Generalized Wigner crystallization in moiré materials

Abstract

Recent experiments on the twisted transition metal dichalcogenide (TMD) material, $\mathrm{WS}{\mathrm{e}}_2/W{\mathrm{S}}_2$, have observed insulating states at fractional occupancy of the moiré bands. Such states were conceived as generalized Wigner crystals (GWCs). In this article, we investigate the problem of Wigner crystallization in the presence of an underlying (moiré) lattice. Based on the best estimates of the system parameters, we find a variety of homobilayer and heterobilayer TMDs to be excellent candidates for realizing GWCs. In particular, our analysis based on $r_s$ indicates that $\mathrm{MoS}{\mathrm{e}}_2$ (among the homobilayers) and $\mathrm{MoS}{\mathrm{e}}_2/WS{\mathrm{e}}_2$ or $\mathrm{Mo}{\mathrm{S}}_2/W{\mathrm{S}}_2$ (among the heterobilayers) are the best candidates for realizing GWCs. We also establish that due to larger effective mass of the valence bands, in general, hole-crystals are easier to realize that electron-crystals as seen experimentally. For completeness, we show that satisfying the Mott criterion $n_{\mathrm{Mott}}^{1/2}{a}_{\ast }=1$ requires densities nearly three orders of magnitude larger than the maximal density for GWC formation. This indicates that for the typical density of operation, HoM or HeM systems are far from the Mott insulating regime. These crystals realized on a moiré lattice, unlike the conventional Wigner crystals, are incompressible due the gap arising from pinning with the lattice. Finally, we capture this many-body gap by variationally renormalizing the dispersion of the vibration modes. We show these low-energy modes, arising from coupling of the WC with the moiré lattice, can be effectively modeled as a Sine-Gordon theory of fluctuations.

arXiv commentv1: 12 pages, 4 figures; v2: new refs added

References in corpus (59)

• 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
• Observation of tightly bound trions in monolayer MoS2
• Ultrafast Charge Transfer in Atomically Thin MoS2/WS2 Heterostructures
• Tuning superconductivity in twisted bilayer graphene
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Graphene bilayer with a twist: electronic structure
• Signatures of moiré-trapped valley excitons in MoSe${}_2$/WSe${}_2$ heterobilayers
• Observation of Moiré Excitons in WSe2/WS2 Heterostructure Superlattices
• k.p theory for two-dimensional transition metal dichalcogenide semiconductors
• Optical detection of Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices
• Magic continuum in twisted bilayer WSe2
• Magic Angle Spectroscopy
• Resonantly hybridised excitons in moiré superlattices in van der Waals heterostructures
• Topological insulators in twisted transition metal dichalcogenide homobilayers
• Hubbard model physics in transition metal dichalcogenide moiré bands
• Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane
• Imaging Electronic Correlations in Twisted Bilayer Graphene near the Magic Angle
• Elastic theory of flux lattices in presence of weak disorder
• Abundance of correlated insulating states at fractional fillings of WSe${}_2$/WS${}_2$ moiré superlattices
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Untying the insulating and superconducting orders in magic-angle graphene
• Electronic crystals: an experimental overview
• Cascade of electronic transitions in magic-angle twisted bilayer graphene
• Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene
• Mapping the twist angle and unconventional Landau levels in magic angle graphene
• Moiré superlattice in a MoSe${}_2$/hBN/MoSe${}_2$ heterostructure: from coherent coupling of inter- and intra-layer excitons to correlated Mott-like states of electrons
• Phase diagrams of flux lattices with disorder
• Evidence for Fast Interlayer Energy Transfer in MoSe2/WS2 Heterostructures
• Large capacitance enhancement and negative compressibility of two-dimensional electronic systems at LaAlO${}_3$/SrTiO${}_3$ interfaces
• Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation
• Mermin-Wagner fluctuations in 2D amorphous solids
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Moiré quantum chemistry: charge transfer in transition metal dichalcogenide superlattices
• Moiré Intralayer Excitons in a MoSe${}_2$/MoS${}_2$ Heterostructure
• Electronic Compressibility of Magic-Angle Graphene Superlattices
• Quantum Phase Diagram of a Moiré-Hubbard Model
• Coulomb Correlations and the Wigner-Mott Transition
• Pinned Wigner Crystals
• Microwave Resonance of 2D Wigner Crystal around integer Landau fillings
• MoS2: a Choice Substrate for Accessing and Tuning the Electronic Properties of Graphene
• Sharp Tunneling Resonance from the Vibrations of an Electronic Wigner Crystal
• Electronic, optical and transport properties of van der Waals Transition-metal Dichalcogenides Heterostructures: A First-principle Study
• Anomalously large capacitance of a plane capacitor with a two-dimensional electron gas
• Charge Transfer Excitations, Pair Density Waves, and Superconductivity in Moiré Materials
• Dynamical screening in monolayer transition-metal dichalcogenides and its manifestations in the exciton spectrum
• Lindemann melting criterion in two dimensions
• Pressure-Induced Metal-Insulator Transition in Twisted Bi-layer Graphene
• Localized interlayer complexes in heterobilayer transition metal dichalcogenides
• Influence of long-range interactions on charge ordering phenomena on a square lattice
• Thermal and quantum melting phase diagrams for a magnetic-field-induced Wigner solid
• Transport across twist angle domains in moiré graphene
• Theory of moiré localized excitons in transition-metal dichalcogenide heterobilayers
• Wigner crystallization in transition metal dichalcogenides: A new approach to correlation energy
• Theory of the collective magnetophonon resonance and melting of the field-induced Wigner solid
• Zero field Wigner crystal
• Quantum Phase Transitions to Charge Order and Wigner Crystal Under Interplay of Lattice Commensurability and Long-Range Coulomb Interaction
• Microwave spectroscopic studies of the bilayer electron solid states at low Landau filling in a wide quantum well

Cited by in corpus (46)

• Magic in twisted transition metal dichalcogenide bilayers
• Observation of Wigner crystal of electrons in a monolayer semiconductor
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Electronic structures, charge transfer and charge orders in twisted transition metal dichalcogenide bilayers
• Correlated insulator of excitons in WSe2/WS2 moiré superlattices
• Excitonic and valleytronic signatures of correlated states at fractional fillings of a moiré superlattice
• Maximally Localized Wannier Orbitals, Interaction Models and Fractional Quantum Anomalous Hall Effect in Twisted Bilayer MoTe2
• Charge-order-enhanced capacitance in semiconductor moiré superlattices
• Spin-Orbit Coupling in Transition Metal Dichalcogenide Heterobilayer Flat Bands
• Topological exact flat bands in two dimensional materials under periodic strain
• Multiple Chern bands in twisted MoTe${}_2$ and possible non-Abelian states
• Tunable quantum criticalities in an isospin extended Hubbard model simulator
• Magnetism and Quantum Melting in Moiré-Material Wigner Crystals
• Melting of generalized Wigner crystals in transition metal dichalcogenide heterobilayer Moiré systems
• Hofstadter states and reentrant charge order in a semiconductor moiré lattice
• Metal-insulator transition in transition metal dichalcogenide heterobilayer: accurate treatment of interaction
• Theory of a continuous bandwidth-tuned Wigner-Mott transition
• Nearly flat Chern band in periodically strained monolayer and bilayer graphene
• Strong-coupling phases of trions and excitons in electron-hole bilayers at commensurate densities
• Nonlinear Dynamics, Avalanches and Noise for Driven Wigner Crystals
• Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems
• Probing magnetism in moiré heterostructures with quantum twisting microscopes
• Vortex Dynamics, Pinning, and Magic Angles on Moiré Patterns
• Pseudogap metal and magnetization plateau from doping moiré Mott insulator
• Doping a Wigner-Mott insulator: Exotic charge orders in transition-metal dichalcogenide moiré heterobilayers
• Competing Generalized Wigner Crystal States in Moiré Heterostructures
• Spin-polarons and ferromagnetism in doped dilute Wigner-Mott insulators
• Phonons of electronic crystals in two-dimensional semiconductor moiré patterns
• Chiral superconductivity from spin polarized Chern band in twisted MoTe${}_2$
• Band structure and band topology in twisted homotrilayer transition metal dichalcogenides
• Dominant 1/3-filling Correlated Insulator States and Orbital Geometric Frustration in Twisted Bilayer Graphene
• Two-dimensional electrons at mirror and twistronic twin boundaries in van der Waals ferroelectrics
• Quantum melting of generalized electron crystal in twisted bilayer MoSe2
• Stability of Wigner crystals and Mott insulators in twisted moiré structures
• Continuous Wigner-Mott transition at $\nu =1/5$
• Magnetic properties of moiré quantum dot arrays
• Spin susceptibility in interacting two-dimensional semiconductors and bilayer systems at first order: Kohn anomalies and spin density wave ordering
• The Wigner localization of interacting electrons in a one-dimensional harmonic potential
• Origin and stability of generalized Wigner crystallinity in triangular moiré systems
• Moiré excitons in generalized Wigner crystals
• Importance of electron-phonon coupling near the electron-liquid to Wigner-crystal transition in two-dimensional atomically thin materials
• Magnetism from multiparticle ring exchange in moiré Wigner crystals
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux
• Spin-textured Chern bands in AB-stacked transition metal dichalcogenide bilayers
• Crystallizing electrons with artificially patterned lattices
• Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe${}_2$