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We applied the quantum kinetic equation method to investigate the influence of confined optical phonons (confined OP) on the photo-stimulated Ettingshausen effect in rectangular quantum wires (RQW) subjected to a perpendicular magnetic field. We considered the case where the confined electrons-confined OP scattering is the dominant mechanism. Analytical expressions for the kinetic tensors, the EC are obtained. The EC is a function of external fields, the temperature of the system, especially the quantum numbers m1 and m2 characterizing confined OP. When the width of the wire increases to infinity, the results of the bulk semiconductors can be gained. The numerical results are numerically evaluated and discussed for the GaAs/AlGaAs RQW. The magnitude of the resonance peaks has been increased for each value of m1, m2, found when examining the dependence of the EC on the photon energy. Furthermore, the EC is decreased considerably when the amplitude of EMW increases, which is obtained when investigating the dependence of the EC on the amplitude of EMW (laser). These results are important for further researches and could be helped to complete the theory of the thermo - magnetoelectric effects in the low dimensional system.

Photo-stimulated quantum thermo-magnetoelectric effects in doped two-dimensional semiconductor superlattices, including the photo-stimulated quantum Ettingshausen effect and the photo-stimulated quantum Peltier effect, have been theoretically studied by using the quantum kinetic equation method. In this work, we assume that the electron-confined acoustic phonon scattering is essential. Moreover, the presence of the laser radiation (LR) is also taken into account to determine the influence of confined phonons on the aforementioned effects. We have defined the analytical expressions for the kinetic tensors and the Ettingshausen and the Peltier coefficients, presented the numerically calculated the theoretical results for the GaAs:Si/GaAs:Be doped semiconductor superlattice and compared them with these for the case of an unconfined acoustic phonon. The results obtained indicated that the formulas for the kinetic tensors, the Ettingshausen coefficient (EC) and the Peltier coefficient (PC) contain the quantum number m specifying the confinement of a phonon and approach the results for an unconfined phonon as m goes to zero. We found that the kinetic tensors, the EC and the PC oscillate with changing magnetic field and that the confinement of a phonon causes a shift of the peaks in these oscillations to lower energy. The dependences of both EC and PC on the temperature were found to be nonlinear. Moreover, all the coefficients level off when the temperature was less than 4.5 K or greater than 5.5 K. The EC also depended on the doping concentration in a nonlinear way and reaches a positive constant value when the semiconductor superlattice was doped with a high concentration. Most of the numerical results showed that the magnitude of the tensors, the EC as well as the PC, within a confined acoustic phonon varie significantly in comparison with the unconfined phonon case. This means that the confinement of the phonon affects the thermo-magnetoelectric effect quantitatively and qualitatively. These results contribute to completing the theory of the thermo-magnetoelectric effects in the low-dimensional semiconductor systems.

Based on the quantum kinetic equation (QKE) for electron, we have theoretically studied the theory of photo-stimulated Ettingshausen effect in a one-dimensional cylindrical quantum wire (CQW). The strong electromagnetic wave (EMW) [Formula: see text] plays a role as photo-stimulation source. We obtain the analytic expressions for the kinetic tensors [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the Ettingshausen coefficient (EC) in the CQW with the dependence on the amplitude and the energy of EMW, the CQW radius, the magnetic field and the temperature for two cases: optical phonon and acoustic phonon. The results are numerically evaluated and graphed for GaAs/AlGaAs CQW model. It is shown that we observe the cyclotron resonance and magneto-phonon resonance effect while surveying EC in terms of magnetic field (with and without EMW) and EMW energy, considered the electron-optical phonon scattering. In case of electron-acoustic phonon scattering, the oscillation of EC is obtained with the transition between low Landau levels (LLs). We also clarify the impact of quantum size effect (QSE) on EC by surveying the influence of EC on the radius of CQW.

This work studies the linear, the third-order nonlinear, and the total optical absorption coefficients (OACs) and the refractive index changes (RICs) caused by both intra- and inter-band transitions in the WSe2 monolayer. The expression for the OACs and RICs in the presence of a magnetic field as well as the Zeeman and electric fields are found by using the compact density matrix approach. The results show that the spin states strongly affect the OACs and RICs, which display the violet-shift behavior with the increase of the magnetic field. The Zeeman fields do not affect the peak positions but slightly reduce peak intensities. The OACs and RICs due to intra-band transition display only one peak in the THz range, while the inter-band spectra show a series of peaks in the near-infrared optical range, making monolayer WSe2 be a promising candidate for novel optoelectronic applications.

The quantum magneto-thermoelectric effect in a two-dimensional compositional superlattice under the influence of an electromagnetic wave (EMW) in two cases is investigated. Two cases of the electron scattering mechanism are considered: the electron-acoustic phonon scattering and electron-optical phonon scattering. Analytical expressions for the quantum Ettingshausen coefficient (EC), the thermopower tensor, the thermoelectric tensor and the kinetic tensor are obtained by using a quantum kinetic equation. These expressions are numerically solved for the two-dimensional compositional superlattice GaAs/AlGaAs and the results are discussed. The results show that in the case of electron-acoustic phonon scattering, the Shubnikov-de Haas oscillations appear when we examine the dependences of the quantum EC, the thermopower tensor and the thermoelectric tensor on the magnetic field. In the case of electron-optical phonon scattering, resonance peaks that satisfy the condition of the inter-subband magneto-phonon resonance appear. In the two cases, the superlattice period (a parameter specific to the material) strongly affects the quantum magneto-thermoelectric effect. When the superlattice period is small, quantum EC oscillations (in the case of electron-acoustic phonon interaction) and quantum EC resonance peaks (in the case of electron-optical phonon interaction) appear. However, when the superlattice period is large, these oscillations and resonance peaks are not observed. Especially, the influence of electromagnetic waves on the quantum magneto-thermoelectric effect is also clarified. The quantum theory of the magneto-thermoelectric effect has been studied from low temperature to high temperature. This overcomes the limitations of the Boltzmann kinetic equation which was studied at high temperature. The results are new and can serve as a basis for further development of the theory of quantum magneto-thermoelectric effects in low-dimensional semiconductor systems.

The electron – optical phonon scattering is considered in detail to studying the Ettingshausen effect in doped semiconductor superlattice under the influence of phonon confinement and laser radiation. The analytical expressions for tensors and the Ettingshausen coefficient are obtained by using the kinetic equation method. The Ettingshausen coefficient depends on temperature of the sample, amplitude and frequency of laser radiation, magnetic field and the quantum number m specific for the confinement of phonon. The dependences are clearly displayed in the numerical results for GaAs:Be/GaAs:Si doped semiconductor superlattice. The magnetic field makes the Ettingshausen coefficient change in quantitative under the influence of temperature or laser amplitude and change the resonance condition. The numerical results show that both resonance condition and resonance peaks position are affected by the increase of quantum number m. We also get the result corresponding to the unconfined optical phonon case when m is set to zero. Due to the change of the wave function and energy spectrum of electrons, most of results for the Ettingshausen effect in doped semiconductor superlattice obtained are different from the case of bulk semiconductor. Moreover, in comparison with the case of unconfined optical phonon, under the influence of phonon confinement effect, the Ettingshausen coefficient changes in magnitude, the number and position of resonance peaks.

The Quantum photo-stimulated Peltier effect has been theoretically studied under the influence of confined acoustic phonon in a cylindrical quantum wires with an infinite potential by using the quantum kinetic equation method. In this work, we assume that the confined electrons-confined acoustic phonons scattering is essential. Moreover, the presence of a strong electromagnetic wave (EMW) is also taken into account to determine the influence of confined phonons on the aforementioned effects. We have defined the analytical expressions for the kinetic tensors and the Peltier coefficients (PC). In detailed consideration, the quantum number m1, m2 were changed in order to characterize the influence of confined acoustic phonon (confined AP). As the radius of the wire increases to infinity, we obtained the results that corresponded to the case of bulk phonons (unconfined AP). The theoretical results have been numerically evaluated and discussed for the GaAs/AlGaAs cylindrical quantum wires (CQW). The change of PC in two cases unconfined AP and confined AP have been found according to augment of EMW frequency. The value of resonant peaks has altered under the effect of confined AP. The difference of PC also has been discovered when investigating its dependence on the cyclotron frequency. Furthermore, the PC reduced suddenly when considering the dependence of PC on the radius of wire and PC on the low temperature. All numerical showed that the magnitude of PC diverse significantly in comparison with unconfined AP case and doped two - dimensional semiconductor superlattice. This means that the confinement of the phonon affects the Peltier effect quantitatively and qualitatively. These results are new and provide to completing the theory of the Peltier effect in low-dimensional semiconductor systems.

The influence of electromagnetic wave (EMW) on the acous- tomagnetoelectric (AME)effect is studied theoretically in a quantum well. The expression of the AME field is obtained. Thedependences of the AME field on the temperature of system, the frequency of acoustic wave, thefrequency and intensity of electromagnetic wave and the parameters of a Quantum well are nonlinear.These dependences in the case of QW are different and more complex than in the case of bulksemiconductor. The results are numerically calculated and discussed for an GaAs/AGaAs QW. Thegraph of the dependence of the AME field on the frequency of acoustic wave shows that the changesof external magnetic field drag on the change of value of AME field and the change of the positionof AME field. The value of the AME field in case with the intensity of EMW is much bigger than incase without the intensity of EMW.

Interaction of external acoustic waves - confined electrons - internal phonons in a cylindrical quantum wire with an infinite potential (CQWIP) has been theoretically studied via the quantum kinetic equation for electrons in the presence of an external magnetic field (EMF). The quantum kinetic equation for the distribution function of electrons interacting with internal and external acoustic phonons is obtained from the Heisenberg equation of motion and the model of CQWIP. The density of acoustomagnetoelectric (AME) current and the analytical expressions for the AME field in the CQWIP in the presence of the EMF are obtained. The theoretical results are numerically evaluated for the specific CQWIP of GaAs/GaAsAl. It is shown that the AME field strongly depends on the system temperature in both cases of the strong magnetic field and the weak magnetic field. However, the graph showing the relationship between the AME field and the system temperature has the peaks in case of the strong magnetic field. The reason may be due to movement of the electrons between the mini-bands. The AME field obtained in this work are then compared with those of bulk semiconductors, superlattices, quantum wells (QW) and rectangular quantum wire (RQW).

The Shubnikov – de Haas magnetoresistance oscillations in the Quantum well (QW) under the influence of confined acoustic phonons, The theoretical results show that the conductivity tensor, the complex magnetic impedance of the magnetic field, the frequency, the amplitude of the laser radiation, the QW width, the temperature of the system and especially the quantum index m characterizes the confinement of the phonon. The amplitude of the oscillations of the Shubnikov-de Haas impedance decreases with the increase of the influence of the confined acoustic phonons. The results for bulk phonons in a QW could be achieved, when m goes to zero. We has been compared with other studies when perform the numerical calculations are also achieved for the GaAs/AlGaAs in the QW. Results show that The Shubnikov-de Haas magnetoresistance oscillations amplitude decrease when phonon confinement effect increasing and when width L of the QW increases to a certain value, The Shubnikov – de Haas magnetoresistance oscillations amplitude completely disappears can not be observed.

The effect of confined optical phonons and laser radiation are taken into account to study the Hall effect in a compositional semiconductor superlattice (CSSL). The new theoretical expressions of the Hall conductivity, the Hall coefficient and the magnetoresistance are obtained as functions of the external fields (the magnetic field B , the laser frequency Ω and amplitude E ), the CSSL parameters (the well length d I , the barrier length d II and height U ) and the quantum number m characterizing the phonon confinement effect. The magneto-confined phonon resonance condition in a CSSL is also carried out to explain the numerical evaluation results for the GaAs / Al x Ga 1 − x As CSSL. When optical phonons are confined, the Hall conductivity has more resonance peaks in comparison with that for bulk phonons. In addition, these sub-peaks are more separate from the main peaks as the CSSL layers thickness decreases. The tighter CSSL period is, the more forcefully the phonon confinement makes. When the CSSL period d is smaller than 30 nm , the contribution of confined optical phonons is significant and could not be neglected. The magnetophonon resonance for bulk semiconductor could be achieved in the limit the CSSL period goes to infinity. Furthermore, the Hall conductivity increases and the Hall coefficient, the magnetoresistance decrease due to the laser radiation and the effect of confined optical phonons. Especially, the near-linear dependence of the magnetoresistance on temperature is in good agreement with the experimental result.

The paper presents research results of structure of the Mullite system (3Al2O3.2SiO2) by Molecular Dynamics simulation (MDs) using the Born–Mayer– Huggins pair interaction and periodic boundary conditions. The simulation is performed with model of 5250 atoms at different pressure and at 3500 K temperature. The structural properties of the system have been clarified through analysis of the pair radial distribution function, the distribution of coordination number, the bond angle and the link between adjacent TOx units.

Based on the quantum kinetic equation for electrons, we have theoretically studied the influence of a Strong Electromagnetic Wave (EMW) on the Magneto-Thermoelectric Effects in a cylindrical quantum wire with an infinite potential (CQWIP) (for electron - optical phonon scattering) under the influence of electric field E1=(0,0,E1), magnetic field B=(0,B,0) and a strong EMW (laser radiation) E= (0,0,E0sinΩt) (where and are amplitude and frequency of EMW, respectively). We obtain the analytic expressions for the kinetic tensors sik, bik, gik, xik and the Ettingshausen coefficient (EC) in the CQWIP with the dependence on the frequency, the amplitude of EMW, the Quantum Wire (CQWIP) parameters, the magnetic field and the temperature. The results are numerically evaluated and graphed for GaAs/GaAsAl quantum wire. Then, the results in this case are compared with the case of the bulk semiconductors and others low-dimension system in order to show the difference and the novelty of the results. Moreover, we realize that as the EMW frequency increases, the EC fluctuates with a stable trend and the appearance of the Shubnikov-de Haas (SdH) oscillations pattern when we survey the dependence of EC on the magnetic field.

The influence of confined optical phonons on the Hall Coefficient (HC) in a Cylindrycal Quantum Wire (CQW) with an infinite potential (for electron – confined optical phonons scattering). Consider a case where CQW is placed in a perpendicular magnetic field , a constant - electric field and an intense electromagnetic wave . By using the quantum kinetic equation for electrons interacting with Confined Optical Phonon (COP), we obtain analytical expressions for (HC), which are different from in comparison to those obtained for the HC in the case of normal bulk semiconductor and in the case of cylindrycal quantum wire with electron – unconfined phonons scattering mechanism. Numerical calculations are also applied for AlGaAs/GaAs/AlGaAs cylindrycal quantum wire, we see the HC depends on magnetic field B, temperature T, frequency Ω and amplitude E0 of laser radiation and especially quantum index m1 and m2 characterizing the phonon confinement. This influence is due to the quantum index m1 and m2, which makes an increase of Hall coefficient by 2,3 times in comparition with the case of unconfined phonons. When the quantum number m1 and m2 goes to zero, the result is the same as in the case of unconfined phonons.

Ettingshausen coefficient (EC) in the compositional semiconductor superlattice under the influence of electromagnetic wave (EMW) is surveyed by using the quantum kinetic equation for electrons. The analytical expressions of the Ettingshausen coefficient are numerically calculated for the GaAs/AlGaAs compositional semiconductor superlattice. It have been showed that the appearance of EMW has changed the EC’s value and the EC decreases nonlinearly when the temperature increases. Studying the dependence of EC on the magnetic field, we discovered that the resonance peaks have appeared and the superlattice period strongly affects the Ettingshausen coefficient.

By using a quantum kinetic equation for electrons, we have studied the Acousto-electric effects in doped semiconductor superlattice (DSSL) under the influence of confined phonon. Considering the case of the electron - acoustic phonon interaction, we have found the expressions of the nonlinear quantum acousto-electric current. From these expression, the acousto-electric current (AEC) depends nonlinearly on temperature, acoustic wave frequency and the characteristic parameters of DSSL (For example: the doped concentration ). Moreover, the expression of the AEC under the influence of confined phonons fairly different from the case of unconfined phonons. The results are numerically calculated for the GaAs:Be/ GaAs:Si DSSL; therefore, it can be easily seen that the dependence of the acousto-electric current on the characteristic parameters of the acoustic wave, temperature, the characteristic parameters of DSSL and the quantum number m characterizing the phonons confinement. The results have showed that the appearance of phonons confinement make the AEC value changes remarkably. The AEC is almost stable in low acoustic wave frequency condition and changes as a parabolic curve when move up. On the other hand, in case of low doped concentration number the AEC surges as a parabolic function in the dependence on , then it remains stability at just below zero in high value. Keywords: Acousto-electric field, Quantum kinetic equation, Doped superlattices, Electron - phonon interaction.

In this paper, we have used the method of quantum kinetic equation to calculate the analytic expression for Ettingshausen coefficient (EC) under the influence of confined phonon. We considered a quantum well in the presence of constant electric field, magnetic field and electromagnetic wave (EMW) with assumption that electron – confined optical phonon (OP) scattering is essential. The EC obtained depends on many quantities in a complicated way such as temperature, magnetic field, frequency or amplitude of EMW and m - quantum number which specify confined OP. Numerical results for GaAs/GaAsAl quantum well (QW) have displayed clearly the differences in comparison with both cases of bulk semiconductor and unconfined phonon. The result of examining the EC’s dependence on magnetic field shows that quantum number m changes resonance condition; m not only makes the increase in the number of resonance peak but also changes the position of peaks. When m is set to zero, we get the results that corresponds to unconfined OP. Keywords: Quantum well, Ettingshausen effect, Quantum kinetic equation, confined optical phonons.

Based on the kinetic equation method, the quantum Peltier effect has been theoretically studied under the influence of confined acoustic phonon in doped semiconductor superlattice in the presence of the electromagnetic wave (laser radiation). There were complicated dependences of the analytical expression of the Peltier coefficient (PC) on quantities such as doped concentration of the superlattice, amplitude of the laser radiation, the cyclotron frequency of electrons and temperature of the system. In detailed consideration, the quantum number m was changed in order to characterize the influence of confined acoustic phonon. When setting the m to zero, we obtained the results that corresponded to the case of unconfined phonon. The theoretical results have been numerically evaluated and discussed for the GaAs:Si/GaAS:Be doped semiconductor superlattice (DSS). We found the oscillation of the PC according to enhancement of cyclotron frequency of electrons. Moreover, position of resonant peaks has shifted under the influence of phonon confinement. In the case of low doped concentration (n D), the PC decreased in non-linear way; then it reached a negative constant in high n D value. The non-linear change of the PC also has been detected when investigating its dependence on the laser amplitude. All numerical results have shown that the magnitude of the PC decreased due to the increase of phonon confinement effect. In short, the confinement of acoustic phonon caused the change of the quantum Peltier effect in DSS of GaAs:Si/GaAS:Be in quantitatively as well as qualitatively.

Based on the quantum kinetic equation method, the quantum Ettingshausen effect has been theoretically studied under the influence of confined acoustic phonon in a cylindrical quantum wire (CQW) with infinite potential in the presence of a strong electromagnetic wave. We considered a quantum wire in the presence of a constant electric field, a magnetic field, an electromagnetic wave (EMW) with an assumption that electron – confined acoustic phonon (CAP) scattering is essential. Analytical results obtained show that the EC depends on the amplitude and the frequency of the EMW in a non-linear way. Besides, the impact of phonon confinement on the above effect characterized by m-quantum number in the expression of the EC. The theoretical results have been numerically calculated for the GaAS/AlGaAs cylindrical quantum wire model. The obtained results show that the phonon confinement contributes to the EC quantitatively and qualitatively. On the other hand m is set to zero, the result obtained is similar to the case of unconfined phonon. Furthermore, by considering the quantum size effect, the values of the EC increases, the position of the magnetic-phonon resonance peak changes, and the number of peak resonant peak increases while the radius of quantum wire declines. These obtained results are different from bulk semiconductor and unconfined phonon case which donates to the theory of the Ettingshausen effect in low-dimensional semiconductor systems.

The acoustomagnetoelectric (AME) effect in an GaAs/AlGaAs rectangular quantum wire with infinite potential (RQWIP) is investigated under the influence of electromagnetic wave (EMW) by using quantum kinetic equation (QKE) method. We obtain the electron distribution function in the interaction with internal and external phonon. By solving the inhomogeneous differential equation, the current density J → and the acoustomagnetoelectric field (E AME ) are obtained in the dependence on the EMW amplitude, external acoustic wave frequency, the system temperature and the RQWIP length. The results are numerically evaluated for GaAs/AlGaAs quantum wire. We compares it to the result obtained in case of the bulk semiconductors and others low-dimension system in order to show the difference and the novelty of the results. The E AME depends non-linearly on the wire length L z and exhibits an oscillatory behavior as the function of wire length, although the stability period in long wire length condition. Moreover, we survey the impact of EMW on EAME with the dependence on the external acoustic wave frequency ω q → The result also indicates that the current density J → amplifies exponentially as the temperature increases.

The influence of confined acoustic phonons on the Shubnikov – de Haas magnetoresistance oscillations in a doped semiconductor superlattice (DSSL), subjected in a magnetic field, DC electric field, and a laser radiation, has been theoretically studied based on quantum kinetic equation method. The analytical expression for the magnetoresistance in a DSSL has been obtained as a function of external fields, DSSL parameters, and especially the quantum number m characterizing the effect of confined acoustic phonons. When m goes to zero, the results for bulk phonons in a DSSL could be achieved. Numerical calculations are also achieved for the GaAs:Si/GaAs:Be DSSL and compared with other studies. Results show that the Shubnikov – de Haas magnetoresistance oscillations amplitude decrease as the increasing of phonon confinement effect., {"references":["Yasuyuki Shimura, Masaki Tsujimoto, Akito Sakai, Bin Zeng, Luis Balicas, Satoru Nakatsuji, \"Shubnikov-de Haas Oscillation in the cubic Γ3-based heavy fermion superconductor PrV2Al20\", Journal of Physics: Conference Series 592, 2015, pp. 012026-1-012026-4.","Fei-Xiang Xiang, Menno Veldhorst, Shi-Xue Dou and Xiao-Lin Wang, \"Multiple Fermi pockets revealed by Shubnikov-de Haas oscillations in WTe2\", Europhysics Letters: a letters journal exploring the frontiers of physics, 112 (3), 2015, pp. 37009-1-37009-5.","F. B. Mancoff, L. J. Zielinski, and C. M. Marcus, \"Shubnikov–de Haas oscillations in a two-dimensional electron gas in a spatially random magnetic field\", Physical review b volume 53, number 12, 1996, pp. 7599-7602.","Naoki Matsumoto, Masaaki Mineharu, Masahiro Matsunaga et al., \"Shubnikov–de Haas measurements on a high mobility monolayer graphene flake sandwiched between boron nitride sheets\", Journal of Physics: Condensed Matter, Volume 29, Number 22, 2017.","R. F. Pires, P. Pureur, M. Behar, J. L. Pimentel Jr., J. Schaf, \"Magnetism, magnetoresistance, and Shubnikov-de Haas oscillations in Na-implanted highly oriented pyrolitic graphite\", Journal of Applied Physics 111, 2012, pp. 093922-093927.","Orest Pavlosiuk, Dariusz Kaczorowski, Piotr Wiśniewski, \"Shubnikovde Haas oscillations, weak antilocalization effect and large linear magnetoresistance in the putative topological superconductor LuPdBi\", Scientific Reports 5, Article number: 9158, 2015, pp. 9518-1-9518-9.","E. M. Epshtein, \"Odd magnetoresistance of nonlinear conductors in timedependent electric fields\", Sov. Lett. J. Theor. Phys, Vol. 2, 1976, pp. 234-237.","Epshtein, E. M., \"Odd magnetophotoresistance effect in semiconductors\", Sov, Phys. Semicond. (Fiz. Tekh. Poluprovodn.), Vol. 10, 1976, pp.1414 – 1415.","N. Q. Bau, B. D. Hoi, \"Investigation of the Hall Effect in Rectangular Quantum Wells with a Perpendicular Magnetic Field in the Presence of a High - frequency Electromagnetic Wave\", International Journal of Modern Physics B, Vol. 28, 145001, 2014, pp.1-14.\n[10]\tN. T. Huong, N. Q. Bau, \"The Hall Coefficient and Magnetoresistance in rectangular Quantum wires with infinitely high potential under the influence of a laser radiation\", International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Vol:10, No:3, 2016, pp.94-99.\n[11]\tN. Q. Bau, B. D. Hoi, \"Influence of a strong electromagnetic wave (laser radiation) on the hall effect in quantum wells with a parabolic potential\", Journal of the Korean Physical Society, 60(1), 2012, pp.59-64.\n[12]\tN. Q. Bau, L. T. Hung and N. D. Nam, \"The Nonlinear Absorption Coefficient of a Strong Electromagnetic Wave by Confined Electrons in Quantum Wells under the Influences of Confined Phonons\", J. of Electromagn. Waves and Appl. 24, 2010, pp 1751-1761.\n[13]\tPhong, T. C, L. V. Tung and N. Q. Bau, \"Parametric Resonance of Acoustic and Optical Phonons in a Doped Semiconductor Superlattice\", J. Korean Phys. Soc. 53, No. 4, 2008, pp. 1971-1981.\n[14]\tD. Abouelaoualim, \"Electron–confined LO-phonon scattering in GaAs-Al0.45Ga0.55As superlattice\", Pramana Journal of physics, Vol 66, 2016, pp.455-465."]}

The light-effect in cylindrical quantum wire with an infinite potential for the case of electrons, optical phonon scattering, is studied based on the quantum kinetic equation. The density of the direct current in a cylindrical quantum wire by a linearly polarized electromagnetic wave, a DC electric field, and an intense laser field is calculated. Analytic expressions for the density of the direct current are studied as a function of the frequency of the laser radiation field, the frequency of the linearly polarized electromagnetic wave, the temperature of system, and the size of quantum wire. The density of the direct current in cylindrical quantum wire with an infinite potential for the case of electrons – optical phonon scattering is nonlinearly dependent on the frequency of the linearly polarized electromagnetic wave. The analytic expressions are numerically evaluated and plotted for a specific quantum wire, GaAs/GaAsAl., {"references":["H. Sigg, S. Graf, M. H. Kwakernaak, B. Margotte, D. Erni, P. Van Son, K. Kohler, Supperlattices Microstruct. Vol 19, pp. 105, 1996.","M. F. Kimmitt, C. R. Pidgeon, D. A. Jaroszynski, R. J. Bakker, A. F. G. Van Der Meer, and D. Oepts, \"infrared free electron laser measurement of the photon darg effect in P-Silicon\", Int. J. Infrared Millimeter Waves, vol 13, No 8, pp. 1065, 1992.","A. Grinberg and Luryi, \"Theory of the photon - drag effect in a two-dimensional electron gas\", Phys. Rev. B 38, pp. 87, 1988.","S. D. Ganichev, H. Ketterl, and W. Prettl, \"spin-dependent terahertz nonlinearities at inter-valance-band absorption in p-Ge\", Physica B 272, pp. 464-466, 1999.","N. Q. Bau, D. M. Hung and L. T. Hung, \"The influences of confined phonons on the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in doping superlattices\", PIER Letters, Vol. 15, pp. 175-185, 2010.","V. L. Malevich Izv, \"High-frequency conductivity of semiconductors in a laser radiation field\", Radiophysics and quantum electronics, Vol. 20, Issue 1, pp. 98-101, 1977.","N. Q. Bau and D. M. Hung, \"Calculating of the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in doping superlattices\", PIER B 25, pp. 39-52, 2010.","N. Q. Bau and B. D. Hoi, \"Influence of a strong electromagnetic wave (Laser radiation) on the Hall effect in quantum well with a parabolic potential\", J. Korean Phys. Soc, Vol. 60, pp. 59-64, 2012.","G. M. Shmelev, G. I. Tsurkan and É. M. Épshtein, \"Photostumilated radioelectrical transverse effect in semiconductors\", Phys. Stat. Sol. B, Vol. 109, pp. 53, 1982.\n[10]\tS. V. Kryuchkov, E. I. Kukhar' and E. S. Sivashova, \"Radioelectric effect in a superlattice under the action of an elliptically polarized electromagnetic wave\", Physics of the Solid State, Vol. 50, No. 6, pp. 1150-1156, 2008.\n[11]\tH. V. Ngoc, N. T. Huong, N. Q. Bau, \"The photon-drag effect in cylindrical quantum wire with a parabolic potential\", int. J. Vol. 54, No. 12, pp. 542-545, 2016. \n[12]\tN. V. Nhan, N. V. Nghia, N. V. Hieu, \"The dependence of a quantum acoustoelectric current on some qualities in a cylindrical quantum wire with an infinite potential GaAs?GaAsAl\", Materials Transactions, Vol. 56, No. 9, pp. 1408-1411, 2015."]}

We have studied magneto-thermoelectric effects in quantum well in the presence of electromagnetic wave. The analytic expression for Ettingshausen coefficient (EC) in the Quantum Well with parabolic potential (QWPP) in the presence of Electromagnetic wave (EMW) is calculated by using the quantum kinetic equation for electrons. The dependence of EC on the frequency, the amplitude of EMW, the Quantum Well parameters and the temperature are obtained. The results are numerically calculated, plotted, and discussed for GaAs/GaAsAl Quantum Well to clearly show the dependence of EC on above parameters and the results in this case are compared with the case in the bulk semiconductors. We realize that as the temperature increases, the EC decreases. The results show appearance of the Shubnikov–de Haas (SdH) oscillations when we survey the dependence of EC on the magnetic field. Keywords: Ettingshausen, Quantum well, Electromagnetic wave, parabolic potential, GaAs/GaAsAl.

The Hall effect is studied theoretically in a doped semiconductor superlattice (DSSL) subjected to a crossed dc electric field and magnetic field in the presence of an intense electromagnetic wave (EMW). By using the quantum kinetic equation for electrons interacting with acoustic phonons at low temperature, we obtain expressions for the magnetoresistance as well as the Hall coefficient in dependence on the external fields and characteristic parameters of the DSSL. Analytical results are numerically evaluated for the GaAs:Si/GaAs:Be DSSL. The dependence of the magnetoresistance on the magnetic field is consistent with the result obtained for some two-dimensional electron systems. The Hall coefficient depends weakly on the magnetic field and its value in the presence of the EMW is smaller than that of the case without EMW.

The dependence of the Hall coefficient on doping concentration in doped semiconductor superlattices (DSSLs) under a crossed dc electric field and magnetic field in the presence of a laser radiation, is investigated by using a quantum kinetic equation for electrons. Analytical results for the resistance and the Hall coefficient (HC) are computationally evaluated and graphically plotted for the GaAs:Si/GaAs:Be DSSL. Numerical results for the magnetoresistance are in accordance with available theories. The dependence of the HC on the doping concentration shows an oscillation whose phase is strongly affected by the laser radiation.

Based on the quantum kinetic equation for electrons, we have theoretically studied the influence of a Strong Electromagnetic Wave on the Ettingshausen Effect (EC) in a rectangular quantum wire with an infinite potential (RQWIP). We obtain the analytic expressions for the kinetic tensor as well as the Ettingshausen coefficient in the rectangular quantum wire with an infinite potential with the dependence on B and Ω…… The results are numerically evaluated and graphed for GaAs/GaAs:Al quantum wire. We survey the electrical and thermal conductivity tensor depend on Electromagnetic Wave frequency and temperature. The results give us appearance of the Shubnikov–de Haas oscillations when we survey the dependence of Ettingshausen coefficient on the magnetic field. Then, we realize that as the temperature increases, the Ettingshausen coefficient decreases. This shows that the Electromagnetic Wave have a clear impact on the effects. These are latest results which have been studied in terms of Ettingshausen effect in rectangular quantum wire.

Analytic expressions for the absorption coefficient (ACF) of a weak electromagnetic wave (EMW) caused by electrons confined in rectangular quantum wires (RQWs) in the presence of laser radiation are calculated using the quantum kinetic equation for electrons in the case of electron-optical phonon scattering. The dependence of the ACF of a weak EMW on the intensity E 01 and the frequency Ω1 of the external laser radiation, the intensity E 02 and the frequency Ω2 of the weak EMW, the temperature T of the system and the size L (L x and L y ) of the RQWs is obtained. The results are numerically calculated and discussed for GaAs/GaAsAl RQWs. The numerical results show that the ACF of a weak EMW in RQWs can have negative values. Thus, in the presence of laser radiation, under proper conditions, a weak EMW is increased. This is different from the similar problem in bulk semiconductors and from the case without laser radiation

The quantum acoustoelectric (QAE) current is studied theoretically in a doped superlattice (DSL). The physical problem is investigated in the region ql ≫ 1 (where q is the acoustic wave number and l is the electrons mean free path). We obtain analytical expression for the QAE current in the DSL by using the quantum kinetic equation for electron-external acoustic wave interaction and electron-acoustic phonon (internal acoustic wave) scattering. A nonlinear dependence of the QAE current on the frequency of external acoustic wave ω q → , the temperature T of the system and the characteristic parameters of DSL is achieved. The computational results for a specific GaAs:Si/GaAs:Be DSL indicates that the existent peaks in the DSL may be due to the transition between mini-bands n → n′. All these results are compared with those for normal bulk semiconductors to show the differences. Finally, the quantum theory of the QAE current in the DSL is newly developed.

The analytic expression for the Hall Coefficient (HC) caused by the confined electrons in the presence of a strong electromagnetic wave (EMW) including the effect of phonon confinement in rectangular quantum wires (RQWs) is calculated by using the quantum kinetic equation for electrons in the case of electron - optical phonon scattering. It is because the expression of the HC for the confined phonon case contains indexes m, m' which are specific to the phonon confinement. The expression in a RQW is different from that for the case of unconfined phonons in a RQW or in 2D. The results are numerically calculated and discussed for a GaAs/GaAsAl RQW. The numerical results show that HC in a RQW can have both negative and positive values. This is different from the case of the absence of EMW and the case presence of EMW including the effect of phonon unconfinement in a RQW. These results are also compared with those in the case of unconfined phonons in a RQW and confined phonons in a quantum well. The conductivity in the case of confined phonon has more resonance peaks compared with that in case of unconfined phonons in a RQW. This new property is the same in quantum well. All results are compared with the case of unconfined phonons to see differences., {"references":["Alexander Balandin and Kang L. Wang, \"Effect of phonon confinement on the thermoelectric figure of merit of quantum wells\", J. Appl. Phys, vol. 84, pp. 6149-6153, 1998.","N. Q. Bau, L. T. Hung, and N. D. Nam, \"The nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in quantum wells under the influences of confined phonons\", JEMWA, J. of Electromagnetic Waves and Appl. Vol. 24, pp. 1751-1761, 2010.","N. Q. Bau, D. M. Hung, and L. T. Hung, \"The influences of confined phonons on the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in doping superlattices\", PIER Letter 15, pp. 175-185, 2010.","Bennett R., Guven K., and Tanatar B, \"Confined-phonon effects in the band-gap renormalization of semiconductor quantum wires\", Phys. Rev. B 57, pp. 3994-3999, 1998.","Osswald S. et al, \"Phonon confinement effects in the Raman spectrum of nanodiamond\", Phys. Rev. B 80, pp. 75419-75427, 2009.","Komirenko S. M., Kim K. W., Kochelap V. A., Stroscio M. A, \"Confinement and amplification of terahertz acoustic phonons in cubic heterostructures\" Physica B 316, pp. 356-358, 2002.","Li W. S., Shi-Wei Gu, Au-Yeung T. C., and Y. Y. Yeung, \"Effects of the parabolic potential and confined phonons on the polaron in a quantum wire\", Phys. Rev. B 46, pp. 4630-4637, 1992.","Borisenko S. I, \"The effect of acoustic phonon confinement on electron scattering in GaAs/AlxGa1-xAs superlattices\" Semiconductors, vol. 38, pp. 824-829, 2004.","Stroscio M. A, \"Interaction between longitudinal-optical-phonon modes of a rectangular quantum wire and charge carriers of a one-dimensional electron gas\", Phys. Rev. B 40, pp. 6428-6431, 1989.\n[10]\tH.C. Tso, P. Vasilopoulos, \"Magnetotransport along a quantum wire\" Int. J. Mod. Phys. B, vol. 44, 7 pages, 1991.\n[11]\tYinlong Sun and George Kirczenow, \"Density – functional theory of the electronic structure of Coulomb- confined quantum wires\" Int. J. Mod. Phys. B, vol. 47, 1993.\n[12]\tH. Akera, T. Ando, \"Theory of the Hall Effect in quantum wires: Effects of scattering\" Int. J. Mod. Phys. B, vol. 41, 1990.\n[13]\tHiroshi Akera, Tsuneya Ando, \"Hall effect in quantum wires\", Int. J. Mod. Phys. B, vol. 39, 1989.\n[14]\tN. T. Huong, N. Q. Bau, \"The Hall Coefficient and Magnetoresistance in rectangular Quantum wires with infinitely high potential under the influence of a laser radiation\", International Scholarly and Scientific Research and Innovation, vol. 10(3), 2016."]}

Using the quantum kinetic equation for electrons interacting with acoustic phonon, the density of the constant current associated with the drag of charge carriers in cylindrical quantum wire by a linearly polarized electromagnetic wave, a DC electric field and a laser radiation field is calculated. The density of the constant current is studied as a function of the frequency of electromagnetic wave, as well as the frequency of laser field and the basic elements of quantum wire with a parabolic potential. The analytic expression of the constant current density is numerically evaluated and plotted for a specific quantum wires GaAs/AlGaAs to show the dependence of the constant current density on above parameters. All these results of quantum wire compared with bulk semiconductors and superlattices to show the difference., {"references":["M. F. Kimmitt, C. R. Pidgeon, D. A. Jaroszynski, R. J. Bakker, A. F. G. Van Der Meer, and D. Oepts, \"Infrared free electron laser measurement of the photon darg effect in P-Silicon\", Int. J. Infrared Millimeter Waves, vol 13, No 8, pp. 1065, 1992.","A. Grinberg and Luryi, \"Theory of the photon - drag effect in a two-dimensional electron gas\", Phys. Rev. B 38, pp. 87, 1988.","S. D. Ganichev, H. Ketterl, and W. Prettl, \"Spin-dependent terahertz nonlinearities at inter-valance-band absorption in p-Ge\", Physica B 272, pp. 464-466, 1999.","G. M. Shmelev, L. A. Chaikovskii and N. Q. Bau, \"HF conduction in semiconductors superlattices\", Sov. Phys. Tech. Semicond, Vol 12, No. 10, pp. 1932, 1978.","N. Q. Bau, D. M. Hung and L. T. Hung, \"The influences of confined phonons on the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in doping superlattices\", PIER Letters, Vol. 15, pp. 175-185, 2010.","V. L. Malevich Izv, \"High-frequency conductivity of semiconductors in a laser radiation field\", Radiophysics and quantum electronics, Vol. 20, Issue 1, pp. 98-101, 1977.","S. V. Kryuchkov, E. I. Kukhar' and E. S. Sivashova, \"Radioelectric effect in a superlattice under the action of an elliptically polarized electromagnetic wave\", Physics of the Solid State, vol 50, No. 6, pp. 1150-1156, 2008.","N. Q. Bau and D. M. Hung, \"Calculating of the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in doping superlattices\", PIER B 25, pp. 39-52, 2010.","N. Q. Bau and B. D. Hoi, \"Influence of a strong electromagnetic wave (Laser radiation) on the Hall effect in quantum well with a parabolic potential\", J. Korean Phys. Soc, Vol. 60, pp. 59-64, 2012.\n[10]\tG. M. Shmelev, G. I. Tsurkan and É. M. Épshtein, \"Photostumilated radioelectrical transverse effect in semiconductors\", Phys. Stat. Sol. B, Vol. 109, pp. 53, 1982.\n[11]\tN. Q. Bau, D. M. Hung and N. B. Ngoc, \"The nonlinear absorption coefficient of a strong electromagnetic wave caused by confined electrons in quantum wells\", J. Korean Phys. Soc 54, pp. 765-773, 2009. \n[12]\tG. M. Shmelev, N. H. Shon, G. I. Tsurkan, \"Photostumulated even acousto-electric effect\", Izv. Vyssh. Uchebn. Zaved. Fiz. 28, pp. 84, 1985."]}

The radioelectric effect (REE) in the Rectangular quantum wires (RQW) with an infinite potential under the influences of confined phonons and a linearly polarized electromagnetic wave (EMW) is theoretically studied by using quantum kinetic equations method. The obtained analytical expression of the Radioelectric field (REF) depends on frequencies of EMW (ω) and the laser (Ω), the size L of wire, the temperature T, and also especially the quantum numbers (m and j) characterizing confined phonons. Numerical calculation for a GaAs/GaAsAl RQW which shows that confined phonons and a linearly EMW impact strongly on the REE. There are differences in values and postures of the REF from the two dismensional systems which caused by differences potentials. The results also show that REF is much greater than that in case of unconfined phonons.

The influence of confined optical phonons on the Hall effect in a quantum well under the present of a perpendicular magnetic field and an in-plane intense electromagnetic wave, has been theoretical studied. The analytical expression of the Hall coefficient for electron — confined optical phonon interaction is obtained base on the quantum kinetic equation method. It is found that the Hall coefficient depends on the frequency and amplitude of the electromagnetic wave, the magnetic induction, the quantum well width, the temperature of the system and especially the quantum number m characterizing the phonon confinement. Numerical calculations are also applied for AlGaAs/GaAs/AlGaAs quantum well to show the nonlinear dependence of the Hall coefficient on the electromagnetic wave amplitude and the remarkable contribution of confined optical phonons on the magnitude of the Hall coefficient as well as the magneto-phonon resonance condition. All results are compared with that in case of unconfined phonons to see differences.

An analytic expression for the acoustoelectric current (AC) j ac induced by electron-external acoustic wave interactions and electron-internal acoustic wave (internal phonons) scattering in a quantum well (QW) is calculated by using the quantum kinetic equation for electrons. The physical problem is investigated in the region ql ≫ 1 (where q is the acoustic wave number and l is the electrons mean free path). The dependence of the AC j ac on the external acoustic wave frequency $$\omega _{\vec q}$$ , the width of the QW L and the temperature T for a specific QW of AlGaAs/GaAs/AlGaAs is achieved by using a numerical method. The computational results show that the dependence of the AC j ac on the temperature T, the external acoustic wave frequency $$\omega _{\vec q}$$ , the width of the QW L is non-monotonic and that the peaks can be attributed to transitions between mini-bands n → n′. The dependence of the AC j ac on the temperature T and the Fermi energy ∈ F is obtained, and a maximum of the AC j ac for ∈ F = 0.038 eV and $$\omega _{\vec q} = 3 \times 10^{11} s^{ - 1}$$ seen at T = 50 K, which agrees with the experimental results for AlGaAs/GaAs/AlGaAs QWs. All these results are compared with those for normal bulk semiconductors and superlattices to show the differences. Finally, the quantum theory of the acoustoelectric effect in a quantum well is newly developed.

The acoustomagnetoelectric (AME) field in a quantum well with a parabolic potential (QWPP) has been studied in the presence of an external magnetic field. The analytic expression for the AME field in the QWPP is obtained by using the quantum kinetic equation for the distribution function of electrons interacting with external phonons. The dependence of the AME field on the temperature T of the system, the wavenumber q of the acoustic wave and external magnetic field B for the specific AlAs/GaAs/AlAs is achieved by using a numerical method. The problem is considered for both cases: The weak magnetic field region and the quantized magnetic field region. The results are compared with those for normal bulk semiconductor and superlattices to show the differences, and we use the quantum theory to calculate the AME field in the QWPP.

Based on the quantum kinetic equation for electrons, we theoretically study the influence of an electromagnetic wave (EMW) on the Hall effect in a quantum well (QW) with a parabolic potential V(z) = mωzz2/2 (where m and ωz are the effective mass of electron and the confinement frequency of QW, respectively) subjected to a crossed dc electric field \(\vec E_1 \) = (0, 0,E1) and magnetic field \(\vec B\) = (0,B, 0) in the presence of a strong EMW characterized by electric field \(\vec E\) = (E0 sint, Ωt, 0, 0) (where E0 and Ω are the amplitude and the frequency of EMW, respectively). We obtain analytic expressions for the components σzz and σxz of the Hall conductivity as well as a Hall coefficient with a dependence on B, E1, E0, Ω, temperature T of the system and the characteristic parameters of QW. The results are numerically evaluated and graphed for a specific quantum well, GaAs/AlGaAs, to show clearly the dependence of the Hall conductivity and the Hall coefficient on above parameters. The influence of the EMW is interpreted by using the dependences of the Hall conductivity and the Hall coefficient on the amplitude E0 and the frequency Ω of EMW and by using the dependences on the magnetic field B and the dc electric field E1 as in the ordinary Hall effect.

The in∞uences of conflned phonons on the nonlinear absorption coe-cient (NAC) by a strong electromagnetic wave for the case of electron-optical phonon scattering in doped superlattices (DSLs) are theoretically studied by using the quantum transport equation for electrons. The dependence of NAC on the energy (~›), the amplitude E0 of external strong electromagnetic wave, the temperature (T) of the system, is obtained. Two cases for the absorption: Close to the absorption threshold jk~› i~!0j ? " and far away from the absorption threshold jk~› i~!0j ? " " (k = 0;§1;§2;:::;~!0 and " are the frequency of optical phonon and the average energy of electrons, respectively) are considered. The formula of the NAC contains a quantum number m characterizing conflned phonons. The analytic expressions are numerically evaluated, plotted and discussed for a speciflc of the n-GaAs/p-GaAs DSLs. The computations show that the spectrums of the NAC in case of conflned phonon are much difierent from they are in case of unconflned phonon and strongly depend on a quantum number m characterizing conflnement phonon.

Analytic expressions for the nonlinear absorption coe-- cient (nonlinear absorption coe-cient = NAC) of a strong electromag- netic wave (laser radiation) caused by conflned electrons for the case of electron | optical phonon scattering in doping superlattices (dop- ing superlattices = DSLs) are calculated by using the quantum kinetic equation for electrons. The problem is also considered for both the absence and the presence of an external magnetic fleld. The depen- dence of the NAC on the intensity E0 and the energy ~› of the ex- ternal strong electromagnetic wave (electromagnetic wave = EMW), the temperature T of the system, the doping concentration nD and the cyclotron frequency ›B for case of an external magnetic fleld is obtained. Two cases for the absorption: Close to the absorption threshold jk~› i~!0j ? " " and far away from the absorption thresh- old jk~› i~!0j ? " " (k = 0, §1, §2:::, ~!0 and " " are the frequency of optical phonon and the average energy of electrons, respectively) are considered. The analytic expressions are numerically evaluated, plotted, and discussed for a speciflc DSLs n-GaAs/p-GaAs. The com- putations show that the NAC in DSLs in case presence of an external magnetic fleld is much more greater than to it is absence of an external magnetic fleld. The appearance of an external magnetic fleld causes surprising changes in the nonlinear absorption. All the results for the presence of an external magnetic fleld are compared with those for the absence of an external magnetic fleld to show the difierence.

The Hall Coefficient (HC) and the Magnetoresistance (MR) have been studied in two-dimensional systems. The HC and the MR in Rectangular Quantum Wire (RQW) subjected to a crossed DC electric field and magnetic field in the presence of a Strong Electromagnetic Wave (EMW) characterized by electric field are studied in this work. Using the quantum kinetic equation for electrons interacting with optical phonons, we obtain the analytic expressions for the HC and the MR with a dependence on magnetic field, EMW frequency, temperatures of systems and the length characteristic parameters of RQW. These expressions are different from those obtained for bulk semiconductors and cylindrical quantum wires. The analytical results are applied to GaAs/GaAs/Al. For this material, MR depends on the ratio of the EMW frequency to the cyclotron frequency. Indeed, MR reaches a minimum at the ratio 5/4, and when this ratio increases, it tends towards a saturation value. The HC can take negative or positive values. Each curve has one maximum and one minimum. When magnetic field increases, the HC is negative, achieves a minimum value and then increases suddenly to a maximum with a positive value. This phenomenon differs from the one observed in cylindrical quantum wire, which does not have maximum and minimum values., {"references":["E. M. Epshtein, \"Odd magnetophotoresistance effect in semiconductors\", Sov, Phys. Semicond. (Fiz. Tekh. Poluprovodn), Vol. 10, 1976, pp. 1414 – 1415, (in Russian).","Epshtein, E. M., \"Odd magnetoresistance of nonlinear conductors in time dependent electric fields\", Sov. J. Theor. Phys. Lett., Vol. 2, No. 5, 234 - 237, 1976 (in Russian).","Malevich, V. L. and E. M. Epshtein, \"Photostimulated odd magnetoresistance in semiconductors,\" Sov. Phys. Solid State (Fiz. Tverd. Tela), Vol. 18, 1286 – 1289, 1976 (in Russian).","Pankratov, A. A. and E. M. Epshtein, \"Kinetic theory of longitudinal Hall effect in high frequency electric field,\" Sov. Phys. Semicond. (Fiz. Tekh. Poluprovodn) Vol. 16, No. 9, 1689 – 1691, 1982 (in Russian).","Shmelev, G, M., G. I. Tsurkan, and N. H. Shon, \"The magnetoresistance and cyclotron resonance in semiconductors in the presence of strong electromagnetic wave.\" Sov. Phys. Semicond. (Fiz. Tekh. Poluprovodn.), Vol. 15, No. 1, 156 – 161, 1981 (in Russian).","Bau, N. Q. and B. D. Hoi, \" Investigation of the Hall effect in rectangular quantum wells with a perpendicular magnetic field in the presence of high frequence electromagnetic wave\" Int. J. Mod. Phys. B, Vol. 28, 1450001, 2014.","Bau, N. Q. and B. D. Hoi, \"Influence of a strong electromagnetic wave (laser radiation) on the hall effect in quantum wells with a parabolic potential,\" J. Korean Phys. Soc., Vol 60, 59 – 64, 2012.","N. Q. Bau et al., PIERS Proceedings, \"Influence of a strong electromagnetic Wave (Laser Radiation) on the Hall Coefficient in Doped Semiconductor Superlattices with an In – plane Magnetic field\" March 25 -28, Taipei, (The Electromagnetics Academy, Cambridge, 2013), p. 416.","George Kirczenow, \"Hall effect and ballistic conduction in one dimensional quantum wires\" Int. J. Mod. Phys. B, Vol. 38, 1988.\n[10]\tH.C. Tso, P.Vasilopoulos, \"Magnetotransport along a quantum wire\" Int. J. Mod. Phys. B, Vol. 44, 7 pages, 1991.\n[11]\tYinlong Sun and George Kirczenow, \"Density – functional theory of the electronic structure of Coulomb- confined quantum wires\" Int. J. Mod. Phys. B, Vol. 47, 1993.\n[12]\tH. Akera, T. Ando, \"Theory of the Hall Effect in quantum wires: Effects of scattering\" Int. J. Mod. Phys. B, Vol. 41, 1990.\n[13]\tHiroshi Akera, Tsuneya Ando, \"Hall effect in quantum wires\", Int. J. Mod. Phys. B, Vol. 39, 1989.\n[14]\tJanetta Debora Brand, \"A quantum Hall effect without Landau levels in a quansi one dimensional system\" Stellenbosh University, 2012.\n[15]\tAnton Yu. Alekseev, Vadim V. Cheianov, \"Comparing conductance quantization in quantum wires and quantum Hall systems\" Int. J. Mod. Phys. B, Vol. 54, 3 pages, 1996.\n[16]\tH. Akera, T. Ando, \"Magnetoresistance in quantum wires: Boundary – roughness scattering\" Int. J. Mod. Phys. B, Vol. 43, 1991.\n[17]\tTomoaki Kaneko, Mikito Koshino, and Tsuneya Ando, \"Symmetry crossover in quantum wires with spin orbit interaction\", Physical review B 81, 155310 (2010).\n[18]\tKenichi Asano and Tsuneya Ando, \"Two component cyclotron resonance in quantum Hall systems\", Physical review B 58 (1998).\n[19]\tBau, N. Q. and B. D. Hoi, \"Dependence of the Hall Coefficient on Doping Concentration in Doped Semiconductor Superlattices with a Perpendicular Magnetic Field under the Influence of a Laser Radiation\", Integrated Ferroelectrics: An International Journal, Vol. 155, Iss. 1, pp. 39 – 44.\n[20]\tBau, N. Q. and Huong, N. T, \"Influence of a strong electromagnetic wave (laser radiation) on the Hall effect in a cylindrical quantum wires with infinitely high potential\", 2015 Journal of physics: Conference Series. 627 012023."]}