自陷电子对了解光电材料的光学性质非常重要.近些年来,形变晶格中电子自陷的问题受到研究人员的广泛关注.电子既与声学模耦合,也与光学模相互作用,但电子由自由态向自陷态的转变缘于近程的电子-声学声子耦合.研究表明:声学极化子在大多数半导体以及Ⅲ-Ⅴ族化合物,甚至碱卤化物中都不可能自陷.另一方面,电子-声子耦合在束缚结构,如二维、一维系统中,会有所增强.换言之,电子在低维结构中更容易自陷.Farias等人指出:声学极化子在二维系统中自陷的临界电子-声子耦合常数为定值,不随声子截止波矢的变化而改变.这种结论在物理上不尽合理.通过计算二维系统中的声学极化子基态能量和有效质量,讨论了二维声学极化子自陷问题.研究发现,二维声学极化子自陷转变的临界耦合常数随声子截止波矢的增加朝电子-声子耦合较弱的方向变化.这一特征与前人关于体和表面极化子研究获得的结论定性一致.所得二维声学极化子基态能量的表达式与Farias 等人一致,但自陷的结果与Farias 等人的结果在定性和定量上均有不同,我们认为Farias等人关于二维声学极化子自陷转变点的确定方式有不妥之处.通过改进自陷转变点的确定方式,得到了在物理上更合理的结果.%The trapping electrons have been used to explore the luminous property of the photoelectric materials. The self-trapping of an electron in a deformable lattice has been maintained interests of many scientists in the past decades. For weak electron-phonon (e-p) coupling, one expects that the electron behaves as a quasi-free particle ("free polaron") and should be de-localized over all sites, whereas for very strong coupling it is conceivable that the electron is self-trapped by phonons. Various calculations for the ground-state energies of the polarons as functions of the e-p coupling strength have led to a transition from the quasi-free state to the self-trapped state. This transition phenomenon was also called "phase transition", though it is not a real phase transition in the general sense. An electron interacts with the acoustic and optical modes of the lattice vibration in a polar crystal. However, the abrupt change of the polaron state from the quasi-free state to the self-trapping state is usually caused by the short-range acoustic interaction, i.e. the electron-longitudinal-acoustic-phonon (e-LA-p) coupling, but not by the long range longitudinal-optical (LO)-phonon interaction. It has been indicated that the acoustic polarons in three-dimensional (3D) bulk materials are difficult to be trapped in most semiconductors and Ⅲ-Ⅴ compounds, even in alkali halides. Otherwise, the e-p coupling effects would be substantially enhanced in confined structures, such as two-dimensional (2D) and one-dimensional (1D) systems, so that the self-trapping transition may be easier to be realized. Farias et al pointed out that the critical e-LA-p coupling constant of the self-trapping transition of acoustic polarons in 2D systems is a certain value and independent of the cutoff wave vector. This conclusion is doubtful in Physics. The ground state energy and effective mass of the acoustic polaron in 2D systems are calculated by using the Huybrechts-like approach in two-step according to the weak and strong e-p coupling ranges. The self-trapping of the 2D acoustic polaron is discussed. The new self-trapping transition point is determined by the intersection point of the lines of ground state energies in weak and strong coupling ranges. It is found that the critical coupling constant of the self-trapping transition of the 2D acoustic polaron shifts toward the weaker e-p coupling with the increasing cutoff wave vector. The characters of the self-trapping of the 2D acoustic polron are qualitative consistent with the previous works of surface polaron and 3D acoustic polaron. There are both the quantitative and the qualitative differences in the critical coupling constants of the self-trapping of the 2D acoustic polarons obtained in this paper and the results given by Farias et al. Our results are more intelligible than that given by Farias et al in sense of the physics.
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