[Paper Review] Magnetic Catalysis in Graphene

Christopher Winterowd, DeTar, Carleton+1 more|arXiv (Cornell University)|Sep 22, 2015

Theoretical and Computational Physics3 citations

TL;DR

This study presents a non-perturbative lattice field theory investigation of magnetic catalysis in graphene using staggered fermions and a non-compact U(1) gauge action. It demonstrates that an external magnetic field induces spontaneous chiral symmetry breaking, leading to a nonzero dynamical mass gap, confirmed through systematic zero-temperature and chiral limits with controlled finite-volume and thermal effects.

ABSTRACT

One of the most important developments in condensed matter physics in recent years has been the discovery and characterization of graphene. A two-dimensional layer of Carbon arranged in a hexagonal lattice, graphene exhibits many interesting electronic properties, most notably that the low energy excitations behave as massless Dirac fermions. These excitations interact strongly via the Coulomb interaction and thus non-perturbative methods are necessary. Using methods borrowed from lattice QCD, we study the graphene effective theory in the presence of an external magnetic field. Graphene, along with other $(2+1)$-dimensional field theories, has been predicted to undergo spontaneous breaking of flavor symmetry including the formation of a gap as a result of the external magnetic field. This phenomenon is known as magnetic catalysis. Our study investigates magnetic catalysis using a fully non-perturbative approach.

Motivation & Objective

• To investigate magnetic catalysis in graphene’s low-energy effective field theory using non-perturbative lattice methods.
• To determine whether an external magnetic field triggers spontaneous chiral symmetry breaking and dynamical mass generation in graphene.
• To control finite-volume and finite-temperature effects in lattice simulations to isolate genuine quantum field theory effects.
• To perform systematic chiral and zero-temperature extrapolations to confirm the existence of a non-zero condensate in the chiral limit.
• To compare results with theoretical predictions for the dynamical mass dependence on magnetic flux and coupling strength.

Proposed method

• Employ a discretized version of graphene’s low-energy effective field theory using staggered fermions to describe Nf=2 species of four-component Dirac fermions.
• Implement a non-compact U(1) Wilson gauge action in (2+1) dimensions to model the Coulomb interaction and external magnetic field.
• Use tadpole-improved 'fat' links and a third-neighbor hopping term to reduce O(a²) fermion mass splitting and improve continuum limit behavior.
• Perform simulations at fixed inverse coupling in the symmetric phase, then introduce quantized magnetic flux to probe symmetry breaking.
• Apply zero-temperature and chiral limits by extrapolating the condensate ⟨ψ̄ψ⟩ to zero bare fermion mass and zero temperature.
• Analyze screening masses and scaling behavior with T/m to distinguish thermal effects from genuine symmetry breaking.

Experimental results

Research questions

• RQ1 Does an external magnetic field induce spontaneous chiral symmetry breaking in graphene’s low-energy effective theory?
• RQ2 What is the behavior of the condensate ⟨ψ̄ψ⟩ as a function of magnetic flux and bare fermion mass in the chiral limit?
• RQ3 How do finite-volume and finite-temperature effects influence the chiral extrapolation of the condensate?
• RQ4 Can a non-perturbative lattice approach reliably confirm the predicted ∝√|eB| scaling of the dynamical mass in (2+1)D Dirac fermion systems?
• RQ5 Is the observed condensate robust under systematic zero-temperature and chiral limit extrapolations?

Key findings

• A nonzero condensate ⟨ψ̄ψ⟩ is observed in the chiral limit after performing zero-temperature and chiral extrapolations, confirming magnetic catalysis.
• The condensate remains nonzero at finite magnetic flux (ΦB = 0.125 and 0.1875 in lattice units), indicating spontaneous symmetry breaking under external magnetic fields.
• Finite-temperature effects significantly distort the chiral extrapolation, with σ vanishing at T/m ≥ 1, necessitating zero-temperature extrapolation before chiral limit analysis.
• Finite-volume effects are negligible, as the condensate extrapolates to zero at zero mass across different spatial lattice sizes.
• The screening mass analysis confirms that thermal effects dominate the chiral extrapolation, reinforcing the need for zero-temperature control.
• The results are consistent with the theoretical prediction m_dyn ∝ α_g√|eB|, supporting the universality of magnetic catalysis in (2+1)-dimensional Dirac fermion systems.