The Properties of the Ground State of the Fröhlich Bipolaron with Rashba Spin-Orbit Coupling in a Quantum Dot∗

Abstract

The properties of the ground state of bipolarons with Rashba spin-orbit (SO) coupling in a quantum dot (QD) are studied by using the Lee-Low-Pines-Tokuda variational method. The results of numerical calculation indicate that the condition to form the stable bipolaron structure in the QD (binding energy E b > 0) is naturally satisfied with the electron-phonon strong coupling (coupling constant α > 6). The binding energy of bipolarons E b increases with the increase of the confinement strength ω 0 of the QD, electron-phonon coupling strength α, Coulomb bound potential β and velocity u of polarons. The ground energy of bipolarons E splits into E(+) and E(−), corresponding to spin both “up” and both “down” of two electrons, respectively, and $\left | {E(-)} \right |>\left | {E(+)} \right |$ . The grouenergy of bipolarons E in the QD is composed of the electron-phonon coupling energy E e-ph, confinement potential of the QD E couf, Coulomb energy between two electrons E coul and Rashba SO coupling energy E SO. E e-ph is always negative and plays a dominant role. The weights of E coul and E couf are only next to E e-ph. Though the weight of the Rashba SO coupling energy E SO is the smallest one, it can influence other parts of the ground-state energy through interacting with the phonon. Therefore, the bipolaron effect and Rashba SO coupling must not be ignored when investigating the QD.