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arXiv 0911.0376cond-mat.mes-hall
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石墨烯中的二体问题

Two-body problem in graphene

J. Sabio, F. Sols, F. Guinea

摘要:

我们研究了两个狄拉克粒子通过非相对论性势相互作用的问题,并限制在一个二维片,这是石墨烯层的相关情况。由于质心和相对坐标之间的非平凡耦合,即使在中心势存在的情况下,两体问题也不能映射到单个粒子的问题。我们专注于零总动量的情况下,这是相当于一个单一的粒子在Sutherland晶格。我们表明,零能态诱导引人注目的新功能,如在相对波函数的不连续性,通过一个步骤的潜在的粒子相互作用,和浓度的相对密度附近的经典转折点,如果粒子通过库仑势相互作用。在后一种情况下,我们也发现,两体系统变得不稳定的临界耦合以上。这些现象可能与石墨烯中强耦合相的性质有关。

英文摘要:

We study the problem of two Dirac particles interacting through non-relativistic potentials and confined to a two-dimensional sheet, which is the relevant case for graphene layers. The two-body problem cannot be mapped into that of a single particle, due to the non-trivial coupling between the center-of-mass and the relative coordinates, even in the presence of central potentials. We focus on the case of zero total momentum, which is equivalent to that of a single particle in a Sutherland lattice. We show that zero-energy states induce striking new features such as discontinuities in the relative wave function, for particles interacting through a step potential, and a concentration of relative density near the classical turning point, if particles interact via a Coulomb potential. In the latter case we also find that the two-body system becomes unstable above a critical coupling. These phenomena may have bearing on the nature of strong coupling phases in graphene.

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