Equations of motion method for triplet excitation operators in graphene

TL;DR

This paper develops an equations of motion approach for triplet excitation operators in graphene, revealing bound state solutions below the particle-hole continuum using a Hubbard interaction model.

Contribution

It introduces a novel method to analyze triplet excitations in graphene, deriving a factorized eigenvalue equation that predicts bound states below the continuum.

Findings

Bound states exist below the particle-hole continuum in undoped graphene.

The equations can be factorized into two first order equations, simplifying analysis.

A solution below the continuum is explicitly obtained.

Abstract

Particle-hole continuum in Dirac sea of graphene has a unique window underneath,which in principle leaves a room for bound state formation in the triplet particle hole channel [Phys. Rev. Lett. {\bf 89}, 016402 (2002)]. In this work, we construct appropriate triplet particle-hole operators, and using a repulsive Hubbard type effective interaction, we employ equations of motions to derive approximate eigen-value equation for such triplet operators. While the secular equation for the spin density fluctuations gives rise to an equation which is second order in the strength of the short range interaction, the explicit construction of the triplet operators obtained here shows that in terms of these operators, the second order can be factorized to two first order equations, one of which gives rise to a solution below the particle-hole continuum of Dirac electrons in undoped graphene.