Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides

Abstract

We investigate the phase diagram of moiré double bilayer transition metal dichalcogenides with ABBA stacking as a function of twist angle and applied pressure. At hole filling $\nu =2$ per moiré unit cell, the noninteracting system hosts a Dirac semimetal with graphene-like low-energy bands in the moiré Brillouin zone. At small twist angles, the Fermi velocity is reduced and interactions dominate the low-temperature behavior. A strong-coupling analysis identifies insulating ferromagnetic and antiferromagnetic ground-state candidates, characterized by spin-density modulations set by the moiré scale. Using a realistic continuum model with long-range Coulomb interactions, we perform self-consistent Hartree-Fock calculations to study the competition between these states. Varying the twist angle or pressure drives a transition from a Dirac semimetal to an antiferromagnetic insulator, which breaks SU(2) spin rotation and two-fold lattice rotation symmetries. Within a renormalization group analysis of the most general symmetry-allowed low-energy field theory, we show that this semimetal-to-insulator transition is continuous and belongs to the (2+1)D relativistic Gross-Neveu-Heisenberg universality class with $N=2$ four-component Dirac fermions. Finite heterostrain, relevant in realistic samples, induces a crossover from Gross-Neveu-Heisenberg universality at intermediate temperatures to conventional (2+1)D Heisenberg criticality at the lowest temperatures. Further decreasing the twist angle can cause a level crossing from the antiferromagnetic insulator into a ferromagnetic insulator with spin-split bands. Our results provide a comprehensive theoretical framework that complements and elucidates recent experiments in twisted double bilayer WSe${}_2$.

21 pages, 11 figures; v2: renormalization group analysis added, screening effects incorporated, further discussion of strong-coupling limit

References in corpus (82)

• Moire bands in twisted double-layer graphene
• All-graphene integrated circuits via strain engineering
• Origin of Magic Angles in Twisted Bilayer Graphene
• Localization of Dirac electrons by Moire patterns in graphene bilayers
• Spectroscopic signatures of many-body correlations in magic angle twisted bilayer graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Continuous Mott transition in semiconductor moiré superlattices
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Designing Flat Band by Strain
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• \textit{Ab-initio} Tight-Binding Hamiltonian for Transition Metal Dichalcogenides
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Relativistic Mott criticality in graphene
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• $\Gamma$-Valley Transition-Metal-Dichalcogenide Moirè Bands
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Quantum phase transitions in d-wave superconductors
• Emergence of supersymmetry at a critical point of a lattice model
• Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality
• Strain-induced quantum phase transitions in magic angle graphene
• Asymptotic safety: a simple example
• The electronic structure and elastic property of monolayer and bilayer transition metal dichalcogenides MX${}_2$ (M=Mo,W;X=O,S,Se,Te): A comparative first-principles study
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• Electronic structures, charge transfer and charge orders in twisted transition metal dichalcogenide bilayers
• Renormalization group theory of nematic ordering in d-wave superconductors
• Internal screening and dielectric engineering in magic-angle twisted bilayer graphene
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Maximally Localized Wannier Orbitals, Interaction Models and Fractional Quantum Anomalous Hall Effect in Twisted Bilayer MoTe2
• UV fixed-point structure of the three-dimensional Thirring model
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Critical behavior of the (2+1)-dimensional Thirring model
• Interaction induced Dirac fermions from quadratic band touching in bilayer graphene
• Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Attractive electron-electron interactions from internal screening in magic angle twisted bilayer graphene
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• NanoSQUIDs: Basics & recent advances
• Observation of flat $\Gamma$ moiré bands in twisted bilayer WSe${}_2$
• Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization
• Tunable spin and valley excitations of correlated insulators in $\Gamma$-valley moiré bands
• Tunable $\Gamma -K$ Valley Populations in Hole-Doped Trilayer WSe${}_2$
• Competition of Density Waves and Superconductivity in Twisted Tungsten Diselenide
• Large $N_f$ quantum field theory
• Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited
• Quantum phase transitions in Dirac fermion systems
• Competing nodal d-wave superconductivity and antiferromagnetism
• Critical role of device geometry for the phase diagram of twisted bilayer graphene
• Numerical evidence of conformal phase transition in graphene with long-range interactions
• Metallic and Deconfined Quantum Criticality in Dirac Systems
• On the Critical Flavor Number in the 2+1$d$ Thirring Model
• Effective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model
• Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching
• Interacting models for twisted bilayer graphene: a quantum chemistry approach
• Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Momentum dependence of quantum critical Dirac systems
• Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses
• Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene
• Nematic Quantum Criticality in Dirac Systems
• Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe${}_2$
• Wilson-Fisher fixed points in presence of Dirac fermions
• Line of Fixed Points in Gross-Neveu Theories
• Realizing a tunable honeycomb lattice in ABBA-stacked twisted double bilayer WSe${}_2$
• Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
• Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Critical properties of metallic and deconfined quantum phase transitions in Dirac systems
• Twist-tuned quantum criticality in moiré bilayer graphene
• Pressure-tuned many-body phases through $\Gamma$-K valleytronics in moiré bilayer WSe${}_2$
• Ferromagnetic semimetal and charge-density wave phases of interacting electrons in a honeycomb moiré potential
• Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry
• Gross-Neveu-XY quantum criticality in moiré Dirac materials
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Superconductivity of Incoherent Electrons near the Relativistic Mott Transition in Twisted Dirac Materials

Cited by in corpus (1)

• Lattice Field Theory Analysis of the Chiral Heisenberg Model