Influence of the Dirac Sea on Phase Transitions in Monolayer Graphene under Strong Magnetic Fields

TL;DR

This paper investigates how the Dirac sea influences phase transitions in monolayer graphene under strong magnetic fields, revealing the importance of dielectric screening and non-perturbative effects on ground states.

Contribution

It introduces a two-step, non-perturbative approach combining renormalization group analysis and Hartree-Fock calculations to study magnetic anisotropic energies in graphene.

Findings

Ground state transitions from antiferromagnetic to Kekulé-Distorted states with reduced screening.

Dirac sea significantly impacts magnetic anisotropic energy at small dielectric constants.

Predicted phase transitions at specific filling fractions under varying magnetic fields.

Abstract

Recent scanning tunneling microscopy experiments have found Kekul\'e-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 $\epsilon$. This variation suggests that the magnetic anisotropic energy is sensitive to 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 account for the leading logarithmic divergences arising from quantum fluctuations by solving renormalization group flow equations in the absence of magnetic field from the carbon lattice scale up to the much larger magnetic length. Subsequently, we used these renormalized coupling constants to perform non-perturbative, self-consistent Hartree-Fock calculations. Our results demonstrate that the ground state at neutrality ($\nu=0$) transitions from a AF state to a spin-singlet KD state when dielectric screening and magnetic fields become small, consistent with experimental observations. For filling fraction $\nu=\pm1$, we predict a transitions from spin-polarized charge-density wave states to 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 $\epsilon$ is small. Our work provides insights into how the Dirac sea, which contributes to one electron per graphene unit cell, affects the small magnetic anisotropic energy in graphene.