Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
arXiv:2506.22417 · doi:10.1103/qbg3-3yxv
Abstract
Robust flavor-polarized phases are a striking hallmark of many flat-band moiré materials. In this work, we trace the origin of this spontaneous polarization to a lesser-known quantum-geometric quantity: the quantum-geometric dipole. Analogous to how the quantum metric governs the spatial spread of wavepackets, we show that the quantum-geometric dipole sets the characteristic size of particle-hole excitations, e.g. magnons in a ferromagnet, which in turn boosts their gap and stiffness. Indeed, the larger the particle-hole separation, the weaker the mutual attraction, and the stronger the excitation energy. In topological bands, this energy enhancement admits a lower bound within the local-mode approximation, highlighting the crucial role of topology in flat-band ferromagnetism. We illustrate these effects in microscopic models, emphasizing their generality and relevance to moiré materials. Our results establish the quantum-geometric dipole as a predictive geometric indicator for ferromagnetism in flat bands, a crucial prerequisite for topological order.
arXiv comment9+9 pages, 3+2 figures
References in corpus (92)
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Berry Phase Effects on Electronic Properties
- Maximally-localized generalized Wannier functions for composite energy bands
- Maximally localized Wannier functions: Theory and applications
- Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
- Fractional quantum Hall states at zero magnetic field
- Topological insulators in twisted transition metal dichalcogenide homobilayers
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Observation of Fractionally Quantized Anomalous Hall Effect
- Fractional quantum Hall effect in the absence of Landau levels
- First principles calculations of the Shift Current Bulk Photovoltaic Effect in Ferroelectrics
- Superfluidity in topologically nontrivial flat bands
- Fractional Chern Insulator
- Moiré heterostructures as a condensed matter quantum simulator
- Integer and fractional Chern insulators in twisted bilayer MoTe2
- Fractional Quantum Hall Physics in Topological Flat Bands
- Isospin magnetism and spin-triplet superconductivity in Bernal bilayer graphene
- Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
- A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
- Strong coupling phases of partially filled twisted bilayer graphene narrow bands
- Superfluidity and Quantum Geometry in Twisted Multilayer Systems
- Fractional topological insulators
- Band geometry of fractional topological insulators
- Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
- Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
- Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
- Exact Landau Level Description of Geometry and Interaction in a Flatband
- Ferromagnetic Mott State in Twisted Graphene Bilayers at the Magic Angle
- Ferromagnetism in narrow bands of moiré superlattices
- Essay: Where Can Quantum Geometry Lead Us?
- Fractional Chern Insulator in Twisted Bilayer MoTe
- Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
- Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
- Cascade of isospin phase transitions in Bernal bilayer graphene at zero magnetic field
- Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
- Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene
- Correlated Insulator and Chern Insulators in Pentalayer Rhombohedral Stacked Graphene
- Programming Correlated Magnetic States via Gate Controlled Moiré Geometry
- Orbital Multiferroicity in Pentalayer Rhombohedral Graphene
- Effective theory and emergent symmetry in the flat bands of attractive Hubbard models
- Quantum geometry induced nonlinear transport in altermagnets
- A Microscopic Perspective on Moiré Materials
- Superfluid weight bounds from symmetry and quantum geometry in flat bands
- Topological aspects of quantum spin Hall effect in graphene: Z topological order and spin Chern number
- Mapping twist-tuned multiband topology in bilayer WSe
- Topological and stacked flat bands in bilayer graphene with a superlattice potential
- Topological aspects of nonlinear excitonic processes in noncentrosymmetric crystals
- Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
- Shift current bulk photovoltaic effect influenced by quasiparticles and excitons
- Quantum geometry in condensed matter
- Fundamental bound on topological gap
- The quantum geometric origin of capacitance in insulators
- Fractional Topological Insulators -- a Pedagogical Review
- Quantum Metric Induced Phases in Moiré Materials
- Ideal Chern bands are Landau levels in curved space
- Twisted photovoltaics at terahertz frequencies from momentum shift current
- Topological exact flat bands in two dimensional materials under periodic strain
- Quantum Geometry and Stability of Moiré Flatband Ferromagnetism
- Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
- Flat-band ferromagnetism in twisted bilayer graphene
- Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene
- Gate-tunable flat bands in van der Waals patterned dielectric superlattices
- Sublattice structure and topology in spontaneously crystallized electronic states
- Multilayer graphene with a superlattice potential
- Topological bound on structure factor
- Theory of topological exciton insulators and condensates in flat Chern bands
- Bridging the small and large in twisted transition metal dicalcogenide homobilayers: a tight binding model capturing orbital interference and topology across a wide range of twist angles
- Gate-tunable topological phases in superlattice modulated bilayer graphene
- Instantaneous response and quantum geometry of insulators
- Geometric Stiffness in Interlayer Exciton Condensates
- Universal signatures of Dirac fermions in entanglement and charge fluctuations
- Chiral model of twisted bilayer graphene realized in a monolayer
- Signature of Correlated Insulator in Electric Field Controlled Superlattice
- Superconductivity in twisted WSe from topology-induced quantum fluctuations
- Quantum Geometric Exciton Drift Velocity
- Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe
- Keldysh field theory of dynamical exciton condensation transitions in nonequilibrium electron-hole bilayers
- Spinon pairing induced by chiral in-plane exchange and the stabilization of odd-spin Chern number spin liquid in twisted
- Topological Kondo semimetal and insulator in AB-stacked heterobilayer transition metal dichalcogenides
- Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings
- Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
- Two-particle collisional coordinate shifts and hydrodynamic anomalous Hall effect in systems without Lorentz invariance
- Patterned bilayer graphene as a tunable, strongly correlated system
- Attractive Haldane bilayers for trapping non-Abelian anyons
- Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
- Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices
- Topological magnons and domain walls in twisted bilayer MoTe
- Topologically protected flatness in chiral moiré heterostructures
- Exact ground state of interacting electrons in magic angle graphene
- Many-Body Quantum Geometric Dipole
- Superfluid stiffness bounds in time-reversal symmetric superconductors
- Plasmonic Transverse Dipole Moment in Chiral Fermion Nanowires