Broken-symmetry $\nu =0$ quantum Hall states in bilayer graphene: Landau level mixing and dynamical screening

Abstract

For bilayer graphene in a magnetic field at the neutral point, we derive and solve a full set of gap equations including all Landau levels and taking into account the dynamically screened Coulomb interaction. There are two types of the solutions for the filling factor $\nu =0$: (i) a spin-polarized type solution, which is the ground state at small values of perpendicular electric field $E_{\perp }$, and (ii) a layer-polarized solution, which is the ground state at large values of $E_{\perp }$. The critical value of $E_{\perp }$ that determines the transition point is a linear function of the magnetic field, i.e., $E_{\perp ,\mathrm{cr}}=E_{\perp }^{\mathrm{off}}+aB$, where $E_{\perp }^{\mathrm{off}}$ is the offset electric field and $a$ is the slope. The offset electric field and energy gaps substantially increase with the inclusion of dynamical screening compared to the case of static screening. The obtained values for the offset and the energy gaps are comparable with experimental ones. The interaction with dynamical screening can be strong enough for reordering the levels in the quasiparticle spectrum (the $n=2$ Landau level sinks below the $n=0$ and $n=1$ ones).

20 pages, 9 multi-panel figures; final published version with a more detailed comparison of the results with the experimental data

References in corpus (29)

• Quantum Hall Ferromagnetism in Graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene
• Interaction-Driven Spectrum Reconstruction in Bilayer Graphene
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Quantum Anomalous Hall State in Bilayer Graphene
• Electron interactions in graphene in a strong magnetic field
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Theory of integer quantum Hall effect in graphene
• Intra-Landau level Cyclotron Resonance in Bilayer Graphene
• Collective modes of doped graphene and a standard 2DEG in a strong magnetic field: linear magneto-plasmons versus magneto-excitons
• Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems
• Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids
• Spontaneous Symmetry Breaking and Quantum Hall Effect in Graphene
• Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects
• Intrinsic Zeeman Effect in Graphene
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Long range Coulomb interaction in bilayer graphene
• Spin-Polarized to Valley-Polarized Transition in Graphene Bilayers at $\nu =0$ in High Magnetic Fields
• Dynamics and phase diagram of the $\nu =0$ quantum Hall state in bilayer graphene
• Spin-flip excitations, spin waves, and magneto-excitons in graphene Landau levels at integer filling factors
• Pseudo-zero-mode Landau levels and collective excitations in bilayer graphene
• Broken-symmetry states and phase diagram of the lowest Landau level in bilayer graphene
• Field induced quantum-Hall ferromagnetism in suspended bilayer graphene
• Intra-Landau level magnetoexcitons and the transition between quantum Hall states in undoped bilayer graphene
• Effect of the band structure topology on the minimal conductivity for bilayer graphene with symmetry breaking

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• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
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• Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene
• Magnetic Catalysis: A Review
• Fermions on bilayer graphene: symmetry breaking for B=0 and nu=0
• Gapped broken symmetry states in ABC trilayer graphene
• Quantum Hall ferromagnetic phases in the Landau level N=0 of a graphene bilayer
• Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene
• Distinct Competing Ordered ν=2 States in Bilayer Graphene
• Classification of massive and gapless phases in bilayer graphene
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• Theory of integer quantum Hall effect in insulating bilayer graphene
• Transport Measurement of Landau level Gaps in Bilayer Graphene
• Half Metallic Bilayer Graphene
• Gap generation in ABC-stacked multilayer graphene: screening vs band flattening
• Theory of inter-Landau level magnetoexcitons in bilayer graphene
• Phase diagram of a graphene bilayer in the zero-energy Landau level
• Localized states due to expulsion of resonant impurity levels from the continuum in bilayer graphene
• Quantum multicriticality of bilayer graphene in the presence of a tunable energy gap
• Symmetry characterization of the collective modes of the phase diagram of the $\nu =0$ quantum Hall state in graphene: Mean-field and spontaneously broken symmetries
• Validity of the two-band model of bilayer and trilayer graphene in a magnetic field
• Possible Broken Inversion and Time-Reversal Symmetry State of Electrons in Bilayer Graphene
• Energetics of complex phase diagram in a tunable bilayer graphene probed by quantum capacitance
• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene
• Spin-valley Hall transport induced by spontaneous symmetry breaking in half-filled zero Landau level of bilayer graphene
• Spectrum of edge states in the $\nu =0$ quantum Hall phases in graphene
• Ordered-Current State of Electrons in Bilayer Graphene
• Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene
• Electromagnetic absorption and Kerr effect in quantum Hall ferromagnetic states of bilayer graphene
• Spin-Polarized-Current State of Electrons in Bilayer Graphene
• Broken symmetry states in bilayer graphene in electric and in-plane magnetic fields
• Signatures of electronic ordering in transport in graphene flat bands
• Current orderings of interacting electrons in bilayer graphene
• Temperature-induced phase transitions in the quantum Hall magnet of bilayer graphene
• Landau Level Phases in Bilayer Graphene under Pressure at Charge Neutrality
• Phase boundary of spin-polarized-current state of electrons in bilayer graphene