Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2009-11-02
Phys.Rev.B81:045428,2010
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
13 pages, 7 figures, final version
Scientific paper
10.1103/PhysRevB.81.045428
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.
Guinea Francisco
Sabio Javier
Sols Fernando
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