标题： 完全屏蔽磁极化子在横向限制的各向异性二维电子系统中的约简为各向同性系统 显示英文标题

标题： Reduction of fully screened magnetoplasmons in a laterally confined anisotropic two-dimensional electron system to an isotropic one

摘要： 我们研究了在横向受限的电子系统（如二维材料、量子阱或半导体中的反转层）中自然存在的二维磁等离子体模式的性质，这些系统的费米面呈椭圆形。 系统中的电导率是在动态各向异性德鲁德模型中考虑的。 问题是在完全屏蔽极限下解决的，即假设二维电子系统与附近的金属栅极之间的距离远小于系统中的所有其他长度，包括等离子体波长。 值得注意的是，在此限制下，各向异性二维受限系统的等离子体振荡等效于通过某种拉伸得到的各向同性二维电子系统的等离子体振荡，即使考虑了电磁迟滞效应也是如此。 此外，考虑电磁迟滞效应只会导致载流子有效质量的重正化，类似于相对论中的情况。 作为示例，我们将描述带栅极圆盘中各向异性二维电子气等离子体的方程简化为描述各向同性椭圆振荡的方程。 在没有磁场的情况下，我们对其进行解析求解并找到本征频率。 为了在磁场中找到解，我们将等离子体振荡的电流展开为完整的马蒂厄函数集。 保留展开式的主项，我们近似地找到并分析最低模式的磁色散关系。 显示英文摘要

摘要： We investigate the properties of natural two-dimensional (2D) magnetoplasma modes in laterally confined electron systems, such as 2D materials, quantum wells, or inversion layers in semiconductors, with an elliptic Fermi surface. The conductivity of the system is considered in a dynamical anisotropic Drude model. The problem is solved in the fully screened limit, i.e., under the assumption that the distance between the two-dimensional electron system and the nearby metal gate is small compared to all other lengths in the system, including the wavelength of plasmons. Remarkably, in this limit plasma oscillations in an anisotropic 2D confined system are equivalent to plasma oscillations in an isotropic 2D electron system obtained by some stretching, even when the electromagnetic retardation is taken into account. Moreover, accounting for electromagnetic retardation leads only to a renormalization of the effective masses of carriers, somewhat like in relativity. As an example, we reduce the equations describing plasmons in a gated disk with an anisotropic two-dimensional electron gas to the equations describing oscillations in an isotropic ellipse. Without a magnetic field, we solve them analytically and find eigenfrequencies. To find a solution in a magnetic field, we expand the current of plasma oscillations in the complete set of Mathieu functions. Leaving the leading terms of the expansion, we approximately find and analyze magnetodispersion for the lowest modes.