基于维格纳方程的电子的古斯-汉欣位移

通过求解电子的维格纳方程研究二维电子气中电子的输运性质。我们发现电子在倾斜入射到势垒界面并反射时, 出现与光波类似的古斯-汉欣位移。通过维格纳方程可以得到电子的瞬态演化, 不仅可以计算古斯-汉欣位移还能研究电子在势垒内部的运动轨迹以及出现稳定古斯-汉欣位移的时间。与稳定相位法得到的古斯-汉欣位移对比发现, 考虑古斯-汉欣位移的界面反射较几何光学反射在时间上有一定迟缓, 这种迟缓与入射角无关, 但会随着势垒宽度的增加而增加; 电子的古斯-汉欣位移与势垒厚度无关, 随着入射角或入射能量的增大而增大。基于此, 我们提出一种电子分束器模型, 向输入端注入初始动能不同的高斯波包, 当电子能量低于0.01 eV时, 约85%的电子运动至第二输出端; 而当电子能量高于0.07 eV时, 约85%的电子运动至第一输出端。

Goos-Hanchen Shift of Electrons Based on Wigner Equation

We studied transport properties of electrons in two-dimensional electron gas with Wigner equation. It was found that as electrons enter the barrier interface obliquely and are reflected, Goos-Hanchen shift similar to light waves presents. With Wigner equation we get transient evolution of electrons, with which we can calculate Goos-Hanchen shift and study trajectory of electrons inside the potential barrier as well. Compared with Goos-Hanchen shift obtained with the stable phase method, it is found that the interface reflection considering Goos-Hanchen shift has a certain retardation in time compared with geometric optical reflection, which is independent of incident angle, but increases with the increase of width. However, Goos-Hanchen shift of electrons is independent of barrier width and increases with the incident angle or incident energy. According to this, we propose an electron beam splitter model in which Gaussian wave packets with different initial kinetic energies inject into the input. As electron energy is below 0. 01 eV, about 85% of the electrons move to the second output, while as electron energy is above 0. 07 eV, about 85% of the electrons move to the first output.