低维系统中声学极化子及其自陷转变
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摘要
本文讨论低维系统中声学极化子及其自陷转变的相关问题.
指出了Farias等人在文献[66]中给出的二维声学极化子自陷转变的临界电子—声子耦合常数为定值,不随声子截止波矢的改变而变化的结论不符合声学极化子自陷的一般规律.我们采用与该文相同的哈密顿量,运用Huybrechts变分法重新计算了二维声学极化子基态能量和有效质量.通过改进自陷转变点的确定方式,得出了二维声学极化子自陷的转变点随声子截止波矢的增大向电子—声子耦合较弱的方向移动的结论.该结论与三维声学极化子自陷的结论定性一致,在物理上较为合理.
导出了描述二维电子—纵声学声子相互作用的新哈密顿量,通过计算基态能量和有效质量及其对电子—声子耦合常数的数值导数,考察了二维声学极化子自陷的条件,获得了自陷转变的判据.为便于比较,重新计算并给出了三维声学极化子基态能量及其导数的数值结果.比较后发现,我们的三维结果与前人采用Feynman路径积分方法所得结果基本一致.声子截止波矢相同的条件下,声学极化子在二维系统中自陷的临界电子—声子耦合常数比在三维情形要小得多.运用本文获得的判据,理论判断了几种实际材料中声学极化子自陷的可能性.结果表明:虽然GaN中的空穴、AlN中的电子和轻空穴不会在三维结构中发生自陷转变,但有可能在二维系统中自陷.
考虑到极化子自陷时的局域特性,我们采用高斯型束缚波函数计算了二维声学极化子基态能量.结果表明:采用高斯型束缚波函数的变分计算结果与运用类Huybrechts变分法引入坐标、动量线性组合算符描述所得结果相同.从理论推导和数值计算两方面佐证了Huybrechts变分法适用于整个电子—声子耦合区间,是研究声学极化子自陷行之有效的方法.
进一步导出了一维电子—声学声子相互作用哈密顿量.通过计算一维声学极化子基态能量和有效质量,以及基态能量对电子—声子耦合常数的一阶、二阶导数,考察了一维声学极化子自陷的相关问题,获得了一维声学极化子自陷转变的判据.类似于二维和三维结果,其临界电子—声子耦合常数与声子截止波矢的乘积趋于定值,但比二维和三维情形的相应值都小得多.比较后发现:声学极化子自陷的可能性随其维度的降低而增大.理论判定声学极化子在GaN和AlN,以及碱卤化物的一维结构中能够自陷.
根据Yu等人给出的电子—声子相互作用哈密顿量,采用变分法计算了不同半径的柱型量子线中声学极化子基态能量及其对电子—声子耦合常数的数值导数,考察了柱型量子线中声学极化子自陷的可能性,获得了相应的判据.结果表明:量子线中声学极化子自陷的临界电子—声子耦合常数随着声子截止波矢的增大向耦合较弱的方向变化;声学极化子在量子线中自陷的临界点介于在一维和三维系统中自陷的临界点之间;半径越小,量子线中声学极化子的自陷转变越容易发生.
Self-trapping transition of acoustic polarons in lower dimensional systems and the relative problems are studied in this thesis.
Farias et al pointed out that the critical electron-longitudinal acoustic-phonon (e-LA-p) coupling constant of the self-trapping transition of acoustic polarons in two dimensional(2D) systems is a certain value and independent of the cut-off wave vector.This conclusion is doubtful in Physics.The ground-state energy and effective mass of acoustic polarons in 2D systems are recalculated by using Huybrechts-like approach.The new self-trapping transition point is determined by a modified method. It is found that the critical point of the transition shifts toward the weaker e-LA-p coupling with increasing the cut-off wave vector.The results are qualitatively consistent with the previous works of the 3D acoustic polarons and more intelligible physically than that given by Farias et al.
A new 2D e-LA-p interaction Hamiltonian is derived.The numerical results for the ground-state energy and effective mass of the acoustic polarons in 2D system and their derivatives with respect to the e-LA-p coupling constant are obtained and used to investigate the criterion of the self-trapping transition.For ease of comparison,the ground-state energies of the acoustic polarons in 3D and their derivatives are also calculated here.The 3D results agree with those obtained by using the Feynman path-integral approach.It is found that the critical coupling constant of the transition from the quasi-free state to the self-trapped state in the 2D case is much smaller than that in 3D for the given cut-off wave vector.The theory has been used to judge the possibility of the self-trapping transition for several real materials.The results indicate that the self-trappings of the electrons and light holes in A1N and the holes in GaN are expected to be observed in 2D systems.
Considering the localization of the self-trapped states of acoustic polarons,the ground-state energy of the 2D acoustic poalron as a function of the e-LA-p coupling constant is investigated by using the localized Gaussian wave function.The results indicated that the Huybrechts-like approach is equivalent to the variational approach by using the Gaussian wave function.It is confirmed that the Huybrechts approach is an effective method to calculate the ground-state energies of acoustic polarons in the whole coupling range and investigate the self-trapping.
The ground-state energy and effective mass of the 1D acoustic polarons are calculated by using an e-LA-p interaction Hamiltonian derived here.The first and second derivatives of the ground-state energy are calculated.The self-trapping of the acoustic polarons is discussed.It is found that the products of the critical coupling constant by the cut-off wave vector tend to a certain value.The critical coupling constant of the transition from quasi-free state to the self-trapped state in 1D case is much smaller than that in 3D and 2D systems for a given cut-off wave vector.The self-trapping transition of acoustic polarons is expected to be observed in the one dimensional systems of alkali halides and wide-band-gap semiconductors.
The ground-state energies and their derivatives of the acoustic polarons in cylindrical quantum wire with different radius are variationally calculated by using the e-LA-p coupling Hamiltonian given by Yu et al.The possibility of self-trapping transition of the acoustic polarons is investigated.It is indicated that the critical coupling constant shifts toward the weaker e-LA-p coupling with increasing the cut-off wave vector.The critical value of self-trapping transition of the acoustic polarons in the quantum wire is between those in ID and 3D systems.The self-trapping transition of acoustic polarons occurs easier with decreasing the radius of the quantum wire.
指出了Farias等人在文献[66]中给出的二维声学极化子自陷转变的临界电子—声子耦合常数为定值,不随声子截止波矢的改变而变化的结论不符合声学极化子自陷的一般规律.我们采用与该文相同的哈密顿量,运用Huybrechts变分法重新计算了二维声学极化子基态能量和有效质量.通过改进自陷转变点的确定方式,得出了二维声学极化子自陷的转变点随声子截止波矢的增大向电子—声子耦合较弱的方向移动的结论.该结论与三维声学极化子自陷的结论定性一致,在物理上较为合理.
导出了描述二维电子—纵声学声子相互作用的新哈密顿量,通过计算基态能量和有效质量及其对电子—声子耦合常数的数值导数,考察了二维声学极化子自陷的条件,获得了自陷转变的判据.为便于比较,重新计算并给出了三维声学极化子基态能量及其导数的数值结果.比较后发现,我们的三维结果与前人采用Feynman路径积分方法所得结果基本一致.声子截止波矢相同的条件下,声学极化子在二维系统中自陷的临界电子—声子耦合常数比在三维情形要小得多.运用本文获得的判据,理论判断了几种实际材料中声学极化子自陷的可能性.结果表明:虽然GaN中的空穴、AlN中的电子和轻空穴不会在三维结构中发生自陷转变,但有可能在二维系统中自陷.
考虑到极化子自陷时的局域特性,我们采用高斯型束缚波函数计算了二维声学极化子基态能量.结果表明:采用高斯型束缚波函数的变分计算结果与运用类Huybrechts变分法引入坐标、动量线性组合算符描述所得结果相同.从理论推导和数值计算两方面佐证了Huybrechts变分法适用于整个电子—声子耦合区间,是研究声学极化子自陷行之有效的方法.
进一步导出了一维电子—声学声子相互作用哈密顿量.通过计算一维声学极化子基态能量和有效质量,以及基态能量对电子—声子耦合常数的一阶、二阶导数,考察了一维声学极化子自陷的相关问题,获得了一维声学极化子自陷转变的判据.类似于二维和三维结果,其临界电子—声子耦合常数与声子截止波矢的乘积趋于定值,但比二维和三维情形的相应值都小得多.比较后发现:声学极化子自陷的可能性随其维度的降低而增大.理论判定声学极化子在GaN和AlN,以及碱卤化物的一维结构中能够自陷.
根据Yu等人给出的电子—声子相互作用哈密顿量,采用变分法计算了不同半径的柱型量子线中声学极化子基态能量及其对电子—声子耦合常数的数值导数,考察了柱型量子线中声学极化子自陷的可能性,获得了相应的判据.结果表明:量子线中声学极化子自陷的临界电子—声子耦合常数随着声子截止波矢的增大向耦合较弱的方向变化;声学极化子在量子线中自陷的临界点介于在一维和三维系统中自陷的临界点之间;半径越小,量子线中声学极化子的自陷转变越容易发生.
Self-trapping transition of acoustic polarons in lower dimensional systems and the relative problems are studied in this thesis.
Farias et al pointed out that the critical electron-longitudinal acoustic-phonon (e-LA-p) coupling constant of the self-trapping transition of acoustic polarons in two dimensional(2D) systems is a certain value and independent of the cut-off wave vector.This conclusion is doubtful in Physics.The ground-state energy and effective mass of acoustic polarons in 2D systems are recalculated by using Huybrechts-like approach.The new self-trapping transition point is determined by a modified method. It is found that the critical point of the transition shifts toward the weaker e-LA-p coupling with increasing the cut-off wave vector.The results are qualitatively consistent with the previous works of the 3D acoustic polarons and more intelligible physically than that given by Farias et al.
A new 2D e-LA-p interaction Hamiltonian is derived.The numerical results for the ground-state energy and effective mass of the acoustic polarons in 2D system and their derivatives with respect to the e-LA-p coupling constant are obtained and used to investigate the criterion of the self-trapping transition.For ease of comparison,the ground-state energies of the acoustic polarons in 3D and their derivatives are also calculated here.The 3D results agree with those obtained by using the Feynman path-integral approach.It is found that the critical coupling constant of the transition from the quasi-free state to the self-trapped state in the 2D case is much smaller than that in 3D for the given cut-off wave vector.The theory has been used to judge the possibility of the self-trapping transition for several real materials.The results indicate that the self-trappings of the electrons and light holes in A1N and the holes in GaN are expected to be observed in 2D systems.
Considering the localization of the self-trapped states of acoustic polarons,the ground-state energy of the 2D acoustic poalron as a function of the e-LA-p coupling constant is investigated by using the localized Gaussian wave function.The results indicated that the Huybrechts-like approach is equivalent to the variational approach by using the Gaussian wave function.It is confirmed that the Huybrechts approach is an effective method to calculate the ground-state energies of acoustic polarons in the whole coupling range and investigate the self-trapping.
The ground-state energy and effective mass of the 1D acoustic polarons are calculated by using an e-LA-p interaction Hamiltonian derived here.The first and second derivatives of the ground-state energy are calculated.The self-trapping of the acoustic polarons is discussed.It is found that the products of the critical coupling constant by the cut-off wave vector tend to a certain value.The critical coupling constant of the transition from quasi-free state to the self-trapped state in 1D case is much smaller than that in 3D and 2D systems for a given cut-off wave vector.The self-trapping transition of acoustic polarons is expected to be observed in the one dimensional systems of alkali halides and wide-band-gap semiconductors.
The ground-state energies and their derivatives of the acoustic polarons in cylindrical quantum wire with different radius are variationally calculated by using the e-LA-p coupling Hamiltonian given by Yu et al.The possibility of self-trapping transition of the acoustic polarons is investigated.It is indicated that the critical coupling constant shifts toward the weaker e-LA-p coupling with increasing the cut-off wave vector.The critical value of self-trapping transition of the acoustic polarons in the quantum wire is between those in ID and 3D systems.The self-trapping transition of acoustic polarons occurs easier with decreasing the radius of the quantum wire.
引文
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