We construct the coherent states for charge carriers in a graphene layer immersed in crossed external electric and magnetic fields. For that purpose, we solve the Dirac-Weyl equation in a Landau-like gauge avoiding applying techniques of special relativity, and thus we identify the appropriate rising and lowering operators associated to the system. We explicitly construct the coherent states as eigenstates of a matrix annihilation operator with complex eigenvalues. In order to describe the effects of both fields on these states, we obtain the probability and current densities, the Heisenberg uncertainty relation and the mean energy as functions of the parameter $\beta=c\,\mathcal{E}/(v_{\rm F}B)$. In particular, these quantities are investigated for magnetic and electric fields near the condition of the Landau levels collapse ($\beta\rightarrow1$).

中文翻译：

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交叉电场和磁场相互作用下石墨烯的相干态

我们在浸入交叉的外部电场和磁场中的石墨烯层中构建电荷载流子的相干态。为此，我们在类似朗道的规范中求解 Dirac-Weyl 方程，避免应用狭义相对论技术，从而确定与系统相关的适当上升和下降算子。我们明确地将相干状态构造为具有复特征值的矩阵湮灭算子的特征状态。为了描述这两个场对这些状态的影响，我们获得概率和电流密度、海森堡不确定性关系和平均能量作为参数 $\beta=c\,\mathcal{E}/(v_{ \rm F}B)$。特别是，研究了朗道能级坍塌 ($\beta\rightarrow1$) 条件附近的磁场和电场的这些量。