论文标题
电石墨烯表面上电子动力学的数值准形式转换
Numerical quasi-conformal transformations for electron dynamics on strained graphene surfaces
论文作者
论文摘要
一般静态电石石墨烯表面中低能电子的动力学是通过曲线时空中的Dirac方程来数学建模的。在笛卡尔坐标中，可以直接获得表面的参数化，但是所得的狄拉克方程对于一般的表面变形来说是复杂的。引入了两种不同的策略来简化此问题：对角线度量近似以及变量变化为等温坐标。这些坐标是从以Beltrami方程为特征的准符合形式转换获得的，其解决方案给出了两个坐标系之间的映射。为了实施第二种策略，引入了最小二乘有限元数值方案来解决Beltrami方程。然后，通过在伪缓存表示中的精确伪柔性数值方法来求解dirac方程，该方法具有明确的单一进化和对标准的显式统一进化和保护。比较这两种方法，并应用于高斯形石墨烯表面变形上电子的散射。证明电子波包可以由这些局部紧张的区域聚焦。
The dynamics of low energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a parametrization of the surface can be straightforwardly obtained, but the resulting Dirac equation is intricate for general surface deformations. Two different strategies are introduced to simplify this problem: the diagonal metric approximation and the change of variables to isothermal coordinates. These coordinates are obtained from quasi-conformal transformations characterized by the Beltrami equation, whose solution gives the mapping between both coordinate systems. To implement this second strategy, a least square finite-element numerical scheme is introduced to solve the Beltrami equation. The Dirac equation is then solved via an accurate pseudo-spectral numerical method in the pseudo-Hermitian representation that is endowed with explicit unitary evolution and conservation of the norm. The two approaches are compared and applied to the scattering of electrons on Gaussian shaped graphene surface deformations. It is demonstrated that electron wave packets can be focused by these local strained regions.
