Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene

Abstract

We study ferromagnetism and its stability in twisted bilayer graphene. We work with a Hubbard-like interaction that corresponds to the screened Coulomb interaction in a well-defined limit where the Thomas-Fermi screening length $l_{\text{TF}}$ is much larger than monolayer graphene's lattice spacing $l_g\ll l_{\text{TF}}$ and much smaller than the Moiré super lattice's spacing $l_{\text{TF}}\ll l_{\text{Moireˊ}}$. We show that in the perfectly flat band "chiral" limit and at filling fractions $\pm 3/4$, the saturated ferromagnetic (spin and valley polarized) states are ideal ground states candidates in the large band-gap limit. By assuming a large enough substrate (hBN) induced sub-lattice potential, the same argument can be applied to filling fractions $\pm 1/4$. We estimate the regime of stability of the ferromagnetic phase around the chiral limit by studying the exactly calculated spectrum of one-magnon excitations. The instability of the ferromagnetic state is signaled by a negative magnon excitation energy. This approach allows us to deform the results of the idealized chiral model (by increasing the bandwidth and/or modified interactions) towards more realistic systems. Furthermore, we use the low energy part of the exact one-magnon spectrum to calculate the spin-stiffness of the Goldstone modes throughout the ferromagnetic phase. The calculated value of spin-stiffness can determine the excitation energy of charged skyrmions.

arXiv comment5 pages, 3 figures, 3 pages of supplementary material

References in corpus (54)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Tuning superconductivity in twisted bilayer graphene
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
• Dielectric function, screening, and plasmons in 2D graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Magic Angle Spectroscopy
• Origin of Magic Angles in Twisted Bilayer Graphene
• Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
• Imaging Electronic Correlations in Twisted Bilayer Graphene near the Magic Angle
• Electric Field Tunable Correlated States and Magnetic Phase Transitions in Twisted Bilayer-Bilayer Graphene
• Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
• Continuum Model of the Twisted Bilayer
• Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Correlated states in twisted double bilayer graphene
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• All "Magic Angles" Are "Stable" Topological
• Nearly Flat Chern Bands in Moiré Superlattices
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
• Fragile Topology and Wannier Obstructions
• Ferromagnetism in the Hubbard Model-- Examples from Models with Degenerate Single-Electron Ground States
• A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
• Strong coupling phases of partially filled twisted bilayer graphene narrow bands
• Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
• Dynamic band structure tuning of graphene moiré superlattices with pressure
• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• An exact continuum model for low-energy electronic states of twisted bilayer graphene
• Quantum Ferromagnetism and Phase Transitions in Double-Layer Quantum Hall Systems
• Magic Angle Hierarchy in Twisted Graphene Multilayers
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Phonon-induced giant linear-in-$T$ resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity
• Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Ferromagnetism in narrow bands of moiré superlattices
• Moiré Flat Bands in Twisted Double Bilayer Graphene
• Even denominator fractional quantum Hall states at an isospin transition in monolayer graphene
• Ferromagnetism in Hubbard Models
• Multiple topological transitions in twisted bilayer graphene near the first magic angle
• Accurate Gap Determination in Monolayer and Bilayer Graphene/h-BN Moire Superlattices
• Internal screening and dielectric engineering in magic-angle twisted bilayer graphene
• Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands
• Topological flat bands in twisted trilayer graphene
• SU(N) Quantum Hall Skyrmions
• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• Ferromagnetism and superconductivity in twisted double bilayer graphene
• Metallic ferromagnetism in the Hubbard model: A rigorous example
• Observation of superconductivity in bilayer graphene/hexagonal boron nitride superlattices
• Impurity scattering induced carrier transport in twisted bilayer graphene
• On the nature of the correlated insulator states in twisted bilayer graphene

Cited by in corpus (32)

• Electrical switching of magnetic order in an orbital Chern insulator
• Imaging orbital ferromagnetism in a moiré Chern insulator
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
• Symmetry breaking and skyrmionic transport in twisted bilayer graphene
• Moiré Commensurability and the Quantum Anomalous Hall Effect in Twisted Bilayer Graphene on Hexagonal Boron Nitride
• Cascades between light and heavy fermions in the normal state of magic angle twisted bilayer graphene
• Quantum Metric and Correlated States in Two-dimensional Systems
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Exciton band topology in spontaneous quantum anomalous Hall insulators: applications to twisted bilayer graphene
• Hybrid Wannier Chern bands in magic angle twisted bilayer graphene and the quantized anomalous Hall effect
• Evidence of orbital ferromagnetism in twisted bilayer graphene aligned to hexagonal boron nitride
• Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene
• Pseudo-magnetic fields, particle-hole asymmetry, and microscopic effective continuum Hamitonians of twisted bilayer graphene
• Interaction-Driven Filling-Induced Metal-Insulator Transitions in 2D Moiré Lattices
• Twistronics in graphene-based van der Waals structures
• Lattice model for the Coulomb interacting chiral limit of the magic angle twisted bilayer graphene: symmetries, obstructions and excitations
• Bilayer graphene encapsulated within monolayers of WS${}_2$ or Cr${}_2$Ge${}_2$Te${}_6$: Tunable proximity spin-orbit or exchange coupling
• Lattice Collective Modes from a Continuum Model of Magic-Angle Twisted Bilayer Graphene
• Excitonic Chern insulator and kinetic ferromagnetism in MoTe${}_2$/WSe${}_2$ moiré bilayer
• Current Driven Magnetization Reversal in Orbital Chern Insulators
• Trions in Twisted Bilayer Graphene
• Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings
• Scaling theory of intrinsic Kondo and Hund's rule interactions in magic-angle twisted bilayer graphene
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Charge and spin correlations in insulating and incoherent metal states of twisted bilayer graphene
• Band manipulation and spin texture in interacting moiré helical edges
• Magnon bands in twisted bilayer honeycomb quantum magnets
• Topological magnons and domain walls in twisted bilayer MoTe${}_2$
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Quantum Magnetism in Wannier-Obstructed Mott Insulators
• Gauging away the Stoner model: Engineering unconventional metallic ferromagnetism with artificial gauge fields