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.     

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.     

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。     

Electron-Phonon Interaction in an Annular Quantum Dot

The confined longitudinal-optical （LO） phonon and surface-optical （SO） phonon modes of a free-standing annular cylindrical quantum dot are derived within the framework of dielectric continuum approximation. It is found that there exist two types of SO phonon modes： top SO （TSO） mode and side SO（SSO） mode in a cylindrical quantum annulus. Numerical calculation on CdS annulus system has been performed. Results reveal that the two different solutions of SSO mode distribute mainly at the inner or outer surfaces of the annulus. The dispersion relations and the coupling intensions of phonons in a quantum annulus are compared with those in a cylindrical quantum dot. It is found that the dispersion relations of the two different structures are similar, but the coupling intension of the phonon-electron interaction in quantum annulus is larger than that in quantum dot. The Hamiltonians describing the free phonon modes and their interactions with electrons in the system are also derived.     

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.     

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.     

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.     

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.     

Phonon States and Dispersive Spectra of Polar Optical Phonons in Quasi-One-Dimensional Nanowires of Wurtzite ZnO and Zinc-Blend MgO Semiconductors

Within the framework of the macroscopic dielectric continuum model and Loudon's uniaxial crystal model, the phonon modes of a wurtzite/zinc-blende one-dimensional (1D) cylindrical nanowire (NW) are derived and studied. The analytical phonon states of phonon modes are given. It is found that there exist two types of polar phonon modes, i.e. interface optical (IO) phonon modes and the quasi-confined (QC) phonon modes existing in 1D wurtzite/zinc-blende NWs. Via the standard procedure of field quantization, the Fröhlich electron-phonon interaction Hamiltonians are obtained. Numerical calculations of dispersive behavior of these phonon modes on a wurtzite/zinc-blende ZnO/MgO NW are performed. The frequency ranges of the IO and QC phonon modes of the ZnO/MgO NWs are analyzed and discussed. It is found that the IO modes only exist in one frequency range, while QC modes may appear in three frequency ranges. The dispersive properties of the IO and QC modes on the free wave-number k_z and the azimuthal quantum number m arediscussed. The analytical Hamiltonians of electron-phonon interaction obtained here are quite useful for further investigating phonon influence on optoelectronics properties of wurtzite/zinc-blende 1D NW structures.     

Vibration Spectra of Quasi-confined Optical Phonon Modes in an Asymmetric Wurtzite AlxGa1-xN/GaN/AlyGa1-yN Quantum Well

Based on the dielectric continuum model and Loudon's uniaxial crystal model,the properties of the quasiconfined (QC) optical phonon dispersions and the electron-QC phonons coupling functions in an asymmetric wurtzite quantum well (QW) are deduced via the method of electrostatic potential expanding.The present theoretical scheme can naturally reduce to the results in symmetric wurtzite QW once a set of symmetric structural parameters are chosen.Numerical calculations on an asymmetric A1N/GaN/Al0.15Ga0.85N wurtzite QW are performed.A detailed comparison with the symmetric wurtzite QW was also performed.The results show that the structural asymmetry of wurtzite QW changes greatly the dispersion frequencies and the electrostatic potential distributions of the QC optical phonon modes.     

Electron–Phonon Interaction and Quantum Fluctuations in the Time-Dependent Damped Capacitance-Coupled Electric Circuit

Starting from the electron–phonon interaction, the time-dependent capacitance-coupled electric circuit is quantized. Quantum fluctuations derived by this method are different from former ones.     

Bi4Se3薄膜的声子结构及电声子相互作用的第一性原理研究

基于密度泛函微扰理论,运用第一性原理研究两种终结面的Bi₄Se₃薄膜的声子结构和电-声子相互作用.结果表明两种终结面的Bi₄Se₃薄膜体系都是动力学稳定的. Bi₄Se₃薄膜中插入的Bi₂双原子层与Bi₂Se₃五原子层的声子投影态密度并不完全匹配,这会阻碍部分声子的输运,降低热导,从而有利于提高材料的热电性能.另外,两种终结面的Bi₄Se₃薄膜的电-声子耦合系数都不太大（约0.278）,有利于制备基于室温工作的电子学器件.     

Three‐Phonon and Four‐Phonon Interaction Processes in a Pair‐Condensed Fermi Gas

We study the interactions among phonons and the phonon lifetime in a pair‐condensed Fermi gas in the BEC‐BCS crossover in the collisionless regime. To compute the phonon‐phonon coupling amplitudes we use a microscopic model based on a generalized BCS Ansatz including moving pairs, which allows for a systematic expansion around the mean field BCS approximation of the ground state. We show that the quantum hydrodynamic expression of the amplitudes obtained by Landau and Khalatnikov apply only on the energy shell, that is for resonant processes that conserve energy. The microscopic model yields the same excitation spectrum as the Random Phase Approximation, with a linear (phononic) start and a concavity at low wave number that changes from upwards to downwards in the BEC‐BCS crossover. When the concavity of the dispersion relation is upwards at low wave number, the leading damping mechanism at low temperature is the Beliaev‐Landau process 2 phonons ? 1 phonon while, when the concavity is downwards, it is the Landau‐Khalatnikov process 2 phonons ? 2 phonons. In both cases, by rescaling the wave vectors to absorb the dependence on the interaction strength, we obtain a universal formula for the damping rate. This universal formula corrects and extends the original analytic results of Landau and Khalatnikov [ZhETF 19 , 637 (1949)] for the 2?2 processes in the downward concavity case. In the upward concavity case, for the Beliaev 1? 2 process for the unitary gas at zero temperature, we calculate the damping rate of an excitation with wave number q including the first correction proportional to q ⁷ to the q ⁵ hydrodynamic prediction, which was never done before in a systematic way.     

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.     

GaMnAs合金中等离子体激元-LO声子耦合模的拉曼光谱研究

理论分析了两种阻尼条件下重掺杂GaAs中的等离子体激元-LO声子耦合模,证实在小阻尼条件下耦合模的拉曼谱分为两支,而在大阻尼条件下只有一个耦合模可以被观测到。推导得到了只出现一个耦合模所需的最小阻尼的解析表达式。测量了Mn组分从2.6%到9%的GaMnAs合金的拉曼光谱。利用等离子体激元-LO声子耦合模理论进行了谱形拟合,得到了所测的GaMnAs合金中的空穴浓度。     

Interface and propagating optical phonon mixing modes in a wurtzite GaN-based quantum dot

The polar optical phonon vibrating modes of a quasi-zero-dimensional (Q0D) wurtzite cylindrical quantum dot (QD) are solved exactly based on the dielectric continuum model and Loudon’s uniaxial crystal model. The result shows that there exist four types of polar mixing optical phonon modes in the Q0D wurtzite cylindrical QD systems, which is obviously different from the situation in blende cylindrical QDs. The dispersive equations for the interface-optical-propagating (IO-PR) mixing modes are deduced and discussed. It is found that the dispersive frequency of IO-PR mixing modes in wurtzite QD just take a series of discrete values due to the three-dimensional confined properties. Moreover, once the radius or the height of the QD approach infinity, the dispersive equations of the IO-PR mixing modes in the wurtzite Q0D cylindrical QD can naturally reduce to those of the IO and PR modes in Q2D QWs or Q1D QWWs systems. This has been analyzed reasonably from both physical and mathematical viewpoints. The analytical expressions obtained in the paper are useful for further investigating phonon influence on physical properties of the wurtzite Q0D QD systems.     

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 k_z 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 k_z 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.     

Phonon Excitation and Energy Redistribution in Phonon Space for Energy Dissipation and Transport in Lattice Structure with Nonlinear Dispersion

We first propose fundamental solutions of wave propagation in dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive chain and homogenous harmonic chain using stationary phase approximation. Solution is also compared with numerical results from molecular dynamics(MD) simulations. Locally dominant phonon modes(k-space) are introduced based on these solutions. These locally defined spatially and temporally varying phonon modes k(x, t) are critical to the concept of the local thermodynamic equilibrium(LTE). Wave propagation accompanying with the nonequilibrium dynamics leads to the excitation of these locally defined phonon modes. It is found that the system energy is gradually redistributed among these excited phonons modes(k-space). This redistribution process is only possible with nonlinear dispersion and requires a finite amount of time to achieve a steady state distribution. This time scale is dependent on the spatial distribution(or frequency content) of the initial perturbation and the dispersion relation. Sharper and more concentrated perturbation leads to a faster energy redistribution and dissipation. This energy redistribution generates localized phonons with various frequencies that can be important for phonon-phonon interaction and energy dissipation in nonlinear systems.Depending on the initial perturbation and temperature, the time scale associated with this energy distribution can be critical for energy dissipation compared to the Umklapp scattering process. Ballistic type of heat transport along the harmonic chain reveals that at any given position, the lowest mode(k = 0) is excited first and gradually expanding to the highest mode(kmax(x, t)), where kmax(x, t) can only asymptotically approach the maximum mode kBof the first Brillouin zone(kmax(x, t) → kB). No energy distributed into modes with kmax(x, t) k kBdemonstrates that the local thermodynamic equilibrium cannot be established in harmonic chain. Energy is shown to be uniformly distributed in all available phonon modes k ≤ kmax(x, t) at any position with heat transfer along the harmonic chain. The energy flux along the chain is shown to be a constant with time and proportional to the sound speed(ballistic transport).Comparison with the Fourier's law leads to a time-dependent thermal conductivity that diverges with time.     

抛物量子线中弱耦合极化子的有效质量和光学声子平均数

讨论电子与体纵光学(LO)声子弱耦合时对抛物量子线中极化子性质的影响.采用Tokuda改进的线性组合算符法、Lagrange乘子和变分法,导出了抛物量子线中弱耦合极化子的有效质量和光学声子平均数随拉格朗日乘子变化的规律及极化子振动频率随量子线约束强度的变化规律.并以ZnS量子线为例进行了数值计算,结果表明:抛物量子线中弱耦合极化子的有效质量m^*和光学声子平均数N随着拉格朗日乘子u的增加而增大;该结论与体材料中结论基本一致,但量子线中的效应比体材料更明显,表明量子线对电子约束的增强,使极化子效应更明显.同时,极化子振动频率λ随约束强度ω₀的增强而增大.     

Linear and Nonlinear Optical Properties in Spherical Quantum Dots

We calculate the energy eigenvalues and the sate functions of one-electron Quantum Dot （QD） by using a combination of Quantum Genetic Algorithm （QGA） and Hartre-Fock-Roothaan （HFR） method. The linear and the third-order nonlinear optical absorption coefficients for the 1s-1p, 1p-1d, and 1d-1f transitions are examined as a function of the incident photon energy for three different values of the stoichiometric ratio. The results show that the stoichiometric ratio, impurity, relaxation time, and dot size have great influence on the optical absorption coefficients of QDs.