标题： 石墨烯中狄拉克电子的非均匀磁场下的朗道能级 显示英文标题

标题： Landau levels of a Dirac electron in graphene from non-uniform magnetic fields

摘要： 量子力学中，当带电粒子受到均匀磁场作用时，会出现朗道能级，这是众所周知的。 考虑到近期对石墨烯电子性质的兴趣，石墨烯在狄拉克点附近的色散关系是动量的线性关系，我们以狄拉克哈密顿量的精神重新审视朗道能级的问题，并询问是否存在某些非均匀磁场也会导致由朗道能级组成的谱。 我们证明，答案是肯定的。 具体来说，通过考虑均匀磁场的等谱变形，我们给出了严格等谱于其均匀对应物的非均匀磁场的显式表达式，从而支持朗道能级。 显示英文摘要

摘要： The occurrence of Landau levels in quantum mechanics is well known when a charged particle is subjected to a uniform magnetic field. Considering the recent interest in the electronic properties of graphene which admits a dispersion relation which is linear in the momentum near the Dirac points, we revisit the problem of Landau levels in the spirit of the Dirac Hamiltonian and ask if there are certain non-uniform magnetic fields which also lead to a spectrum consisting of the Landau levels. The answer, as we show, is in the affirmative. In particular, by considering isospectral deformations of the uniform magnetic field, we present explicit expressions for non-uniform magnetic fields that are strictly isospectral to their uniform counterpart, thus supporting the Landau levels.