Influence of the Dirac sea on phase transitions in monolayer graphene under strong magnetic fields

Recent scanning tunneling microscopy experiments have found Kekulé-distorted (KD) ordering in graphene subjected to strong magnetic fields, a departure from the antiferromagnetic (AF) state identified in earlier transport experiments on double-encapsulated devices with larger dielectric screening constant ϵ. This variation suggests that the magnetic anisotropic energy is sensitive to the dielectric screening constant. To calculate the magnetic anisotropic energy without resorting to perturbation theory, we adopted a two-step approach. First, we derived the bare valley-sublattice-dependent interaction coupling constants from microscopic calculations and accounted for the leading logarithmic divergences arising from quantum fluctuations by solving renormalization group flow equations in the absence of a magnetic field, from the carbon lattice scale up to the much larger magnetic length. Subsequently, we used these renormalized coupling constants to perform nonperturbative, self-consistent Hartree-Fock calculations. Our results demonstrate that the ground state at neutrality (ν=0) transitions from an AF state to a spin-singlet KD state when dielectric screening and magnetic fields become small, consistent with experimental observations. For filling fraction ν=±1, we predict a transition from spin-polarized charge-density wave states to a spin-polarized KD state when dielectric screening and magnetic fields become small. Our self-consistent Hartree-Fock calculations, which encompass a large number of Landau levels, reveal that the magnetic anisotropic energy receives substantial contributions from the Dirac sea when ϵ is small. Our paper provides insights into how the Dirac sea, which contributes one electron per graphene unit cell, affects the small magnetic anisotropic energy in graphene.