[Paper Review] Electric field control of spins in bilayer graphene: Local moment formation and local moment interactions

Matthew Killi, Dariush Heidarian+1 more|arXiv (Cornell University)|Jan 6, 2011

Quantum and electron transport phenomena48 references35 citations

TL;DR

This paper investigates electric field control of local magnetic moments and their interactions in bilayer graphene (BLG) using a mean-field Anderson impurity model. It demonstrates that applying a perpendicular electric field can switch local moments on or off by tuning the impurity energy level relative to the BLG band gap, while also enabling dynamic control of RKKY interactions via band structure engineering.

ABSTRACT

We study local moment formation for adatoms on bilayer graphene (BLG) within a mean-field theory of the Anderson impurity model. The wavefunctions of the BLG electrons induce strong particle-hole asymmetry and band dependence of the hybridization, which is shown to result in unusual features in the impurity model phase diagram. We also study the effect of varying the chemical potential, as well as varying an electric field perpendicular to the bilayer; the latter modifies the density of states of electrons in BLG and, more significantly, shifts the impurity energy. We show that this leads to regimes in the impurity phase diagram where local moments can be turned on or off by applying modest external electric fields. Finally, we show that the RKKY interaction between local moments can be varied by tuning the chemical potential (as has also been suggested in monolayer graphene) or, more interestingly, by tuning the electric field so that it induces changes in the band structure of BLG.

Motivation & Objective

• To understand how local moment formation on plaquette-centered adatoms in bilayer graphene is influenced by electronic structure and external fields.
• To investigate the role of particle-hole asymmetry and band-dependent hybridization in shaping the impurity phase diagram.
• To explore how an external electric field perpendicular to the bilayer can tune the impurity energy and control local moment formation.
• To examine the tunability of RKKY interactions between local moments through electric field and chemical potential tuning.
• To contrast the behavior of chiral BLG with a non-chiral model system to isolate the effects of BLG's unique band structure.

Proposed method

• Formulates an Anderson impurity model for plaquette-centered adatoms on bilayer graphene, incorporating band structure, hybridization, and electron-electron interactions.
• Applies mean-field theory to solve the impurity model, including self-energy corrections with momentum and band-dependent coupling.
• Uses a minimal tight-binding model for BLG with nearest-neighbor and interlayer hopping (t = 1, t⊥ ≈ 0.15t) to describe the electronic dispersion.
• Introduces a perpendicular electric field (bias) that splits the bands and shifts the impurity energy, enabling control over the effective chemical potential.
• Constructs phase diagrams by sweeping chemical potential and bias, identifying regimes of local moment formation and Coulomb blockade.
• Compares results with a fictitious non-chiral system having the same density of states but no band or momentum dependence to isolate chiral effects.

Experimental results

Research questions

• RQ1 Can an external electric field be used to switch local magnetic moments on or off in bilayer graphene?
• RQ2 How does the chiral, band-dependent hybridization in BLG affect the formation of local moments compared to conventional systems?
• RQ3 What is the role of particle-hole asymmetry and band structure in determining the phase diagram of the Anderson impurity model in BLG?
• RQ4 How can the RKKY interaction between local moments be tuned via electric field or chemical potential?
• RQ5 To what extent do the unique wavefunctions of BLG lead to non-trivial self-energy and spectral peak renormalization?

Key findings

• Applying a perpendicular electric field shifts the impurity energy level, enabling on/off switching of local moments even with small field changes.
• A regime exists where any finite U leads to local moment formation due to Coulomb blockade, identifiable in the phase diagram when the impurity level is centered in the band gap.
• The self-energy acquires a large real part with non-trivial frequency dependence due to chiral wavefunctions and momentum-dependent hybridization, renormalizing the spectral peak position.
• The phase diagram exhibits strong particle-hole asymmetry and band dependence, unlike conventional systems, due to the chiral nature of BLG’s quasiparticles.
• RKKY interactions between local moments can be tuned by adjusting the chemical potential or by applying an electric field that modifies the BLG band structure.
• The comparison with a non-chiral system confirms that chiral hybridization and band structure are essential for the observed non-trivial phase diagram features.