中文摘要：

我们研究了包含自旋轨道耦合与杂质散射在内的石墨烯量子磁振荡对外加电磁场的响应．我们发现，石墨烯中自旋轨道耦合、电磁场以及边界共同修正了朗道能谱，且当电场与磁场比值超过某一临界值时，量子磁振荡会突然消失，这与非相对论二维电子气的情况显著不同．这种现象可以通过朗道量子化轨道由封闭转化为开放的半经典理论来解释．此外，我们还发现杂质散射和温度的共同作用会使得磁振荡振幅衰减．我们的结果可用于分析石墨烯及其类似结构（硅烯、锗烯、锡烯等）的费米能级与朗道能谱的相互作用，进而探测自旋轨道耦合引起的能隙．

英文摘要：

We have investigated the quantum magnetic oscillations of graphene subjected to the spin-orbit interaction （SOI） in the presence of crossed uniform electric and magnetic fields and scattered from impurities at finite temperatures. Landau levels are shown to be modified in an unexpected fashion by the spin-orbit interaction, the electrostatic potential and magnetic confinement; this is strikingly different from the non-relativistic 2D electron gas. Furthermore, we derive the analytical expressions of the thermodynamic quantities subject to the SOI, such as density of states, thermodynamic potential, magnetization, and magnetic susceptibility etc. At finite temperatures, the magnetization and magnetic susceptibility can both be predicted to oscillate periodically as a function of reciprocal field 1/B and shown to be modulated through the SOI and the dimensionless parameter （β = E/vFB）. As β approaches unity, the values of magnetization and magnetic susceptibility finally move to infinity, indicating a transformation of closed orbits into open trajectories, thereby, leading to the vanishing of magnetic oscillations. And, the magnetic susceptibility depends largely on the external fields, suggesting that graphene should be a non-linear magnetic medium. Besides, the associative effect of impurity scattering and temperature may make the standard 2D electron gas be deemed as the consequence of the relativistic type spectrum of low energy electrons and holes in graphene. Also, we comment on a possibility of using magnetic oscillations for detecting a gap that may open in the spectrum of quasiparticle excitations due to the SOI.