Orbital and interlayer Skyrmions crystals in bilayer graphene

Abstract

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies $E=\pm \sqrt{N(N+1)}\hslash {\omega }_c^{\ast }$ where ${\omega }_c^{\ast }$ is the effective cyclotron frequency and All Landau levels but N=0 are four times degenerate counting spin and valley degrees of freedom. The Landau level N=0 has an extra degeneracy due to the fact that orbitals $n=0$ and $n=1$ both have zero kinetic energies. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignement in space of the valley and orbital pseudospins. These quantum Hall pseudo-ferromagnetic states support topological charged excitations in the form of orbital and valley Skyrmions. Away from integer fillings, these topological excitations can condense to form a rich variety of Skyrme crystals with interesting properties. We study in this paper different crystal phases that occur when an electric field is applied between the layers. We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture of electrical dipoles that can be controlled by an in-plane electric field. Moreover, the modulation of electronic density in the crystalline phases are experimentally accessible through a measurement of their local density of states

18 pages with 13 figures

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• The electronic properties of graphene
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• Pseudospin vortex-antivortex states with interwoven spin textures in double layer quantum Hall systems

Cited by in corpus (29)

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• Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Weak-field Hall Resistivity and Spin/Valley Flavor Symmetry Breaking in Magic-Angle Twisted Bilayer Graphene
• Quantum Hall ferromagnetic phases in the Landau level N=0 of a graphene bilayer
• Distinct Competing Ordered ν=2 States in Bilayer Graphene
• Lattice Collective Modes from a Continuum Model of Magic-Angle Twisted Bilayer Graphene
• Quantum Hall to charge-density-wave phase transitions in ABC-trilayer graphene
• Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene
• Wigner crystal phases in bilayer graphene
• Bilayer graphene as an helical quantum Hall ferromagnet
• Transport Measurement of Landau level Gaps in Bilayer Graphene
• Unique Spin Vortices in Quantum Dots with Spin-orbit Couplings
• Tuning the Topological Features of Quantum-Dot Hydrogen and Helium by a Magnetic Field
• Skyrme crystal in bilayer and multilayer graphene
• Vortex core order and field-driven phase coexistence in the attractive Hubbard model
• Orbital Lamb shift and mixing of the pseudo-zero-mode Landau levels in ABC-stacked trilayer graphene
• Skyrmion-like textures in superconductors with competing order
• Particle-hole symmetry and bifurcating ground state manifold in the quantum Hall ferromagnetic states of multilayer graphene
• Excitation Gap of Fractal Quantum Hall States in Graphene
• Many-body effects, orbital mixing and cyclotron resonance in bilayer graphene
• Lagrangian formulation for emergent elastic waves in magnetic emergent crystals
• Charge and spin textures of Ising quantum Hall ferromagnet domain walls
• Interaction-enhanced electron-hole and valley asymmetries in the lowest Landau level of ABA-stacked trilayer graphene
• Orbital mixing in few-layer graphene and non-Abelian Berry phase
• Skyrmionic Transport and First Order Phase Transitions in Twisted Bilayer Graphene Quantum Hall Ferromagnet