磁诱导三维拓扑绝缘体波导中的导模

Guide Modes in Three-dimensional Topological Insulator Waveguide Induced by Magnetic Fields

在三维拓扑绝缘体表面上外加铁磁条形成的磁势垒量子阱,通过控制入射电子能量,使得入射电子波限制在势阱中传播,并由波函数的连续性求得磁诱导三维拓扑绝缘体波导的色散方程.由于此方程是超越方程,不能解析求解,因此本文采用图解法求解色散方程的解.研究表明:在入射电子能量大于磁势垒和小于磁势垒的情况下,都能够形成波导;当入射电子的能量大于磁矢势时,波导能够支持基模,而且模式阶数也依次递增;而当入射电子能量小于磁矢势时,波导能够承载的导模数量有所减少.通过研究波导中导模几率密度的空间分布,发现三维拓扑绝缘体表面上磁场诱导的电子波导能够很好地束缚电子,而且低阶模对电子的束缚能力强于高阶模.此外,本文也推导出了波导的几率流密度分布的公式.

A magnetic quantum well created by putting two ferromagnetic metal stripes on the three-dimensional topological insulator is investigated.The incident electron waves are confined in the quantum well by controlling the incident energy.The dispersion equation of the waveguide is obtained with the continuity of the wave functions.The graphical method is applied to solve this equation since it is a transcendental equation,of which the solution can not be obtained with analytic method.Whether the energy of the incident electrons is higher than the magnetic barrier or not,the electron waveguide can be formed.The waveguide supports the fundamental mode for the higher incident electron energy.The order of the modes increases with the increasing electron energy.The number of the guided modes decreases for the lower incident electron energy.The probability density of spatial distribution is studied.It shows that the three-dimensional topological insulator waveguide induced by magnetic fields can confine electrons well and the lower guided modes can confine electrons better than the higher guided modes.Moreover,the function of the probability current density distribution in the waveguide is also presented.