The temperature effects of the tunable zero-Landau lever (LL) energy are studied using the Lee-Low-Pines (LLP) variational and quantum statistical theory in the presence of a magnetic field $B$ on monolayer graphene of different polar substrates. This zero-LL energy was induced by the surface optical phonon polaron in monolayer graphene on polar substrates. We found that zero-LL splitting energy can be tuned by controlling the polarization strength $\eta$of the polar substrate, confinement strength parameter g, magnetic field $B$, and temperature $T$. The magnetic field has a negligible impact on the zero-LL splitting energy. And the temperature effect of zero-LL splitting energy of graphene substrates is further enhanced by Coulomb potential. The results obtained in the study provide new information about the fundamental properties of graphene on substrates at different temperatures $T$.

在存在磁场的情况下，使用 Lee-Low-Pines (LLP) 变分和量子统计理论研究了可调零朗道杠杆 (LL) 能量的温度效应 $乙$在不同极性基材的单层石墨烯上。这种零 LL 能量是由极性基底上单层石墨烯中的表面光学声子极化子引起的。我们发现可以通过控制极化强度来调整零 LL 分裂能量$\eta$极性基体，约束强度参数 g，磁场 $乙$, 和温度 $吨$. 磁场对零 LL 分裂能的影响可以忽略不计。库仑势进一步增强了石墨烯衬底的零 LL 分裂能的温度效应。研究中获得的结果提供了有关石墨烯在不同温度下基板上的基本特性的新信息$吨$.