Ng R A, Wild A, Portnoi M E, Hartmann R R
Physics Department, De La Salle University, 2401 Taft Avenue, 0922, Manila, Philippines.
Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK.
Sci Rep. 2022 May 10;12(1):7688. doi: 10.1038/s41598-022-11742-3.
We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given one-dimensional (1D) potential are known, then they can be used to obtain the eigenvalues and eigenfunctions for the same potential, orientated at an arbitrary angle, in a 2D Dirac material possessing tilted, anisotropic Dirac cones. This simple set of transformations enables all the exact and quasi-exact solutions associated with 1D quantum wells in graphene to be applied to the confinement problem in tilted Dirac materials such as 8-Pmmn borophene. We also show that smooth electron waveguides in tilted Dirac materials can be used to manipulate the degree of valley polarization of quasiparticles travelling along a particular direction of the channel. We examine the particular case of the hyperbolic secant potential to model realistic top-gated structures for valleytronic applications.
我们证明，如果已知给定一维（1D）势的（2 + 1）维无质量狄拉克方程的解，那么在具有倾斜、各向异性狄拉克锥的二维狄拉克材料中，这些解可用于获得同一势在任意角度取向时的本征值和本征函数。这组简单的变换使得与石墨烯中一维量子阱相关的所有精确和准精确解都能应用于诸如8 - Pmmn硼烯等倾斜狄拉克材料中的限制问题。我们还表明，倾斜狄拉克材料中的光滑电子波导可用于操纵沿通道特定方向传播的准粒子的谷极化程度。我们研究了双曲正割势的特殊情况，以模拟用于谷电子学应用的实际顶部栅极结构。
