Global phase diagram of charge neutral graphene in the quantum Hall regime for generic interactions

Abstract

Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Previous theoretical work, based on a stringent ultra short-range assumption on the symmetry-allowed interactions, predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, inter-valley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunneling studies universally find Kekulé bond order, and sometimes also charge density wave order. Recently, it was found that if one relaxes the stringent assumption mentioned above, a phase with coexisting canted antiferromagnetic and Kekulé order exists in the region of the phase diagram believed to correspond to real samples. In this work, starting from the continuum limit appropriate for experiments, we present the complete phase diagram of $\nu =0$ graphene in the Hartree-Fock approximation, using generic symmetry-allowed interactions, assuming translation invariant ground states up to an intervalley coherence. Allowing for a sublattice potential (valley Zeeman coupling), we find numerous phases with different types of coexisting order. We conclude with a discussion of the physical signatures of the various states.

27 pages, 32 figures

References in corpus (29)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Spin-orbit gap of graphene: First-principles calculations
• Landau Level Splitting in Graphene in High Magnetic Fields
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Origin of band gaps in graphene on hexagonal boron nitride
• Edge States and the Quantized Hall Effect in Graphene
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Evidence for a Spin Phase Transition at ν=0 in Bilayer Graphene
• Theory of integer quantum Hall effect in graphene
• Interplay of Coulomb and electron-phonon interactions in graphene
• Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet
• Moiré band model and band gaps of graphene on hexagonal boron nitride
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Evidence for a finite temperature phase transition in a bilayer quantum Hall system
• Entanglement Skyrmions in multicomponent quantum Hall systems
• Strong-Magnetic-Field Magnon Transport in Monolayer Graphene
• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
• Gapless Spin Wave Transport through a Quantum Canted-Antiferromagnet
• SU(4) spin waves in the $\nu =\pm 1$ quantum Hall ferromagnet in graphene
• Spin-Valley Coherent Phases of the $\nu =0$ Quantum Hall State in Bilayer Graphene
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Theory of broken symmetry quantum Hall states in the $N=1$ Landau level of Graphene

Cited by in corpus (11)

• Spin-valley entangled quantum Hall states in graphene
• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene
• Vanishing bulk heat flow in the nu=0 quantum Hall ferromagnet in monolayer graphene
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• SU(4) Symmetry Breaking and Induced Superconductivity in Graphene Quantum Hall Edges
• Disorder and quantum transport of the helical quantum Hall phase in graphene
• Magnon transmission across $\nu =1|-1|1$ mono-layer graphene junction as a probe of electronic structure
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Hofstadter Butterfly and Broken-Symmetry Quantum Hall States in α-Type Organic Dirac Fermion Systems
• Uniquely identifying quantum Hall phases in charge neutral graphene