Theory of broken symmetry quantum Hall states in the $N=1$ Landau level of Graphene

Abstract

We study many-body ground states for the partial integer fillings of the $N=1$ Landau level in graphene, by constructing a model that accounts for the lattice scale corrections to the Coulomb interactions. Interestingly, in contrast to the $N=0$ Landau level, this model contains not only pure delta function interactions but also some of its derivatives. Due to this we find several important differences with respect to the $N=0$ Landau level. For example at quarter filling when only a single component is filled, there is a degeneracy lifting of the quantum hall ferromagnets and ground states with entangled spin and valley degrees of freedom can become favourable. Moreover at half-filling of the $N=1$ Landau level, we have found a new phase that is absent in the $N=0$ Landau level, that combines characteristics of the Kekulé state and an antiferromagnet. We also find that according to the parameters extracted in a recent experiment, at half-filling of the $N=1$ Landau level graphene is expected to be in a delicate competition between an AF and a CDW state, but we also discuss why the models for these recent experiments might be missing some important terms.

References in corpus (26)

• Electronic Properties of Graphene in a Strong Magnetic Field
• Quantum Hall Ferromagnetism in Graphene
• Evidence for an Anisotropic State of Two-Dimensional Electrons in High Landau Levels
• Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Electron interactions in graphene in a strong magnetic field
• Phase diagram for the $\nu =0$ quantum Hall state in monolayer graphene
• Theory of integer quantum Hall effect in graphene
• Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet
• Spontaneous symmetry breakings in graphene subjected to in-plane magnetic field
• Composite Fermions and Broken Symmetries in Graphene
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• Theory of the Magnetic-Field-Induced Insulator in Neutral Graphene
• Long-Distance Spin Transport Through a Graphene Quantum Hall Antiferromagnet
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• STM Study of Quantum Hall Isospin Ferromagnetic States of Zero Landau Level in Graphene Monolayer
• Electrical generation and detection of spin waves in a quantum Hall ferromagnet
• Fractional and integer quantum Hall effects in the zeroth Landau level in graphene
• SO(5) symmetry in the quantum Hall effect in graphene
• Broken SU(4) Symmetry and The Fractional Quantum Hall Effect in Graphene
• Experimental determination of the energy per particle in partially filled Landau levels
• Strong-Magnetic-Field Magnon Transport in Monolayer Graphene
• Spin-valley skyrmions in graphene at filling factor $\nu =-1$
• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
• SU(4) spin waves in the $\nu =\pm 1$ quantum Hall ferromagnet in graphene
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride

Cited by in corpus (8)

• Global phase diagram of charge neutral graphene in the quantum Hall regime for generic interactions
• Spin-valley entangled quantum Hall states in graphene
• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Magnon transmission across $\nu =1|-1|1$ mono-layer graphene junction as a probe of electronic structure
• Uniquely identifying quantum Hall phases in charge neutral graphene