发表机构
Zhejiang Normal University（浙江师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
利用狄拉克方程的洛伦兹协变性求解电磁场中的狄拉克费米子，揭示磁区与电区中克莱因隧穿的不同行为，为电磁调控隧穿及新型器件设计提供理论依据。
AI 中文摘要
相对论性狄拉克方程的洛伦兹协变性是不同惯性系中电磁学定律的基本原理。利用这一协变性，我们得到了狄拉克费米子在面内电场 $\oldsymbol{E}$ 和垂直磁场 $\oldsymbol{B}$ 共同作用下的通解，这些解在漂移速度沿 $\oldsymbol{E}\ imes\oldsymbol{B}$ 方向的惯性系中可简化为纯磁场或纯电场情形。这种二分法定义了磁区和电区，由临界场比 $E/B=v_\ ext{F}$ 分隔，其中 $v_\ ext{F}$ 表示狄拉克费米子的费米速度。利用这些解，我们重新审视了通过具有广义电磁势的异质结的克莱因隧穿。在磁区，透射率表现出由法布里-珀罗干涉控制的振荡。在电区，在漂移参考系中正入射时发生完美透射。进一步从布洛赫球上的立体角角度分析了干涉相位，为克莱因隧穿提供了几何解释。最后，我们简要讨论了狄拉克锥倾斜与面内电场之间的关系，建立了欠倾斜和过倾斜情形分别对应于磁区和电区的对应关系。我们的发现揭示了电磁场对克莱因隧穿的调控，为设计新型电子器件提供了理论基础。
英文摘要
The Lorentz covariance of relativistic Dirac equations serves as a fundamental principle underlying the laws of electromagnetism across different inertial frames. Exploiting the covariance, we obtain the general solutions for Dirac fermions under both the in-plane electric $\boldsymbol{E}$ and perpendicular magnetic $\boldsymbol{B}$ fields, which reduce to either a magnetic or electric field in the inertial frame with drift velocity along the $\boldsymbol{E}\times\boldsymbol{B}$ direction. This dichotomy defines the magnetic and electric regimes, separated by the critical field ratio $E/B=v_\text{F}$ with $v_\text{F}$ denoting the Fermi velocity of Dirac fermions. Using these solutions, we revisit Klein tunneling through a heterojunction with generalized electromagnetic potentials. In the magnetic regime, the transmission exhibits oscillations governed by the Fabry-Pérot interference. In the electric regime, perfect transmission occurs at normal incidence in the drifted frame. The interference phase is further analyzed in terms of the solid angles on the Bloch sphere, providing a geometric interpretation of Klein tunneling. Finally, we briefly discuss the relation between the tilting of Dirac cones and the in-plane electric field, establishing the correspondence of the undertilted and overtilted cases to the magnetic and electric regimes, respectively. Our findings reveal the manipulation of Klein tunneling by electromagnetic fields, offering a theoretical basis for designing novel electronic devices.
Comments6 pages, 3 figures
