Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals

Abstract

Magnetic skyrmion crystals with zero net skyrmion charge and zero topological Hall response are interesting candidate phases which can occur at a vanishing magnetic field in centrosymmetric systems. We study a minimal bilayer model of skyrmion crystals having opposite chirality and topological charge in the two layers, and show that it can host nearly flat electronic bands with quasi-uniform Berry curvature and quantum metric. Using Hartree-Fock theory, we show that weak to moderate short-range electron interactions induce two distinct types of symmetry breaking patterns depending on the band dispersion: an intra-unit-cell charge density modulation from Chern band mixing or a layer-imbalanced phase with a nonzero ferroelectric polarization. Both phases break inversion symmetry leading to a spontaneous and large net topological Hall effect, with the phase diagram tunable by external electric fields. Our results may be relevant to centrosymmetric skyrmion materials such as Gd${}_2$PdSi${}_3$ and Gd${}_3$Ru${}_4$Al${}_{12}$ as well as artificially engineered heterostructures. We also discuss its relation to recent work on twisted transition metal dichalcogenide bilayers.

References in corpus (64)

• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Skyrmion Lattice in a Chiral Magnet
• Anomalous Hall effect
• Advances in the Physics of Magnetic Skyrmions and Perspective for Technology
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Graphene Bilayers with a Twist
• Topological insulators in twisted transition metal dichalcogenide homobilayers
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet
• Skyrmion Lattice in a Doped Semiconductor
• Observation of Fractionally Quantized Anomalous Hall Effect
• Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature
• Fractional Chern Insulator
• Berry Phase Theory of Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites
• Topological Hall effect and Berry phase in magnetic nanostructures
• Magnetic bilayer-skyrmions without skyrmion Hall effect
• Skyrmions in Magnetic Multilayers
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field
• Interface-driven topological Hall effect in SrRuO${}_3$-SrIrO${}_3$ bilayer
• Unusual Hall Effect Anomaly in MnSi Under Pressure
• Nearly Flat Chern Bands in Moiré Superlattices
• Skyrmion phase and competing magnetic orders on a breathing kagome lattice
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Exact results for interacting electrons in high Landau levels
• A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
• Band geometry of fractional topological insulators
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi
• Antiferromagnetic Half-skyrmions and Bimerons at room temperature
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings
• Quantized Anomalous Hall Effects in Skyrmion Crystal
• Bubble and Skyrmion Crystals in Frustrated Magnets with Easy-Axis Anisotropy
• Ferromagnetism in narrow bands of moiré superlattices
• Antiferromagnetic skyrmion crystals: generation, topological Hall and topological spin Hall effect
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Enhanced Stability of Skyrmions in Two-Dimensional Chiral Magnets with Rashba Spin-Orbit Coupling
• Fractional Chern Insulators and the W-Infinity Algebra
• Anomalous Hall Effect and Skyrmion Number in Real- and Momentum-space
• Charge Density Wave Ordering in Half Filled High Landau Levels
• Topological Nernst effect of the two-dimensional skyrmion lattice
• Theory of helical spin crystals: phases, textures and properties
• Two - Dimensional Electron Liquid in a Weak Magnetic Field
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Topological magneto-optical effects and their quantization in noncoplanar antiferromagnets
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Skyrmions in Chiral Magnets with Rashba and Dresselhaus Spin-Orbit Coupling
• Valley-Polarized Quantum Anomalous Hall State in Moiré MoTe${}_2$/WSe${}_2$ Heterobilayers
• Theory of Topological Spin Hall Effect in Antiferromagnetic Skyrmion: Impact on Current-induced Motion
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Non-Abelian fractionalization in topological minibands
• Magnetic behavior of Gd3Ru4Al12, a layered compound with a distorted Kagome net
• Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene
• Giant proximity exchange and flat Chern band in 2D magnet-semiconductor heterostructures
• Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice
• Magnetic skyrmion crystal at a topological insulator surface
• Twisted magnetic topological insulators
• High Figure of Merit Magneto Optics from Interfacial Skyrmions on Topological Insulators
• Multipolar Skyrmion Crystals in Non-Kramers Doublet Systems
• Tunable skyrmion crystals and topological quantum oscillations in magnetic metals
• Antiferro skyrmion crystal phases in a synthetic bilayer antiferromagnet under an in-plane magnetic field