Two-body problem in graphene

TL;DR

This paper investigates the complex two-body problem of Dirac particles in graphene, revealing unique quantum phenomena like wave function discontinuities and potential instabilities at strong coupling.

Contribution

It provides a detailed analysis of two interacting Dirac particles in graphene, highlighting non-trivial coupling effects and stability conditions not previously characterized.

Findings

Zero-energy states cause wave function discontinuities.

Coulomb interaction leads to density concentration near classical turning points.

System becomes unstable above a critical Coulomb coupling.

Abstract

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.