices Coupled to the Tunnel Junction,*Phys. Rev. B**67**, 115312 (2003). - A. Yu. Smirnov, L. G. Mourokh, and N. J. M. Horing,
*Current-Voltage Characteristics and Magnetic Moment of a Tunnel-Coupled Double-Wire Structure,*Phys. Rev. B**67**, 113312 (2003). - V. I. Puller, L. G. Mourokh, N. J. M. Horing, and A. Yu. Smirnov,
*Theory of Open Quantum Systems as Applied to Spin Relaxation in Solids*, Problems of Modern Statistical Physics**1**, 63 (2002). - L. G. Mourokh, N. J. M. Horing, and A. Yu. Smirnov,
*Electron Transport through a Parallel Double-Dot System in the Presence of Aharonov-Bohm Flux and Phonon Scattering,*Phys. Rev. B**66**, 085332 (2002). - Yu. A. Romanov, J. Yu. Romanova, L. G. Mourokh, and N. J. M. Horing,
*Self-induced and induced transparencies of two-dimensional and three-dimensional superlattices*, Phys. Rev. B**66**, 045319 (2002). - N. J. M. Horing, V. I. Puller, L. G. Mourokh, and Yu. A. Romanov,
*Green's Function for a Schroedinger Electron in a One-Dimensional Superlattice Miniband with Axial Electric and Magnetic Fields*, Phys. Rev. B**66**, 035304 (2002). - G. R. Aizin, N. J. M. Horing, and L. G. Mourokh,
*Current-driven plasma instabilities in parallel quantum-wire systems,*Phys. Rev. B**65**, 241311(R) (2002). - L. G. Mourokh, A. Yu. Smirnov, V. I. Puller, and N. J. M. Horing,
*Electron relaxation dynamics and Aharonov-Bohm phase control of transport through a parallel double-dot device*, Physica B**334**, 503 (2002). - D. I. Florescu, L. G. Mourokh, F. H. Pollak, D. C. Look, G. Cantwell, and X. Li,
*High spatial resolution thermal conductivity investigation of bulk ZnO (0001)*, J. Appl. Phys.**91**, 890 (2002). - L. G. Mourokh, A. Yu. Smirnov, V. I. Puller, and H. J. M. Horing,
*Dephasing in one-dimensional quantum systems as a result of ensemble averaging,*Phys. Lett.**A 288**, 49 (2001). - V. I. Puller, H. J. M. Horing, L. G. Mourokh, and A. Yu. Smirnov,
*Wave packet dynamics in a one-dimensional superlattice*, Phys. Lett.**A 281**, 70 (2001). - Yu. A. Romanov, J. Yu. Romanova, L. G. Mourokh, and H. J. M. Horing,
*Nonlinear terahertz oscillations in a semiconductor superlattice*, J. Appl. Phys.**89**, 3835 (2001). - L. G. Mourokh, A. Yu. Smirnov, and N. J. M. Horing,
*Domain formation in a one-dimensional superlattice,*Appl. Phys. Lett.**78**, 1412 (2001). - L. G. Mourokh, L. Malikova, F. H. Pollak, B. Q. Shi, and C. Nguyen,
*Photoreflectance Characterization of an AlInAs/GaInAs Heterojunction Bipolar Transistor Structure with a Chirped Superlattice,*J. Appl. Phys.**89**, 2500 (2001). - A. Yu. Smirnov, N. J. M. Horing, and L. G. Mourokh,
*Aharonov-Bohm Phase Effect and Inelastic Scattering**in Transport through a Parallel Tunnel-Coupled Symmetric Double-Dot Device,*Appl. Phys. Lett.**77**, 2578 (2000). - L. G. Mourokh, A. Yu. Smirnov, and N. J. M. Horing,
*Diffusion in a one-dimensional superlattice,*Phys. Lett.**A 269**, 175 (2000). - A. Yu. Smirnov, N. J. M. Horing, and L. G. Mourokh,
*Relaxation to a bistable state in a quantum cell,*J. Appl. Phys.**87**, 4525 (2000). - L. G. Mourokh,
*Electromagnetic wave effects on electron-phonon scattering in semiconductor quantum wires*, Physica B**252**, 21 (1998). - L. G. Mourokh and A. Yu. Smirnov,
*Theory of the electron transport in a superlattice miniband,*J. Phys.: Condens. Matter**10**, 3213 (1998). - L. G. Mourokh,
*Current-voltage instability in free-standing semiconductor quantum wires,*Phys. Rev. B**57**, 6297 (1998). - A. Yu. Smirnov and L. G. Mourokh,
*Electrophonon resonance and localization in a superlattice miniband*, Phys. Lett.**A 231**, 429 (1997). - L. G. Mourokh,
*Temperature dependence of electron mobility in semiconductor quantum wires: Fluctuation effects*, J. Phys: Condens. Matter**9**, 8489 (1997). - L. G. Mourokh and S. N. Zheltov,
*Nonlinear transport and fluctuations in polar semiconductors*. Physica B**228**, 305 (1996). - G. F. Efremov, L. G. Mourokh, and A. Yu. Smirnov,
*Noise-induced relaxation of quantum oscillator interacting with a thermal bath.*Phys. Lett.**A****175**, 89 (1993).