AI 中文总结
研究指数衰减磁场中倾斜各向异性狄拉克费米子的朗道量子化，通过各向异性缩放和洛伦兹变换转化问题，得到隐式量子化条件与可允许态条件，建立统一框架，还能在适当极限下恢复已知均匀场能谱。
AI 中文摘要
我们为指数衰减磁场中倾斜各向异性狄拉克费米子的朗道量子化建立了一种解析理论。利用各向异性缩放和洛伦兹变换，将实验室坐标系问题转化为增强坐标系中的各向同性狄拉克方程，在此指数衰减磁场问题有精确解。将增强坐标系中的能谱转换回实验室坐标系得到一个具有内在能量依赖引导中心参数的隐式量子化条件。我们确定了物理可允许态的条件。进一步表明该形式体系在适当极限下恢复了倾斜各向异性狄拉克费米子的已知均匀场能谱。我们的结果建立了一个统一的洛伦兹协变框架，用于描述存在指数衰减磁场时倾斜各向异性狄拉克材料中的朗道量子化。
英文摘要
We develop an analytical theory of Landau quantization for tilted anisotropic Dirac fermions in an exponentially decaying magnetic field. Using anisotropy scaling and a Lorentz transformation, we recast the laboratory-frame problem into the isotropic Dirac equation in the boosted frame, where the exponentially decaying magnetic-field problem admits an exact solution. Transforming the boosted-frame spectrum back to the laboratory frame yields an implicit quantization condition with an intrinsically energy-dependent guiding-center parameter. We identify the conditions for physically admissible states. We further show that the formalism recovers the known uniform-field spectrum of tilted anisotropic Dirac fermions in the appropriate limit. Our results extend the Lorentz-covariant treatment of tilted anisotropic Dirac fermions to an exponentially decaying magnetic field and reveal the energy-dependent guiding-center structure generated by the inverse transformation to the laboratory frame.
Comments7 pages, 2 figures
