论文标题
温度对2D材料中磁振荡的影响
Temperature effect on the magnetic oscillations in 2D materials
论文作者
论文摘要
我们考虑垂直电场和磁场，研究带有弯曲蜂窝晶格的2D材料中的磁振荡（MO）。在零温度下，MO由四个锯齿振荡的总和组成，具有两个独特的频率和相。这些频率的值取决于费米的能量和电场，这又决定了MO中击败现象的条件。我们通过考虑Fermi-Dirac喜欢功能给出的每个磁化峰上的局部校正来分析MO中的温度效应。我们表明，这些功能的宽度与观察MO中旋转和山谷特性所需的最低温度有关。特别是，我们发现要观察自旋分裂，宽度必须低于MO相差。同样，为了观察山谷混合效应，宽度必须低于MO周期。我们还表明，在高温下，MO中的所有最大值和最小值都转移到恒定值，在这种情况下，我们获得了MO及其包膜的简单表达式。获得的结果显示了由山谷和自旋之间的相互作用给出的2D材料中MO中的独特特征。
We study the magnetic oscillations (MO) in 2D materials with a buckled honeycomb lattice, considering a perpendicular electric and magnetic field. At zero temperature the MO consist of the sum of four sawtooth oscillations, with two unique frequencies and phases. The values of these frequencies depend on the Fermi energy and electric field, which in turn determine the condition for a beating phenomenon in the MO. We analyse the temperature effect in the MO by considering its local corrections over each magnetization peak, given by Fermi-Dirac like functions. We show that the width of these functions is related to the minimum temperature necessary to observe the spin and valley properties in the MO. In particular, we find that in order to observe the spin splitting, the width must be lower than the MO phase difference. Likewise, in order to observe valley mixing effects, the width must be lower than the MO period. We also show that at high temperatures, all the maxima and minima in the MO are shift to a constant value, in which case we obtain a simple expression for the MO and its envelope. The results obtained show unique features in the MO in 2D materials, given by the interplay between the valley and spin.
