Research researchof quantum theory on the kinetic effects in quantum wires under the influence of an external field

In this paper, we present the results of theoretical studies on the opticalelectric-magnetic properties of quantum wires in one-dirction semiconductors in two cases in the presence or absence of external magnetic fields.

Scientific Journal − No27/2018 81 RESEARCH OF QUANTUM THEORY ON THE KINETIC EFFECTS IN QUANTUM WIRES UNDER THE INFLUENCE OF AN EXTERNAL FIELD Nguyen Thu Huong1, Nguyen Vu Nhan2 Faculty of Basic Sciences, Air Force - Defense Force Academy Science-Technology Center, Hanoi Metropolitan University Abstract: In this paper, we present the results of theoretical studies on the opticalelectric-magnetic properties of quantum wires in one-dirction semiconductors in two cases in the presence or absence of external magnetic fields Physical problems are studied on the basis of quantum kinetic equations in two main directions: The theory of nonlinear absorption of electromagnetic waves by confined electrons in quantum wires (first problem) and quantum theory on a acoustoelectric (AE) field and a acoustomagnetoelectric (AME) field in a quantum wire under the influence of an external magnetic field (second problem) Analytical expressions for the absorption coefficient of electromagnetic wave in the first problem and the analytical expression of the AE field and AME field were obtained in the second problem The numerical theoretical results for the GaAs / GaAlAs quantum wires are cylindrical and rectangular in size with different types of potential Calculated results are compared to the corresponding results, but in bulk semiconductors, quantum wells and semiconductor superlattices show differences such as the appearance of new resonance peaks in the absorption spectrum as well as in the graph of the AE field and AME field Keywords: Quantum wires, one-direction semiconductor, 1D semiconductor Email: huong146314@gmail.com Received 15 November 2018 Accepted for publication 15 December 2018 INTRODUCTION The advances in solid-state physics in recent decades have been characterized by the shift of major study subjects from three-dimensional structural crystals to low-dimensional structures In a low-dimensional structure, the free movement of conductor particles is limited to two-dimensional, one-dimensional or non-dimensional Most of the optical properties of electricity in these systems are changing Some new features, called the size effect appears [1-4] The transition from three-dimensional electronics to two-dimensional electronics (quantum loops, superlattices ) or one-dimensional (quantum wires ) has 82 Ha Noi Metroplolitan University significantly changed both quantitatively and quantitatively the physical properties of which are the optical properties of the material Structural studies as well as physical phenomena in low dimensional materials show that the structure has dramatically changed many properties of the material and added many new superior properties not found in 3D electronics New materials with these semiconductor structures have helped to create components and devices based on completely new principles and revolutionary modern technologies in general engineering and engineering in the field of optics-electronics in particular In this section we present the results of theoretical studies on some optical-electronicelectron properties in low-dimensional semiconductors such as quantum wells, quantum wires in two cases: in the presence or absence of external magnetic fields The physical problems mentioned in this report in two main directions are: The nonlinear electromagnetic absorption by confined electrons in low-dimensional semiconductors and theory of AE field and AME field in low-dimensional semiconductors under the influence of external wave field The results presented below are aggregate results from scientific works obtained in recent years CONTENTS 2.1 Theory of absorbing weak electromagnetic waves in quantum wires in the presence of strong electromagnetic waves The study of physical problems of the weak electromagnetic absorption coefficient in low-dimensional semiconductors in the presence of magnetic field and no magnetic field has been studied by many scientists and our group in recent decades, and many scientifically significant results obtained Recently, we have expanded the problem by considering a second electromagnetic wave with strong amplitude and high frequency Below, we present two typical research results in this direction in the rectangular and rectangular quantum wiring of the one-dimensional semiconductor 2.1.1 The absorption of weak electromagnetic waves in cylindrical quantum wires in the presence of strong electromagnetic waves Using the quantum-kinetic equation method, we construct quantum-kinetic equations for electrons in cylindrical quantum wires with an infinite potential From there, perform calculus and get the expressions of the current density vector and weak electromagnetic absorption coefficient by confined electrons in cylindrical quantum wires in the presence of strong electromagnetic waves In calculations, we assumed that the weak electromagnetic wave is straight and linearly polarized, and satisfying high frequency Scientific Journal − No27/2018 83 conditions ωτ >> The energy spectrum of electrons in quantum wires is quantized according to the discontinuity levels assumed in the z axis direction As a result, we obtained the expressions for the z component of the line density vector (1) and the coefficient of weak electromagnetic wave absorption in presence of strong electromagnetic wave (2) with Formulas for A1, A2, A3 received due to the contribution of the absorption process and the radiation of a photon of weak electromagnetic waves formulas for B1, B2 received due to the contribution in the absorption and radiation of a photon of weak electromagnetic waves and strong electromagnetic waves B3 received by contributions in the absorption and emission of a photon of weak electromagnetic waves and two photons of strong electromagnetic waves Expressions defined Fs, m, Ls, m, Ms, m is written in the following format: The analytical expression (3) gives a weak electromagnetic absorption coefficient when there is a strong electromagnetic field in the cylindrical quantum wire with an infinite potential as a function, nonlinear dependence on the strong electromagnetic wave amplitude, and frequency of two waves as well as strong dependence on temperature T of the system and radius R of quantum wires These results are different in comparison with bulk semiconductors and quantum wells The results show that: In a quantum wells, the Ha Noi Metroplolitan University 84 state of an electron is characterized by its quantum number n and wave vector , and in the quantum wires this dependency is much more complex For example, in expression (3) there are four sums with four running indices, while in quantum wells there are only two sums with two running indices Differences are also expressed in numerical and in the graph of the absorption spectrum The absorption coefficient (3) is calculated for the quantum wires GaAs / GaAsAl and graphing The graph in Fig is the dependence of the absorption coefficient α on the temperature with the strong electromagnetic wave amplitude E01 is different correspond to two frequency values of Ω1= 3.1013 Hz and Ω2= 1013 Hz with wire radius R =30 nm Found that, when the temperature T increasing from 20K to 400K, the absorption curve has a maximum and a minimum In Figure is the dependence of the absorption coefficient α on the frequency of strong electromagnetic wave Ω1 with three different temperature values corresponding to Ω2= 1013 Hz, R =30 nm and E01= 14.105V / m Absorption spectra show that in the investigated domain there is only one maximum and no minimum Figure 1: The dependence of α on the temperature T Figure 2: The dependence of α on the frequency Ω1 Figure 3: The dependence of α on the frequency Ω2 Figure 4: The dependence of α on the amplitude E01 The curve in Figure shows the absorption spectrum α depending on the weak electromagnetic wave frequency Ω2 with three different temperature values corresponding to Ω1= 3.1013 Hz, R =30 nm and E01= 15.106 V / m Absorption spectra show a peak at Scientific Journal − No27/2018 85 Ω2= ω0 and another peak is lower when Ω2 ≠ ω0 Because optical phonons are strong oscillators, when the frequency of weak electromagnetic waves Ω2 equal ω0 of the phonon optical, the resonance peaks will appear and the absorption coefficient of the crystal is best The difference with the semiconductor semiconductor is the appearance of the second largest peak, which occurs due to a transition between the mini-regions of the electron in the quantum wires The graph in Figure represents the dependence of the absorption coefficient α on the amplitude of strong electromagnetic wave E01 with Ω1= 6.1013Hz, Ω2= 3.1013Hz and R= 30nm The absorption curve has a resonant region and this area moves to the right as the temperature decreases The graph in Figure shows the absorption spectrum of α on the amplitude of strong electromagnetic wave E01 with a different wire radius corresponding to Ω1= 6.1013Hz, Ω2= 3.1013Hz and T= 80K The absorption curve has a resonant region and this area moves to the right in the direction of the radius of the wire In Figure 6, the absorption curve of the absorption coefficient α depends on the wire radius with three values of temperature corresponding to Ω1= 3.1013Hz, Ω2= 7.1013Hz, E01= 15.106V / m Notice that apart from the main resonant peak, there are more sub-resonant on the left side in the direction of the reduction of the wire radius Obviously, the quantum size effect of the quantum wire has resulted in these sub-resonant Figure 5: The dependence of the absorption coefficient α the amplitude E01 Figure 6: The dependence of the absorption coefficient α on the radius of quantum wire In summary, the numerical results show that, the absorption coefficient of weak electromagnetic wave in the presence of strong electromagnetic waves in the cylindrical quantum wire GaAs / GaAsAl with infinite potential, complex dependencies on Ω1, Ω2, E01, R and T The absorption curves found several resonant peaks Under the influence of strong electromagnetic waves, the absorption coefficient can be negative This means that under the influence of strong electromagnetic waves with condition is satisfied, the absorption coefficient transforms into a weak electromagnetic wave enhancement factor From (3) if given E01= we will get back the weak electromagnetic absorption coefficient in the cylindrical quantum wire in the absence of strong electromagnetic waves The findings are published in [5] 86 Ha Noi Metroplolitan University 2.1.2 The absorption of weak electromagnetic waves in rectangular quantum wires in the presence of strong electromagnetic waves Similar to the physical problem in part 2.1, based on the quantum-kinetic equation, we construct a quantum-kinetic equation for confined electrons in rectangular quantum wires with an infinite potentials in the presence of weak electromagnetic waves (weak amplitudes, high frequency) and strong electromagnetic waves (strong amplitude, high frequency) Calculations with the assumption that weak electromagnetic waves are linear with frequency ω satisfying high frequency conditions ωτ >> , the electron energy spectrum in quantum wires is quantized according to the degree of discontinuity along the z axis From there, calculated the density vector of current and the absorption coefficient of weak electromagnetic wave by the confined electronic in the rectangular quantum wires in the presence of strong electromagnetic waves As a result, we obtain analytical expressions for the absorption coefficients written as: with Scientific Journal − No27/2018 87 The absorption coefficient of weak electromagnetic wavse (4) in the presence of strong electromagnetic waves in the rectangular quantum wire with infinite potential is highly complex dependence and depends only on the amplitude of strong electromagnetic wave E01, the frequency of two electromagnetic waves, the temperature T and the size of the quantum wires (Lx, Ly) These results are different in comparison to normal semiconductors, quantum wells and cylindrical quantum wires From expression (4) when given E01= we will get back the absorption coefficient of weak electromagnetic waves in the rectangular quantum wires with an infinite potential in the absence of strong electromagnetic waves The absorption coefficient (4) is calculated and graphed for the rectangular quantum wires GaAs / GaAsAl The graph in Figure is the dependence of the absorption coefficient α on the temperature with the different amplitude of the wave E01 with respect to Ω1= 3.1013 Hz, Ω2= 1013 Hz and R =30 nm Figure 7: The dependence of the absorption coefficient α on the frequency Ω2 Figure 8: The dependence of the absorption coefficient α on the frequency Ω1 The graph in Figure shows the dependence of the absorption coefficient of weak electromagnetic wave α on the frequency Ω2 of weak electromagnetic waves with different temperatures correspond to E01 and Ω1= 3.1013 Hz, Lx= 24nm, Ly= 26nm, E01=15.106Hz Notice that, on the absorption curve there is a main peak at Ω2= ω0 and several sub peak are smaller when Ω2≠ ω0 It is easy to see that the main peak changes insignificantly when the temperature changes Figure shows the curve representing the absorption spectrum of the coefficient α on the amplitude of strong electromagnetic wave E01 with three different temperature values corresponding to Ω1= 6.1013 Hz, Ω2= 3.1013 Hz, Lx= 24nm, Ly= 26nm On the absorption spectrum there is a maximum, the position of the peak is shifted to the right when the temperature decreases 88 Ha Noi Metroplolitan University The graph in Figure shows the dependence of the absorption coefficient α on the size Lx of quantum wires with three different temperature values corresponding to Ω1= 3.1013 Hz, Ω2= 7.1013 Hz, Ly= 26nm, E01=15.106Hz On the absorption curve, many peaks appear These peaks appear by quantum size effects when the Lx small, the resonance peak in this area is clearer and sharper than the remaining peaks The numerical results also show another important conclusion that, under the influence Figure 9: The dependence of absorbtion coefficient α on Lx of strong electromagnetic waves and under certain conditions, the absorption coefficient of electromagnetic waves in the rectangular quantum wire can receive negative value That is, in this case the absorption coefficient transforms into a amplification coefficient of weak electromagnetic wave This is different than in normal semiconductors This difference is due to the quantum wire being one-dimensional semiconductors The findings are published in [6] 2.2 The theory of AE field and AME field in cylindrical quantum wires with infinite potential Studying the physical properties of low-dimensional semiconductor structures, scientists have paid much attention to the influence of sound wave to the properties of lowdimensional materials such as AE effects and AME effects The propagation of external sound waves into the semiconductor increases the transfer of energy and momentum of sound waves to conductive particles in the semiconductor and produces an electro-acoustic effect along the direction of sound waves If the material creates a closed circuit, it creates an AE current that runs along the direction of the sound wave, if the open circuit produces an AE field When there is an external magnetic field, in this semiconductor sample there is another effect called a AME effect and to appear a AME field Recently, this problem has been studied by scientists in both theory and experiment in normal semiconductor, Kane semiconductor, two-dimension semiconductor However, in the one-dimension semiconductors (quantum wires) is left open Therefore, we are interested in studying the theory of AE effects and AME effects in cylindrical quantum wires with infinite potential Scientific Journal − No27/2018 89 2.2.1 The density of AE current in the cylindrical quantum wire when there is no external magnetic field Proceed from the Hamiltonian operator describes the interaction of the sound waveelectron system and scattering between confined electron with the acoustic phonon in the cylindrical quantum wire with infinite potential is written as follows: H = ∑ ε n ,l , pz a n+,l , p z a n ,l , p z + ∑ I nn,'l,l ' C k a n+' ,l' , p z + k an' ,l' , p' (bk + b−+k ) n ,l , p z + ∑ ℏω k bk bk + ∑ C qU k Unn,',ll ' = z n ,l ,n' ,l ' ,k + n ,l ,n' ,l ' ,q n' ,l ' n ,l a + n' ,l ' , p z + q a n' ,l' , p' bq exp( −iω q t ) (5) z R 2exp(−kl L) R * n ',l ' ψ ( r ) ψ ( r )exp iq r dr ; I = J|n−n'| (q⊥ R)ψ n*',l ', p 'z (r )ψ n,l , pz (r )rdr ( ⊥ ) n,l ∫0 n',l ', p 'z n,l , pz R2 L R2 ∫0 (6) For calculating the AE currents in a cylindrical quantum wire with infinite potential, it is necessary to establish quantum-kinetic equations for confined electrons in quantum wires Performing the calculations with the assumption that the momentum recovery time of electrons is approximately constant, we obtain the analytical expression for the density of AE current in the cylindrical quantum wire with the infinite potential write in the form: 3  eτ Λ f0  2m  βεF  βℏ2   −ξ+  2mξ+  n',l' Bn,l  ξ+ e    e ∑ In,l exp −  K3 (ξ+ ) + 3K2 (ξ+ ) + 3K1(ξ+ ) + K0 (ξ+ ) 2π ℏ ρvsmωq  ℏβ  n,l,n',l'  ℏβ    2m   3/2  2mξ   eτ Λ vl ωq f0ϕπ  4m  βε  βℏ2  n',l' − F +ξ−3e−ξ−  Bn,l  ×  K3 (ξ− ) + 3K2 (ξ− ) + 3K1(ξ− ) + K0 (ξ− )+   e ∑ Un,l exp − ℏ ρFSvs n,l,n',l'  β   ℏβ    2m  j=−      × e−χ+ χ+5/2 K5 (χ+ ) + 3K3 (χ+ ) + 3K1 (χ+ ) + K (χ+ ) −e−χ− χ−5/2 K5 (χ− ) + 3K3 (χ− ) + 3K1 (χ− ) + K (χ− ) − −   2 2   2 2  (7) here: ξ± = ℏ2β 2m ℏβω k  ℏ( Bn2' ,l' − Bn2,l )   ± mωq  ; χ ± = ξ ± ±  2R   The β = /kBT; εF is Fermi energy; Kn- the Bessel function of type two From equation (7), found the nonlinear dependence of the AE current on the temperature T, wave numbers, frequencies of external sound wave, and radius of quantum wires These results are completely different from the results in normal semiconductor and in the quantum wells of the same problem The findings are published in [7] 2.2.2 The AME field in the rectangular quantum wires with infinite potential in the presence of external quantum field Assume that external sound waves have frequencies ωq propagate along a cylindrical quantum wire with an infinite potential, considering the practical case from the Ha Noi Metroplolitan University 90 experimental point at low temperature, when ωq/η=νS|q| /η > (η is the frequency of oscillation of the electron, vS sound velocity, q is the number of sound waves outside and d is the average free path of electrons We consider external sound waves as phonon streams Derivative of Hamiltonian describes the interaction between electrons and external phonon and electron scattering on the acoustic phonon in cylindrical quantum wire with the infinite potential in the presence of an external magnetic field in the second quantization writed in the form: H = ∑ ε nB,l ,N , p z a n+,l , p z a n ,l , p z + n ,l ,N , p z + ∑ ℏω k bk bk + ∑ C qU + n ,l ,n' ,l ' ,q k ∑ n ,l ,N ,n' ,l ' ,N ' ,k n' ,l ' n ,l a I nn,'l,l' C k J NN ' ( u )a n+' ,l' , p z + k a n' ,l' , p' (bk + b−+k ) + n' ,l ' , p z + q (8) z a n' ,l ' , p' bq exp( −iω q t ) z , ∞ with J N ' ( u ) = ∫ψ * ( r − a ( p − k ))e iq⊥ pzψ ( r − a p )dr N n' ,l ' ,N ' ⊥ c z n ,l ,N ⊥ c z −∞ − =2 N '− N  N!     N '!  Sgn ( N ' − N )  i    1  N '− N exp  − ac2 kx k y  exp  − ac2 kz2  Sgn( N '− N )ac k y + iac kx  Lmin( N ', N )  ac2 kz2      2  (9) here u = ac q ⊥2 / ; r⊥ is the position of the electron in the cyclotron orbit, LNN '− N (x) is Laguerre conjugate polynomial Performing the calculations, we obtain the expression for the density of AME currents in the cylindrical quantum wire with an infinite potential when there is an external magnetic field is written in the form: ji = e2 m {a1δij − ωca2εijk hk + ωc2a3hi hj } E j + {b1δij − ωcb2εijk hk + ωc2b3hi hj }ϕ j + {c1δij − ωcc2εijk hk + ωc2c3hi hj }ϕ j , (10) ℏ (10) and obtained the general expression for the AME field in the cylindrical quantum wire with infinite potential when there is an external magnetic field: EAME = ℏτ 0ϕ ( A1 + A2 )[Y1 − Y2 − ( χ − ANn,l sin φ )M sin φ ] , ∑ 4e m n,n ',l ,l ' N , N ' χ M1 + 2χ ANn,l M + ( ANn,l sin φ )2 M + ANn,l M with: Y1 = [ χ sinϕ ( − cos ϕ ) + ANn ,l (cos ϕ − sin ϕ )]Y The Y2 = χ ( + sin ϕ )[ ci( x ) sin( x ) − si( x ) cos( x )] M = [ ci( x ) cos( x ) − si( x ) sin( x )] ( + sin ϕ ) + sin ϕ [( ci ( x ) − si ( x )) − 2Y cosϕ ] M = Y ( sin ϕ − ) − sin ϕ cosϕ ( ci ( x ) cos ( x ) + si ( x ) sin ( x )) M = [ ci ( x ) + si ( x )] − cos ϕY − M ; M = [ ci( x ) cos( x ) + si ( x ) sin( x )] Y = [ ci ( x ) − si ( x )] sin( x ) cos( x ) + ci( x )si( x )[sin2 ( x ) − cos ( x )] ; χ = xk BT (11) Scientific Journal − No27/2018 si( x ) = − 91 k 2k ∞ ( −1 ) x ( −1 ) k x k −1 ;x= ; ci( x ) = − ln( x ) + ∑ ; k =1 2k ( 2k )! k =1 ( 2k − )( 2k − )! τ 0ω c π ∞ +∑ χ= k BT τ 0ω c a) Consider the case of the weak magnetic field: In weak magnetic field and high temperature ωc kBT, ωc>> η, the AME field expression in the cylindrical quantum wires with infinite potential in the presence of an external magnetic field of the form: E AME = − sinϕ( A1 + A2 )[ µ1 cosϕ + µ2 sinϕ ]( χµ2 + µ1 ANn ,l ) ℏφ ∑ e m n ,n' ,l ,l' ,N ,N ' sin2 ϕ [ χµ2 + µ1 ANn ,l ] + [ µ ( χ cosϕ − ANn ,l ) − µ1 ( χ − ANn ,l cosϕ )] (13) 2.2.3 Numerical calculation and discussion In this section we calculate numerically and plot the AE current, and AME fields in the cylindrical quantum wires GaAs / GaAsAl The graph in Figure 10 shows the dependence of AE current J on the radius of quantum wire R (dotted line: T = 290 K; stripline: T = 295 K, solid line: T = 300 K), ω q = 1,0 × 1011 s −1 Figure 10: The dependence of the AE current on the radius R Figure 11: The dependence of the AE current on the radius R and the temperature T 92 Ha Noi Metroplolitan University The graph shows that there is a maximum peak received when the following condition is satisfied (occurring due to transition between sub-bands): 2 2 ωq = ωk + ℏ ( Bn ',l ' − Bn,l ) / (2mR ) , n ≠ n' and l ≠ l' In the case of intrasubband transitions: n = n' and l = l' , the numerical calculation for this case, we obtained J = 0, this means that there is only a intersubband transition for contribution to the AE current This result is different from the result in normal semiconductor When the diameter of the wire is μm, the confinement of the electrons is ignored, so that this peak is absent, in qualitative will be similar to the results in the normal semiconductor Compared to the results in the semiconductor superlattice [4], it is completely different in terms of graph shape and number of peaks Figure 11 gives us an overview of the dependention of J on radius of quantum wire R and temperature T The graph shows that as the radius of wire increases, the quantum size effect decreases rapidly Figure 12: The dependence of the AME field on the temperature (the weak magnetic field) Figure 13: The dependence of the AME field on the temperature (the strong magnetic field) The curve in Figure 12 shows the dependence of the AME field (12) in the weak magnetic field on the temperature T For high temperature cases at different values of the magnetic field B (dotted line: B = 0.10T, solid line: B = 0.12T; R = 30nm), the dependence of the AME field on temperature indicates that when the temperature rises,it fincreases monotonically However, this field reaches a maximum value at temperature T = 145K then fell sharply This peak is moved toward the smaller temperature when the magnetic field increase In Figure 13, the graph shows the dependence of the AME field (13) on the temperature in the strong magnetic field B = 2.0T at R = 35nm (dashed line) and R = 30nm (solid line) This result is different from the result in normal semiconductor with linear graphs This result is also different from the results in quantum wells with parabol potential [2, 3] in that the peaks are sharper In addition, the graph shows that the positions of the peaks are almost non-moving when the radius of the quantum wires change, reaching the maximum value at the temperature T about 14K with intensity of magnetic field B= 2.0T Scientific Journal − No27/2018 93 and values of AME field approximately 2.1 V / m at radius R = 35nm and 2.8 V / m at R = 30 nm The results of this study are published in [8, 9] CONCLUSION Based on the quantum-kinetic equation method, we have investigated some opticalacoustic-electronic properties in quantum wires when there is an external electromagnetic field The results are summarized as follows: The problem of studying the absorption coefficient of a weak electromagnetic wave by confined electrons in the cylindrical and rectangular quantum wires, in the presence of strong electromagnetic waves with the electron-phonon optical scattering mechanism The general expression for the level and conductivity tensors in the quantum wires From there, The analytical expressions for the absorption coefficients of weak electromagnetic waves by confined electronic in quantum wires are obtained The results of numerical calculattion show that the absorption coefficient depends strongly on the temperature, frequency of the two electromagnetic waves and the characteristic parameters of structures are the radius of rectangular and cylindrical quantum wires The results are compared to similar results in normal semiconductors and quantum wells showing differences Particularly, the numerical results show that under strong electromagnetic waves, under certain conditions to be satisfy , the absorption coefficient can be negative or the absorption coefficient is converted to the increase coefficient When the amplitude of the strong electromagnetic wave is E01= allows us to recover absorption coefficients of weak electromagnetic waves in the absence of strong external electromagnetic waves With the problem of theoretical study of AE field and AME field in cylindrical quantum wires with infinite potential for two cases with external magnetic field and no external magnetic fields Received a quantum-kinetic equation for confined electrons in the cylindrical quantum wires with an infinite potential The analytical expressions for the AE field and AME field are obtained From there, the dependence of the AE field and AME field on the frequency of sound wave, the temperature of system and the radius of quantum wire, as well as the indexs of characteristic energy for quantum wires are nonlinear In addition, the AME field in the cylindrical quantum wire is strongly dependent on the magnitude of the external magnetic field at both the weak magnetic field and the strong magnetic field Results of numerical calculations for cylindrical quantum wires GaAs / GaAsAl show for the condition for the appearance of the peaks of the AE currents are ωq = ωk + ℏ2 ( Bn2',l ' − Bn2,l ) / (2mR ) with n ≠ n' and l ≠ l' and the condition for the appearance of 94 Ha Noi Metroplolitan University the peaks of the AME field are ω q = ω k + ∆Nn ,,nN' ,'l ,l' ( n ≠ n' ,l ≠ l' , N ≠ N ' ) This result is completely different from the results of the same problem in normal semiconductors, quantum wells and semiconductor superlattices The cause of this peaks is by the transfer of electron energy between the sub-bands in the quantum wire In particular, the AE current occurs even when the momentum recovery time of electron is independent of energy, which is quite different from the results of previous studies in normal semiconductors that have not the AE current (J=0) when the momentum recovery time of electron is constant The theory of nonlinear absorption of weak electromagnetic waves and the theory of AE field and AME field in the quantum wires received are the basis for the development, expansion and research of other low-dimensional semiconductor structures The results are new and have a certain scientific significance, which gives us a deeper understanding of the properties of physics of the low-dimensional semiconductor system and the gradual improvement of the material structure suitable for the fabrication technology new generation electronic components Acknowledgments: We would like to thank colleagues in the Department of Theoretical Physics of VNU-Hanoi University of Science for their valuable contributions and funding from the National Science and Technology Development Fund NAFOSTED: 103.01.2011.18 and 103.01-2015.22 helped us complete these works REFERENCES Nguyen Thi Thanh Nhan, Nguyen Vu Nhan, Nguyen Quang Bau (2012), “Ability to increase a weak electromagnetic wave by confined electrons in doped superlattices in the presence of laser radiation modulated by amplitude”, - Journal of Science of HNUE, Mathematical and Physical Sci Vol.57, No 7, pp.113-123 Nguyen Quang Bau Nguyen Van Hieu, Nguyen Vu Nhan 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Presence of an External Magnetic Field”, - PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27-30 (2012), pp.772-777 NGHIÊN CỨU LÝ THUYẾT LƯỢNG TỬ CÁC HIỆU ỨNG ĐỘNG TRONG DÂY LƯỢNG TỬ DƯỚI ẢNH HƯỞNG CỦA TRƯỜNG SĨNG NGỒI Tóm tắ tắt: Trong báo này, chúng tơi trình bày kết nghiên cứu lý thuyết tính chất quang điện từ dây lượng tử thuộc hệ bán dẫn chiều hai trường hợp có mặt khơng có mặt từ trường ngồi Bài tốn vật lý nghiên cứu sở phương trình động lượng tử theo hai hướng chính: Lý thuyết hấp thụ phi tuyến sóng điện từ electron bị giam cầm dây lượng tử (bài toán thứ nhất) lý thuyết lượng tử trường âm điện (AEF-acoustoelectric field) trường âm điện từ (AMEFacoustomagnetoelectric field) dây lượng tử ảnh hưởng từ trường ngồi (bài tốn thứ hai) Đã nhận biểu thức giải tích cho hệ số hấp thụ sóng điện từ toán thứ biểu thức giải tích trường AEF AME tốn thứ hai Các kết lý thuyết tính số cho dây lượng tử GaAs / GaAlAs có kích thước hình trụ kích thước hình chữ nhật với dạng hố khác Kết tính so sánh với kết tương ứng bán dẫn khối, giếng lượng tử siêu mạng bán dẫn cho thấy khác biệt xuất đỉnh cộng hưởng phổ hấp thụ đồ thị AEF AMEF Từ khóa: Dây lượng tử, bán dẫn chiều, bán dẫn 1D  ... Derivative of Hamiltonian describes the interaction between electrons and external phonon and electron scattering on the acoustic phonon in cylindrical quantum wire with the infinite potential in the. .. However, in the one-dimension semiconductors (quantum wires) is left open Therefore, we are interested in studying the theory of AE effects and AME effects in cylindrical quantum wires with infinite... (J=0) when the momentum recovery time of electron is constant The theory of nonlinear absorption of weak electromagnetic waves and the theory of AE field and AME field in the quantum wires received