Within the position-dependent translation operator formalism for quantum systems, we obtain analytical expressions for the eigenstates and the Landau level spectrum of Dirac fermions in graphene in the presence of a perpendicularly applied magnetic field and, as a consequence of the formalism, with a generalized form of the momentum operator. Moreover, we explore the behavior of wave packet dynamics in such a system by considering different initial pseudospin polarizations and metric parameters. Our findings show that the Landau levels, the wave packet trajectories, and velocities are significantly affected by the choice of the metric in the non-Euclidean space of the deformed momentum operator, exhibiting a tunable energy level spacing. In the dynamics analysis, one observes an enhancement of the oscillation amplitude of the average positions for all investigated pseudospin polarizations due to the nonsymmetric evolution of the wave packet induced by the different metrics in the system. The present formalism is shown to be a theoretical platform to describe the effects of two scenarios due to (i) a lattice deformation in graphene, giving rise to a natural Fermi velocity renormalization, or even (ii) a nonuniform mass term, induced by a specific substrate, that varies on a length scale much greater than the magnetic field length.

中文翻译：

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石墨烯中的狄拉克费米子依赖于位置的翻译算符形式

在量子系统的位置相关的平移算符形式主义中，我们获得了存在垂直施加磁场的情况下石墨烯中狄拉克费米子的本征态和朗道能级谱的解析表达式，并且形式主义的结果​​是，动量算子的形式。此外，我们通过考虑不同的初始伪自旋极化和度量参数来探索这种系统中波包动力学的行为。我们的发现表明，在变形动量算子的非欧几里得空间中，度量的选择显着影响了Landau能级，波包轨迹和速度，从而显示出可调整的能级间距。在动力学分析中，人们观察到，由于系统中不同度量引起的波包的非对称演变，所有研究的伪自旋极化的平均位置的振荡幅度都有所提高。当前的形式主义被证明是描述两种情况的理论平台，这两种情况是由于（i）石墨烯的晶格变形导致自然的费米速度重整化，或者甚至（ii）由a引起的非均匀质量项。特定的衬底，其长度尺度变化远大于磁场长度。