在考虑Rashba自旋-轨道耦合效应下，基于Lee-Low-Pines变换，采用Pekar型变分法研究了量子点中双极化子的基态性质。数值结果表明，在电子-声子强耦合(耦合常数α>6)条件下，量子点中形成稳定双极化子结构的条件(结合能Eb >0)自然满足；双极化子的结合能Eb随量子点受限强度ω0、介质的介电常数比η和电子-声子耦合强度α的增大而增加，随Rashba自旋-轨道耦合常数αR 的增加表现为直线增加和减小两种截然相反的情形；Rashba效应使双极化子的基态能量分裂为E (↑↑)， E (↓↓)和E (↑↓)三条能级，分别对应两电子的自旋取向为“向上”、“向下”和“反平行”三种情形；基态能量的绝对值|E|随η和α的增加而增大，随αR 的增加表现为直线增加和减小两种截然相反的情形；在双极化子的基态能量E 中，电子-声子耦合能所占据的比例明显大于Rashba自旋-轨道耦合能所占比例，但电子-声子耦合与Rashba自旋-轨道耦合间相互渗透、彼此影响显著。%In this paper, based on the Lee-Low-Pines transformation, the ground-state properties of the bipolaron with the Rashba spin-orbit coupling effect in the quantum dot are studied by using the Pekar variational method. The expressions for the ground-state interaction energy Eint and binding energy Eb of the bipolaron are derived. The results show that Eint is composed of four parts: the electron-longitudinal optical (LO) phonon coupling energy Ee-ph, confinement potential of the quantum dot Ecouf, Coulomb energy between two electrons Ecoul and additional term in the Rashba spin splitting energy ER-ph originating from the LO phonon, where Ecouf and Ecoul are positive definite. These indicate that Ecouf and Ecoul are the repulsive potential of the bipolaron. Generally, it is unable to form the electron-electron coupling structure in the quantum dot because two electrons repel each other by means of the screened Coulomb potential and confinementpotential of the quantum dot. However, the numerical results show that the ground-state binding energy of the bipolaron Eb is greater than zero under the condition of the electron-phonon strong coupling (coupling strengthα > 6), so the condition of forming the steady bipolaron structure in quantum dots is naturally met (binding energy Eb > 0). In addition, the ground-state energy of the bipolaron E is always less than zero, thus the ground-state biplaron in the quantum dot is in the steady bound state. This can be explained by the physical mechanism. Firstly, the electron-LO phonon coupling energy Ee-ph in the ground-state interaction energy of the bipolaron is always negative. Secondly, the electron-LO phonon coupling interaction in the low-dimensional structures of II-VI semiconductors is great enough (generallyα>6.0) so that the electron-LO phonon coupling energy Ee-ph is dominant in the ground-state energy E and, therefore the screened Coulomb potential and confinement potential of the quantum dot can be overcome and a steady electron-electron structure can be formed. The numerical results also indicate that the binding energy of the bipolaron Eb increases with increasing the confinement strength of quantum dotω0, dielectric constant ratio of mediumηand electron-phonon coupling strength α, but it shows the direct opposite cases from linear increase to decrease with increasing the Rashba spin-obit coupling strength αR; the ground-state energy of the bipolaron splits into three energy levels due to the Rashba effect: E(↑↑), E(↓↓) and E(↑↓), which correspond to spin orientations of two electrons respectively: “up”,“down”and“antiparallel”;the absolute value of ground-state energy|E|increases with increasingη andα, but it shows the direct opposite cases from linear increase to decrease with increasing the Rashba spin-obit coupling strengthαR;the electron-phonon coupling energy obviously accounts for a larger proportion than that of the Rashba spin-obit coupling energy in the ground-state energy of the bipolaron, but the electron-phonon coupling and Rashba spin-obit coupling infiltrate each other and influence each other significantly. In short, the electron in narrow-gap II-VI heterojunctions have higher Rashba spin splitting energy and larger application range. For these quantum dot structures, it is impossible and unnecessary to inhibit the formation of bipolarons. It is more accurate that the bipolaron is chosen as the elementary excitation than the single polaron when investigating the electron-phonon interaction and Rashba spin-orbit coupling, and the bipolaron has more practical significances and potential application values.
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