Quasi-flat-band physics in a two-leg ladder model and its relation to magic-angle twisted bilayer graphene

Abstract

We study the single- and many-particle properties of a two-leg ladder model threaded by a flux with the legs coupled by a spatially varying term. Although a priori unrelated to twisted bilayer graphene (TBG), the model is found to have striking similarities: a quasi-flat low-energy band emerges with characteristics similar to that of magic angle TBG. We study the effect of interparticle interaction in our model using the density matrix renormalization group and find that when the band is quasi-flat, the ground state is a ferromagnetic Mott insulator. As the band becomes more dispersive, the system undergoes a ferromagnetic to antiferromagnetic transition. We discuss how our model is relevant not only to magic-angle physics in TBG, but also in the larger context of one-dimensional correlations and magnetism.

References in corpus (27)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• The density-matrix renormalization group in the age of matrix product states
• Moire bands in twisted double-layer graphene
• Tuning superconductivity in twisted bilayer graphene
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Graphene bilayer with a twist: electronic structure
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• Localization of Dirac electrons by Moire patterns in graphene bilayers
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene
• From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
• Superconductivity without insulating states in twisted bilayer graphene stabilized by monolayer WSe${}_2$
• 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
• Ferromagnetic Mott State in Twisted Graphene Bilayers at the Magic Angle
• Ferromagnetism in Hubbard Models
• Laughlin-like states in bosonic and fermionic atomic synthetic ladders
• Spinless Fermionic ladders in a magnetic field: Phase Diagram
• Chiral currents in one-dimensional fractional quantum Hall states
• Ferromagnetism in the one-dimensional Hubbard model with orbital degeneracy: From low to high electron density
• Fractional charge excitations in fermionic ladders
• Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladder
• The resonant state at filling factor ν = 1/2 in chiral fermionic ladders
• Emergent bosons in the fermionic two-leg flux ladder

Cited by in corpus (17)

• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
• Twisted bilayer graphene.VI. An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene
• Dynamical correlations and order in magic-angle twisted bilayer graphene
• TSTG I: Single-Particle and Many-Body Hamiltonians and Hidden Non-local Symmetries of Trilayer Moiré Systems with and without Displacement Field
• Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem
• TBG as Topological Heavy Fermion: II. Analytical approximations of the model parameters
• TSTG II: Projected Hartree-Fock Study of Twisted Symmetric Trilayer Graphene
• Towards holographic flat bands
• Particle-hole asymmetric phases in doped twisted bilayer graphene