Interplay between the edge-state magnetism and long-range Coulomb interaction in zigzag graphene nanoribbons: quantum Monte Carlo study

TL;DR

This study uses quantum Monte Carlo simulations to explore how long-range Coulomb interactions influence edge magnetism and electronic properties in zigzag graphene nanoribbons, revealing complex effects on spin, charge, and dispersion relations.

Contribution

It provides a detailed analysis of the effects of nonlocal Coulomb interactions on edge states, including velocity enhancement and fluctuation competition, using realistic modeling and quantum Monte Carlo methods.

Findings

Fermi velocity at Dirac points is enhanced by nonlocal interactions.

Edge magnetic moments are reduced due to competing fluctuations.

Edge spin-wave modes become more extended with reduced damping.

Abstract

We perform projective quantum Monte Carlo simulations of zigzag graphene nanoribbons within a realistic model with long-range Coulomb interactions. Increasing the relative strength of nonlocal interactions with respect to the on-site repulsion does not generate a phase transition but has a number of nontrivial effects. At the single-particle level we observe a marked enhancement of the Fermi velocity at the Dirac points. At the two-particle level, spin- and charge-density-wave fluctuations compete. As a consequence, the edge magnetic moment is reduced but the edge dispersion relation increases in the sense that the single-particle gap at momentum $q=\pi/|{\pmb a}_1|$ grows. We attribute this to nonlocal charge fluctuations which assist the spin fluctuations to generate the aforementioned gap. In contrast, the net result of the interaction-induced renormalization of different energy scales is a constant spin-wave velocity of the edge modes. However, since the particle-hole continuum is shifted to higher energies---due to the renormalization of the Fermi velocity---Landau damping is reduced. As a result, a roughly linear spin-wave-like mode at the edge spreads out through a larger part of the Brillouin zone.