利用LLP幺正变换与线性组合算符相结合的方法研究了单层石墨烯(MG)中弱耦合极化子的性质。得出了单层石墨烯中弱耦合极化子的基态能量、第一激发态能量和跃迁能与振动频率、声子的德拜截止波数之间的依赖关系。结果表明,单层石墨烯中极化子的基态能量、第一激发态能量和跃迁能均为德拜截止波数的增函数；当振动频率增大时,基态能量随之增加,第一激发态能量先增加后减小再增加,直到趋于稳定的值,跃迁能量先增加后减小。

The LLP variational method with linear combination operator are used to study the properties of weak coupling polarons in monolayer graphene(MG). The relationships between the ground state energy of weak coupling polarons, Debye wavenumber of the phonon and the vibrational frequency have been investigated. It is found that the first excited state energy and transition energy(TE) of the polaron has a linear relationship with the Debye cut-off wavenumber(DW), and the vibrational frequency. The result of numerical calculation shows that the ground state energy, the first excited state energy and TE of the polaron in MG can be tunabled by controlling the DW and vibrational frequency. The ground state energy increases with the increase of DW and vibrational frequency, while the first excited state energy and transition energy are not monotone function of vibrational frequency.