The effective Hamiltonian for electrons in bilayer graphene with applied magnetic fields is solved through second-order supersymmetric quantum mechanics. This method transforms the corresponding eigenvalue problem into two intertwined one-dimensional stationary Schrdinger equations whose potentials are determined by choosing at most two seed solutions. In this paper new kinds of magnetic fields associated to non-shape-invariant SUSY partner potentials are generated. Analytic solutions for these magnetic fields are found, the associated spectrum is analyzed, and the probability and current densities are explored.

中文翻译：

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超对称产生的磁场中的双层石墨烯

通过二阶超对称量子力学求解具有外加磁场的双层石墨烯中电子的有效哈密顿量。该方法将相应的特征值问题转化为两个相互交织的一维平稳薛定谔方程，其势通过选择最多两个种子解来确定。在本文中，产生了与非形状不变的 SUSY 伙伴电位相关的新型磁场。找到这些磁场的解析解，分析相关的频谱，并探索概率和电流密度。