极性超晶格中电子—声子的相互作用

本文在Wendler、潘金声研究双层极性晶体时得出的声子振动极化场所满足的微分、积分方程及归一化条件的基础上,讨论周期性排列的层状极性晶体中声子振动极化场所满足的微分、积分方程,得到了SO声子的色散关系,SO声子和LO声子极化强度矢量.用声子产生、湮灭算符表出了声子振动能量及电子—声子的相互作用哈密顿量.

ELECTRON-PHONON INTERACTION IN POLAR SUPERLATTICE

In this paper,we extend the theoretic consideration of the electron-phonon inteiaction for a dielectric bilayer system to polar superlattice consisting of two alternately arranged different dielectric layers,assuming that the long wave approximation of the lattice vibration is still suitable for the superlattice.The integral equation characterizing the polarization eigenmodes of the superlattice is derived,as given by(2-3)-(2-5)in the text.One can see from this result that the superlattice can be regarded as an equivelent bilayer system with different boundary condition from simple bilayer.It is also verified that the differential equation satisfied by the polatization vector for the supsrlattice is as the same as for the real bilayer.The dispersion relation is derived from the boundary conditions suited for superlattice,which is given by(4-8).In this expression,a and b are the thickness of each layer,d=a+b,is the periodic length of the superlattice.When N,the number of periodic layers of superlattice,approaches infinity,i.e.N→∞,the dispersion relation is reduced to(4-9).It is droved from calculation that as long as N is larger than 20,such a supeilat-tice can be regarded as one with infinite layer number.If N=0,a→∞ and b→∞,the dispersion relation(4-8)is reduced to(4-11).When a→∞,the dispersion relation(4-8)is reduced to(4-12),and this is just the case of single qauntum well.The interaction Hamiltonian of the charged particle with SO phonon is obtaind,as given by(3-7),(4-15)and(4-16).Because the charged particle interacts only with the LO phonon of the dielectric layer in which the charged particle is located,the interaction Hamiltonian of the charged particle with LO phonons for superlattice is as the same as for the bilayer.We also extend the above discussion to the semi-infinite superlattice.We assume that the semiinfinite superlattice occupying the space oi z>0,and the space of z<0 is vacuum or the third media with dielectric function ε3(ω).In this case,the dispersion relation is derived,as given by(5-12).In addition,the interaction Hamiltonain oi the charged particle with SO and LO phonon is completely as the same as for the infinite superlattice.