Interface-Optical-Phonon Modes in Quasi-one-dimensional Wurtzite Rectangular Quantum Wires

By employing the dielectric continuum model and Loudon‘s uniaxial crystal model, the interface optical(IO) phonon modes in a freestanding quasi-one-dimensional (Q1D) wurtzite rectangular quantum wire are derived and analyzed. Numerical calculation on a freestanding wurtzite GaN quantum wire is performed. The results reveal that the dispersion frequencies of IO modes sensitively depend on the geometric structures of the Q1D wurtzite rectangular quantum wires, the free wave-number kz in z-direction and the dielectric constant of the nonpolar matrix. The degenerating behavior of the IO modes in Q1D wurtzite rectangular quantum wire has been clearly observed in the case of small wave-number kz and large ratio of length to width of the rectangular crossing profile. The limited frequency behaviors of IO modes have been analyzed deeply, and detailed comparisons with those in wurtzite planar quantum wells and cylindrical quantum wires are also done. The present theories can be looked on as a generalization of that in isotropic rectangular quantum wires, and it can naturally reduce to the case of Q1D isotropic quantum wires once the anisotropy of the wurtzite material is ignored.     

纤锌矿氮化镓基阶梯量子阱中界面声子的色散谱与散射率

本文理论分析了纤锌矿GaN-基阶梯量子阱中的电子-界面光学声子散射性质。阶梯量子阱中的解析的界面声子态及Frhlich电子-声子相互作用哈密顿被导出了。在考虑强内建电场效应及能带的非抛物性特性的情况下,阶梯量子阱结构精确解析的电子本征态也被给出了。以一个四层纤锌矿AlN-基阶梯量子阱为例进行了数值计算。结果发现,系统中存在四支界面光学声子模,这一观察明显不同于对称的GaN/AlN单量子阱与双量子阱的情况。这一差异被归结为阶梯量子结构的非对称性。GaN-基阶梯量子阱中的子带内散射率与子带间散射率比GaAs-基阶梯量子阱的结果大一个数量级,这被归因于GaN-基晶体大的电子-声子耦合常数。GaN-基阶梯量子阱的子带内散射率表现出与GaAs-基体系类似的结构参数依赖关系,但两类体系的子带间散射率对阶梯量子阱结构参数依赖则明显不同,这被归结为GaN-基阶梯量子阱结构中强的内建电场效应及带的非抛物性。结果还表明,高频界面声子模相对于低频界面声子模,对散射率的贡献更大。     

Polar Interface Optical Phonon Modes and Fr(o*)hlich Electron-Phonon Interaction Hamiltonians in an Arbitrary Layer-Number Quantum Well System

By using determinant method as in our recent work, the IO phonon modes, the orthogonal relation forpolarization vector, electron-IO phonon Frohlich interaction Hamiltonian, the dispersion relation, and the electron-phonon coupling function in an arbitrary layer-number quantum well system have been derived and investigated withinthe framework of dielectric continuum approximation. Numerical calculation on seven-layer Alx Ga1-x As/GaAs systemshave been performed. Via the numerical results in this work and previous works, the general characters of the IO phononmodes in an n-layer coupling quantum well system were concluded and summarized. This work can be regarded as ageneralization of previous works on IO phonon modes in some fixed layer-number quantum well systems, and it providesa uniform method to investigate the effects of IO phonons on the multi-layer coupling quantum well systems.     

柱形量子线中极化子的电子与LO声子之间相互作用能

采用变分法，研究了柱形量子线中在考虑电子与LO声子相互作用的情况下，极化子在基态时系统的能量以及电子-LO声子之间的相互作用能。数值计算结果表明：随着柱形量子线截面半径的减小，基态能量和电子-LO声子相互作用能的绝对值都增大。     

Confinement of polar optical phonons in quasi-one-dimensional Wurtzite GaN-based quantum well wires: propagating and half-space phonon modes

With the aid of the macroscopic dielectric continuum and Loudon’s uniaxial crystal models, the propagating (PR) and half-space (HS) optical phonon modes and corresponding Fröhlich-like electron-phonon interaction Hamiltonians in a quasi-one-dimensionality (Q1D) wurtzite quantum well wire (QWW) structure are derived and studied. Numerical calculations on a wurtzite GaN/A_l0.15Ga_0.85N QWW are performed, and discussion is focused mainly on the dependence of the frequency dispersions of PR and HS modes on the free wave-number k _z in the z-direction and on the azimuthal quantum number m. The calculated results show that, for given k _z and m, there usually exist infinite branches of PR and HS modes in the high-frequency range, and only finite branches of HS modes in the low-frequency range in wurtzite QWW systems. The reducing behaviors of the PR modes to HS modes, and of the HS mode to interface phonon mode have been observed clearly in Q1D wurtzite heterostructures. Moreover, the dispersive properties of the PR and HS modes in Q1D QWWs have been compared with those in Q2D quantum well structures. The underlying physical reasons for these features have also been analyzed in depth.     

Interface Phonons in Cone-Shaped GaAs/AlxGal-xAs Quantum Dots with a Spherical Top Surface

By using the dielectric continuum model, the side interface optical (SIO) and top interface optical (TIO) phonon modes for a cone-shaped GaAs/Al_xGa_l-xAs quantum dot with a spherical top surface are obtained. It is found that, unlike the TI0 mode which shows the same results as those for spherical GaAs/Al_xGa_l-xAs quantum dots, the SIO phonon frequencies depend on not only the integer l, but also the integer |m| as well as the polar angle α, and the frequency behavior of all the different modes is also strongly dependent on x. It is useful to study the couplings between electrons and phonons for those like this system.     

Quantum Limits of Polarization Switching in Optical Mesoscopic Devices with Distributively Coupled Quantum Modes

The quantum theory of nonlinear dynamics and the switching effect for two distributively coupled modes in optical systems has been developed based on the Hartree approximation. The quantum limits for observation of the switching effect for the polarization characteristics of light has been determined. The creation of a new type of nonclassical mesoscopic states of light like the Schrödinger-cat states and mesoscopic qubit/qutrit states is predicted. The theoretical prediction is confirmed by a numerical estimation of real systems, i.e., tunnel-coupled optical fibers and waveguides, for the experimental realization of the states under consideration.     

声子色散对抛物量子点中极化子基态能量的影响

在声子色散影响下利用压缩态变分法计算了抛物量子点中弱耦合极化子的基态能量。采用的变分方法是基于逐次正则并且利用单模压缩态变换处理通常被我们所忽略的在第一次幺正变换中产生的声子产生湮灭算符的双线性项。计算得出了在考虑声子色散的情况下抛物量子点中弱耦合极化子的基态能量的数学表达式。讨论了抛物量子点中在电子-声子弱耦合情况下,受限长度,电子-声子耦合常数,色散系数与极化子基态能量之间的依赖关系。     

Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well Wires

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes aswell as the corresponding Frohlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-wellwire (Q WW) are derived and studied. Numerical calculations on GaAs/AlxGa1-xAs cylindrical QWW are performed.Results reveal that there are two branches of IO phonon modes and one branch of SO phonon mode, and the dispersionfrequencies ofIO or SO phonon modes sensitively depend on the Al mole fraction x in Alx Ga1-x As material and the wave-vector in z direction, kz. With the increasing of κz and quantum number m, the frequency of each IO mode approaches oneof the two frequency values of the single GaAs/Alx Ga1-xAs heterostructure, and the electrostatic potential distributionof the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the couplingbetween the electron-IO and -SO phonons becomes weaker.     

Electron Transport Properties of Graphene-Based Quantum Wires

We study the electronic transport in quantum wire structures made of graphene. By using the nonequilibrium Green function method, the transmission is studied for varies sizes samples. Our results show that the transmission sensitive depends on the size of the system and exhibits fluctuations due to the mismating of propagating modes between the central region and the leads. The number of resonant transmission peaks increases with the increase of length of the wire, while the width of the leads mainly affect the transmission in the region of low energy. A central energy gap in the transmission spectrum is more likely to appear in the quantum wire system than in the uniform armchair graphene nanoribbons. Moreover, the energy gap can be widened for a certain size of the quantum wire system by changing the width of the leads. These results may have potential applications in designing graphene-based devices.     

Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well Wires

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes as well as the corresponding Fro^ehlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-well wire (QWW) are derived and studied. Numerical calculations on GaAs/AlzGa1-x As cylindrical QWW are performed. Results reveal that there are two branches of IO phonon modes and one branch of SO phonon mode, and the dispersion frequencies of IO or SO phonon modes sensitively depend on the Al mole fraction x in AlzGa1-x As material and the wavevector in z direction, kz. With the increasing of kz and quantum number m, the frequency of each IO mode approaches one of the two frequency values of the single GaAs/AlxGa1-x As heterostructure, and the electrostatic potential distribution of the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the coupling between the electron-IO and -SO phonons becomes weaker.     

纤锌矿MgxZn1-xO/Mg0.3Zn0.7O抛物量子阱中极化子能级

采用改进的Lee-Low-Pines(LLP)中间耦合方法研究纤锌矿Mg x Zn1-x O/Mg0.3Zn0.7O抛物量子阱材料中的极化子能级,给出极化子基态能量、跃迁能量(第一激发态到基态)和不同支长波光学声子对电子态能级的贡献随量子阱宽度d的变化规律。理论计算中考虑了纤锌矿Mg x Zn1-x O/Mg0.3Zn0.7O抛物量子阱材料中声子模的各向异性和介电常数、声子(类LO和类TO)频率等随空间坐标Z变化(SD)效应对极化子能量的影响。结果表明,Mg x Zn1-x O/Mg0.3Zn0.7O抛物量子阱中电子与长波光学声子相互作用对极化子能级的移动很大,使得极化子能量明显降低。阱宽较小时,半空间长波光学声子对极化子能量的贡献较大,而定域长波光学声子的贡献较小;阱宽较大时,情况则正好相反。在d的变化范围内,电子与长波光学声子相互作用对极化子能级的移动(约67~79 meV)比Al x Ga1-x As/Al0.3Ga0.7As抛物量子阱中的相应值(约1.8~3.2 meV)大得多。因此,讨论ZnO基量子阱中电子态问题时要考虑电子与长波光学声子的相互作用。     

左手介质矩形波导导模和表面模的场分布

从麦克斯韦方程组出发,结合电磁场的边界条件,推导出介质矩形波导导模的一般色散方程.对普通介质矩形波导和左手介质矩形波导的导模场分布分别进行了数值模拟.通过对比两种介质矩形波导的导模场分布的模拟结果,发现左手介质矩形波导Ex22模的场分布比普通介质波导Ex00模的场更集中在波导中部.同时,根据处理普通介质矩形波导的Marcatili方法.类比得到左手介质矩形波导表面模的色散方程,并数值模拟了低阶模的场分布,结果表明,能量主要集中在波导的四个角区以及波导的边缘.     

柱形量子线中体纵光学声子平均数

考虑电子与体纵光学声子相互作用时,采用LLP变分方法,研究柱形量子线中极化子性质,导出了柱形量子线中极化子光学声子平均数随量子线截面半径和电子-LO声子耦合强度的变化关系.结果表明柱形量子线中极化子的光学声子平均数随量子线截面半径减小而减小,随电子-LO声子耦合强度增强而增加.     

Dual Space Analyzing Based on Symmetry Properties for Phonons of Si Quantum Dot

Phonon modes in spherical Si quantum dots (QDs) with up to 7.9 nm in diameter are calculated by using the projection operators of the group theory into valence force field model. The phonons of dot modes in each of five irreducible representations (symmetries) are classified by using a dual space analysis method. It is found that the bulk-like modes with localization radius much smaller than the dot‘s radius have clearly pronounced bulk specific-κdefinite bulk band (one in six modes). In Si dots of all sizes, each specific bulk-like dot mode has specific symmetry.TO dot modes and bulk-like X-derived TA and LA dot modes red-shift in frequency with decreasing dot size. There is almost not LO/TO mixing for bulk-like modes. As for the surface-like modes localized at the periphery of the dot,their eigenmodes have not a dominant bulk specific-κ point parentage or a dominant BZ parentage around some special point. They are a superposition of many bulk bands with κ from all over the bulk BZ. They have much significant mode mixing than the bulk-like phonons. The classification of dot modes based on the symmetry of group theory will bring advantageous to the discussion of Ramam spectrum, electron-phonon interaction and other phonon-assisted effects in QDs.     

Vibration Spectrums of Polar Interface Optical Phonons in GaAs/AlAs Cylindrical Quantum Dots

The dispersions of the top interface optical phonons and the side interface optical phonons in cylindrical quantum dots are solved by using the dielectric continuum model. Our calculation mainly focuses on the frequency dependence of the IO phonon modes on the wave-vector and quantum number in the cylindrical quantum dot system. Results reveal that the frequency of top interface optical phonon sensitively depends on the discrete wave-vector in z direction and the azimuthal quantum number, while that of the side interface optical phonon mode depends on the radial and azimuthal quantum numbers. These features are obviously different from those in quantum well, quantum well wire, and spherical quantum dot systems. The limited frequencies of interface optical modes for the large wave-vector or quantum number approach two certain constant values, and the math and physical reasons for this feature have been explained reasonably.     

Propagating Optical Phonon Modes and Their Electron-Phonon Interaction Hamiltonians in Asymmetric Wurtzite Nitride Semiconductor Quantum Wells

Within the framework of the dielectric continuum model and Loudon's uniaxial crystal model, the properties of frequency dispersion of the propagating (PR) optical phonon modes and the coupling functions of electron-PR phonons interaction in an asymmetrical wurtzite quantum well (QW) are deduced and analyzed via the method of electrostatic potential expanding. Numerical calculation on an asymmetrical Al_0.25Ga_0.75 N/GaN/Al_0.15Ga_0.85N wurtzite QW were performed. The results reveal that there are infinite branches of PR phonon modes in the systems. The behaviors of frequency forbidden of PR modes in the asymmetric QWs have been clearly observed. The mathematical and physical origins for these features have been analyzed in depth. The PR optical phonon branches have been distinguished and labelled reasonably in terms of the oscillating properties of the PR modes in the well-layer material. Moreover, the amplitudes and frequency properties of the electron-PR modes coupling functions in the barrier and well materials have also been analyzed from both of the mathematical and physical viewpoints.     

抛物量子线中极化子的激发态性质

研究抛物型量子线中极化子激发态的性质。采用线性组合算符法和Pekar变分法,导出了抛物量子线中强耦合和弱耦合两种情况下极化子的基态能量、第一内部激发能量、激发能和振动频率随量子线的约束强度的变化关系。数值计算结果表明:抛物型量子线中极化子的基态能量、第一内部激发能量、激发能和振动频率都随量子线约束强度的增强而增大,体现了量子线受限强度越大,相应的极化子的能量也越大。     

Effects of Electron-Phonon Interaction on Linear and Nonlinear Optical Absorption in Cylindrical Quantum Wires

The electron-phonon interaction influences on lineax and nonfineax optical absorption in cylindrical quantum wires （CQW） with an infinite confining potential axe investigated. The optical absorption coefficients are obtained by using the compact-density-matrix approach and iterative method, and the numerical results are presented for GaAs CQW. The results show that the electron-phonon interaction makes a distinct influence on optical absorption in CQW. The electron-phonon interaction on the wave functions of electron dominates the values of absorption coefficients and the correction of the electron-phonon effect on the energies of the electron makes the absorption peaks blue shift and become wider. Moreover, the electron-phonon interaction influence on optical absorption with an infinite confining potential is different from that with a finite confining potential.     

Dual Space Analyzing Based on Symmetry Properties for Phonons fo Si Quantum Dot

Phonon modes in spherical Si quantum dots (QDs) with up to 7.9 nm in diameter are calculated by using the projection operators of the group theory into valence force field model. The phonons of dot modes in each of five irreducible representations (symmetries) are classified by using a dual space analysis method. It is found that the bulk-like modes with localization radius much smaller than the dot's radius have clearly pronounced bulk specific-k point parentage, T_λ(n, k_BZ, K_cut), from specific part of the Brillouin zone (BZ) (Γ-derived, X-derived etc.) and from definite bulk band (one in six modes). In Si dots of all sizes, each specific bulk-like dot mode has specific symmetry. The bulk TO(Γ)-like and the bulk LO(Γ)-like dot modes always have T₂ and A₁ symmetries, respectively. Except the bulk-A(Γ)-like dot modes of which the frequencies blue-shift as the dot size reducing, the bulk-like Γ-derived LO and TO dot modes and bulk-like X-derived TA and LA dot modes red-shift in frequency with decreasing dot size. There is almost not LO/TO mixing for bulk-like modes. As for the surface-like modes localized at the periphery of the dot, their eigenmodes have not a dominant bulk specific-k point parentage or a dominant BZ parentage around some special point. They are a superposition of many bulk bands with k from all over the bulk BZ. They have much significant mode mixing than the bulk-like phonons. The classification of dot modes based on the symmetry of group theory will bring advantageous to the discussion of Ramam spectrum, electron-phonon interaction and other phonon-assisted effects in QDs.