Feshbach-type resonances for two-particle scattering in graphene

TL;DR

This paper investigates two-particle scattering in graphene, revealing Feshbach resonances caused by the unique multichannel energy structure and the effects of total momentum, with implications for understanding interactions in graphene systems.

Contribution

It introduces the concept of Feshbach resonances in graphene's two-particle scattering, highlighting the role of multichannel energy segments and total momentum dependence.

Findings

Identification of three Feshbach resonances in the identical-helicity channel.

Survival of one resonance as total momentum approaches zero.

Vanishing of opposite-helicity scattering amplitudes at zero momentum.

Abstract

Two-particle scattering in graphene is a multichannel problem, where the energies of the identical or opposite-helicity channels lie in disjoint energy segments. Due to the absence of Galilean invariance, these segments depend on the total momentum $Q$. The dispersion relations for the two opposite-helicity scattering channels are analogous to those of two one-dimensional tight-binding lattices with opposite dispersion relations, which are known to easily bind states at their edges. When an $s$-wave separable interaction potential is assumed, those bound states reveal themselves as three Feshbach resonances in the identical-helicity channel. In the limit $Q \rightarrow 0$, one of the resonances survives and the opposite-helicity scattering amplitudes vanish.