Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
arXiv:1303.6942 · doi:10.1126/science.1237240
Abstract
Van der Waals heterostructures comprise a new class of artificial materials formed by stacking atomically-thin planar crystals. Here, we demonstrate band structure engineering of a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally-aligned hexagonal boron nitride substrate. The spatially-varying interlayer atomic registry results both in a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. This interplay between short- and long-wavelength effects results in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality, both of which can be tuned by varying the interlayer alignment. Magnetocapacitance measurements reveal previously unobserved fractional quantum Hall states reflecting the massive Dirac dispersion that results from broken sublattice symmetry. At ultra-high fields, integer conductance plateaus are observed at non-integer filling factors due to the emergence of the Hofstadter butterfly in a symmetry-broken Landau level.
6+11 pages, 4 figures main text, 15 figures supplementary text
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Cited by in corpus (678)
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- Topological flat bands without magic angles in massive twisted bilayer graphenes
- Flat band topology of magic angle graphene on a transition metal dichalcogenide
- Triplet Pair-Density Wave Superconductivity on the -flux Square Lattice
- Computational Design of Moiré Assemblies Aided by Artificial Intelligence
- Narrow bands, electrostatic interactions and band topology in graphene stacks
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- Aligned Stacking of Nanopatterned 2D materials -- Towards 3D printing at atomic resolution
- Correlated states of a triangular net of coupled quantum wires: Implications for the phase diagram of marginally twisted bilayer graphene
- Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level
- Resolvent convergence to Dirac operators on planar domains
- Berry Phase Transition in Twisted Bilayer Graphene
- Valley-dependent spin-orbit torques in two dimensional hexagonal crystals
- The selective transfer of patterned graphene
- Structural, electronic, and optical properties of periodic graphene/h-BN van der Waals heterostructures
- Trions in MoS are quantum superpositions of intra- and intervalley spin states
- Chiral channel network from magnetization textures in 2D MnBi2Te4
- Duality between atomic configurations and Bloch states in twistronic materials
- Non-identical moiré twins in bilayer graphene
- Nano-scale displacement sensing based on Van der Waals interaction
- Electrical conductivity in the Hubbard model: orbital effects of magnetic field
- Interferometric 4D-STEM for Lattice Distortion and Interlayer Spacing Measurements in Bilayer and Trilayer Two-dimensional Materials
- Visualization of moiré magnons in monolayer ferromagnet
- SU(4) spin waves in the quantum Hall ferromagnet in graphene
- Raman scattering of graphene based systems in high magnetic fields
- Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point
- Moire miniband features in the angle-resolved photoemission spectra of graphene/hBN heterostructures
- Entropy spikes as a signature of Lifshitz transitions in the Dirac materials
- Optical spectroscopy of interlayer coupling in artificially stacked MoS2 layers
- Magnetoresistance of a three-dimensional Dirac gas
- Moiré phonons in graphene/hexagonal boron nitride moiré superlattice
- Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity
- Wigner localization in a graphene quantum dot with a mass gap
- Nonlinear optical conductivity of a generic two band systems, with application to doped and gapped graphene
- Spectroscopy of the Fractal Hofstadter Energy Spectrum
- Electronic structure of transferred graphene/h-BN van der Waals heterostructures with nonzero stacking angles by nano-ARPES
- HHG-laser-based time- and angle-resolved photoemission spectroscopy of quantum materials
- Localization physics in graphene Moire superlattices
- The optical response of artificially twisted MoS bilayers
- Moiré Landau fans and magic zeros
- Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene
- Anomalous Cyclotron Motion in Graphene Superlattice Cavities
- PT-symmetric optical superlattices
- Effects of Interaction in the Hofstadter regime of the honeycomb lattice
- Imaging bulk and edge transport near the Dirac point in graphene moiré superlattices
- Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands
- Higher-order Bragg gaps in the electronic band structure of bilayer graphene renormalized by recursive supermoiré potential
- Ultrafast carrier-coupled interlayer contraction, coherent intralayer motions, and phonon thermalization dynamics of black phosphorus
- Fractional Hofstadter States in Graphene on Hexagonal Boron Nitride
- Valley Order and Loop Currents in Graphene on Hexagonal Boron Nitride
- Cavity Moiré Materials: Controlling Magnetic Frustration with Quantum Light-Matter Interaction
- High resolution imaging of reconstructed domains and moire patterns in functional van der Waals heterostructure devices
- Magnetic field stabilized Wigner crystal states in a graphene moiré superlattice
- Global phase diagram of charge neutral graphene in the quantum Hall regime for generic interactions
- Multi-flavor Dirac fermions in Kekulé-distorted graphene bilayers
- Magneto-optical response of graphene: probing substrate interactions
- Quantum Geometric Exciton Drift Velocity
- Re-entrant magic-angle phenomena in twisted bilayer graphene in integer magnetic fluxes
- Impact of thermal annealing on graphene devices encapsulated in hexagonal boron nitride
- de Haas-van Alphen spectroscopy and fractional quantization of magnetic-breakdown orbits in moiré graphene
- High density carriers at a strongly coupled graphene-topological insulator interface
- Universal magnetic oscillations of DC conductivity in the incoherent regime of correlated systems
- Ni Foam Assisted Synthesis of High Quality Hexagonal Boron Nitride with Large Domain Size and Controllable Thickness
- Interlayer Transport through a Graphene / Rotated-Boron-Nitride / Graphene Heterostructure
- Heteromoiré Engineering on Magnetic Bloch Transport in Twisted Graphene Superlattices
- Inter-valley spiral order in the Mott insulating state of a heterostructure of trilayer graphene-boron nitride
- Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
- Dynamical signature of moire pattern in non-Hermitian ladder
- Scattering of magnons at graphene quantum-Hall-magnet junctions
- Topological phases of the dimerized Hofstadter butterfly
- Tunable Interband Transitions in Twisted h-BN/Graphene Heterostructures
- Negative quantum capacitance in graphene nanoribbons with lateral gates
- High-order minibands and interband Landau level reconstruction in graphene moire superlattice
- Deconfined Metal-Insulator Transitions in Quantum Hall Bilayers
- Sublattice symmetry breaking and ultra low energy excitations in Graphene-on-hBN Heterostructures
- Reentrant topological transitions with Majorana end states in 1D superconductors by lattice modulation
- Giant Hall photoconductivity in narrow-gapped Dirac materials
- Symmetry-broken Chern insulators in twisted double bilayer graphene
- Quantitative determination of interlayer electronic coupling at various critical points in bilayer MoS2
- Distinct photoluminescence in multilayered van der Waals heterostructures of MoS2/WS2/ReS2 and BN
- Magnonic Floquet Hofstadter Butterfly
- A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
- Two-dimensional spinodal interface in one-step grown graphene-molybdenum carbide heterostructures
- Cloning of Zero Modes in One-Dimensional Graphene Superlattices
- Transport Anisotropy in One-dimensional Graphene Superlattice in the High Kronig-Penney Potential Limit
- Electronic structure of graphene-nanoribbons on hexagonal boron nitride
- Optical Conductivity of Twisted Bilayer Graphene Near the Magic Angle
- Spin liquid in twisted homobilayers group-VI gichalcogenides
- General scatterings and electronic states in the quantum-wire network of moiré systems
- Angle-dependent electron confinement in graphene moiré superlattices
- Spectroscopic and DFT studies of graphene intercalation systems on metals
- Acoustomagnetoelectric effect in two-dimensional materials: Geometric resonances and Weiss oscillations
- Superconductivity in twisted multilayer graphene: a smoking gun in recent condensed matter physics
- Mass-profile quantum dots in graphene
- Thermodynamics of correlated electrons in a magnetic field
- Moiré effects in graphene--hBN heterostructures
- Single-Carrier Transport in Graphene/hBN Superlattices
- Impurity effects and bandgap-closing in massive Dirac systems
- Supercell-core software: a useful tool to generate an optimal supercell for vertically stacked nanomaterials
- Landau level collapse in graphene in the presence of in-plane radial electric and perpendicular magnetic fields
- Replica Higher-Order Topology of Hofstadter Butterflies in Twisted Bilayer Graphene
- Probing miniband structure and Hofstadter butterfly in gated graphene superlattices via magnetotransport
- Large Landau level splitting with tunable one-dimensional graphene superlattice probed by magneto capacitance measurements
- Calculations of Magnetic properties of metals through the magnetic-field-containing relativistic tight-binding approximation method
- High-energy Landau levels in graphene beyond nearest-neighbor hopping processes: Corrections to the effective Dirac Hamiltonian
- Observation of multi Dirac fermion cloning induced by moiré potential in graphene-SiC heterostructure
- Fractal defect states in the Hofstadter butterfly
- The effects of Moire lattice on the electronic properties of graphene
- Deterministic fabrication of graphene hexagonal boron nitride moiré superlattices
- Emergent QCD Quantum Phase Transitions of Fractional Chern Insulators
- Progress on band structure engineering of twisted bilayer and two-dimensional moiré heterostructures
- A non-invasive sub-surface electrical probe to encapsulated layers in van der Waals heterostructures
- Persistence of gaps in the interacting Hofstadter model
- Plasmons in realistic graphene/hexagonal boron nitride moiré patterns
- Thermopower in hBN/graphene/hBN superlattices
- Dimensional reduction from magnetic field in moiré superlattices
- Electrical valley filtering in transition metal dichalcogenides
- Deteriorated Interlayer Coupling in Twisted Bilayer Cobaltites
- Creating better superconductors by periodic nanopatterning
- Pressure-Driven Moiré Potential Enhancement and Tertiary Gap Opening in Graphene/h-BN Heterostructure
- Zero-energy modes and valley asymmetry in the Hofstadter spectrum of bilayer graphene van der Waals heterostructures with hBN
- Band gap formation in commensurate twisted bilayer graphene/hBN moiré lattices
- Playing graphene nanodrums: force spectroscopy of graphene on Ru(0001)
- Quantum Hall effect in epitaxial graphene with permanent magnets
- Interaction-induced metallic state in graphene on hexagonal boron nitride
- In-plane Chiral Tunneling and Out-of-plane Valley-polarized Quantum Tunneling in Twisted Graphene Trilayer
- Theory of ARPES in Graphene-Based Moiré Superlattices
- Enhanced valley polarization of graphene on hBN under circularly polarized light irradiation
- Ab Initio Modeling of Thermal Transport through van der Waals Materials
- One-dimensional Discrete Dirac Operators in a Decaying Random Potential I: Spectrum and Dynamics
- High-mobility compensated semimetals, orbital magnetization, and umklapp scattering in bilayer graphene moire superlattices
- Interaction-driven Spontaneous Ferromagnetic Insulating States with Odd Chern Numbers
- Moiré-Induced Transport in CVD-Based Small-Angle Twisted Bilayer Graphene
- THz conductivity of graphene on boron nitride
- Entropy Signatures of Topological Phase Transitions
- Umklapp electron-electron scattering in bilayer graphene moiré superlattice
- Topological van Hove singularities at phase transitions in Weyl metals
- Reconstruction-induced trefoil knot Fermi contour of Au(111)
- Aharonov-Bohm conductance oscillations and current equilibration in local n - p junctions in graphene
- Universal Moiré Buckling of Freestanding 2D Bilayers
- Electromagnetic field assisted exciton diffusion in moiré superlattices
- Experimental evidence of plasmarons and effective fine structure constant in electron-doped graphene/h-BN heterostructure
- Spontaneously-Induced Dirac Boundary State and Digitization in a Nonlinear Resonator Chain
- Quantum phases of two-component bosons on the Harper-Hofstadter ladder
- Translational symmetry breaking and the disintegration of the Hofstadter butterfly
- Seeing Hofstadter's Butterfly in Atomic Fermi Gases
- Non-adiabatic Hall effect at Berry curvature hot spot
- Impacts of in-plane strain on commensurate graphene/hexagonal boron nitride superlattices
- Velocity renormalization and Dirac cone multiplication in graphene superlattices with various barrier edge geometries
- Wiedemann-Franz law in graphene in the presence of a weak magnetic field
- Engineering Interlayer Hybridization in Energy Space via Dipolar Overlayers
- Hall viscosity and nonlocal conductivity of "gapped graphene"
- Wannier Diagram and Brown-Zak Fermions of Graphene on Hexagonal Boron-Nitride
- Deformable Molecular Crystal on 2D Crystal: A New Way to Build Nanoscale Periodic Trapping Sites for Interlayer Excitons
- Characterization of a graphene-hBN superlattice field effect transistor
- Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model
- Moiré Assisted Fractional Quantum Hall State Spectroscopy
- Absence of Edge States in The Valley Chern Insulator in Moiré Graphene
- Broken symmetries and Kohn's theorem in graphene cyclotron resonance
- Simulating and probing many-body quantum states in waveguide-QED systems with giant atoms
- Orbital magnetic moments in insulating Dirac systems: Impact on magnetotransport in graphene van der Waals heterostructures
- Theory of wavepacket transport under narrow gaps and spatial textures: non-adiabaticity and semiclassicality
- Chiral transport of hot carriers in graphene in the quantum Hall regime
- Fractional Quantum Hall Effect in Hofstadter Butterflies of Dirac Fermions
- Hierarchy of gaps and magnetic minibands in graphene in the presence of the Abrikosov vortex lattice
- Two-dimensional anisotropic Dirac materials PtN4C2 and Pt2N8C6 with quantum spin and valley Hall effects
- Site-selective insulating phase in twisted bilayer Hubbard model
- High-Quality BN-Graphene-BN Nanoribbon Capacitors Modulated by Graphene Side-gate Electrodes
- Imaging the Sub-Moiré Potential Landscape using an Atomic Single Electron Transistor
- Nanoscale view of engineered massive Dirac quasiparticles in lithographic superstructures
- Universal principles of moiré band structures
- Tracing out Correlated Chern Insulators in Magic Angle Twisted Bilayer Graphene
- Spin Transitions in Graphene Butterflies at an Integer Filling Factor
- Insulators at Fractional Fillings in Twisted Bilayer Graphene Partially Aligned to Hexagonal Boron Nitride
- Twist Angle-Dependent Bands and Valley Inversion in 2D Materials/hBN Heterostructures
- Chiral properties of topological-state loops
- The electronic structure and intervalley coupling of artificial and genuine graphene superlattice
- Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
- Many-body effects on Landau-level spectra and cyclotron resonance in graphene
- Designing Band Structures by Patterned Dielectric Superlattices
- Fractional quantum Hall coexistence phases in higher Landau levels of graphene
- Coulomb drag in graphene/hBN/graphene moiré heterostructures
- Competing Laughlin state and Wigner crystal in bilayer graphene
- Impurity induced current in a Chern insulator
- Localization, transport and edge states in a two-strand ladder network in an aperiodically staggered magnetic field
- Flat band and -pairing states in one-dimensional Moiré Hubbard model
- Magnetic oscillations of the anomalous Hall conductivity
- Topological multiferroic phases in the extended Kane-Mele-Hubbard Model in the Hofstadter regime
- Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian
- Gate-tunable exciton-polaron Rydberg series with strong roton effect
- Charge transport and electron-hole asymmetry in low-mobility graphene/hexagonal boron nitride heterostructures
- Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
- Non-linear Landau fan diagram for graphene electrons exposed to a moiré potential
- Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
- Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe bilayers
- Efficient algorithm to compute the Berry conductivity
- Spin and valley ordering of fractional quantum Hall states in monolayer graphene
- Notes on Quantum oscillation for Hatsugai-Kohmoto model
- Crystallographic orientation errors in mechanical exfoliation
- Moiré plane wave expansion model for scanning tunneling microscopy simulations of incommensurate two-dimensional materials
- Localization transitions and mobility edges in quasiperiodic ladder
- Low-temperature thermal transport in moiré superlattices
- Moiré induced electronic structure modifications in monolayer VS on Au(111)
- Equilibrium current distributions and W_{infinity} gauge theory in quantum Hall systems of conventional electrons and Dirac electrons
- Electronic structure of 2D van der Waals crystals and heterostructures investigated by spatially- and angle-resolved photoemission
- Radiation-induced magnetoresistance oscillations with massive Dirac fermions
- Metal-Insulator transition in strained Graphene: A quantum Monte carlo study
- Tuning equilibration of quantum Hall edge states in graphene - role of crossed electric and magnetic fields
- Long-wavelength gauge symmetry and translations in a magnetic field for Dirac electrons in graphene
- Three-dimensional non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly trios
- Integrated impedance bridge for absolute capacitance measurements at cryogenic temperatures and finite magnetic fields
- Massive Dirac Fermions Signal in Raman Spectrum of Graphene
- Coexisting Kagome and Heavy Fermion Flat Bands in YbCrGe
- Correlation effects in the capacitance of a gated carbon nanotube
- Chiral second-sound collective mode at the edge of 2D systems with nontrivial Berry curvature
- Dynamical preparation of an atomic condensate in a Hofstadter band
- Many-body effects, orbital mixing and cyclotron resonance in bilayer graphene
- Moiré pattern of spin liquid and Neel magnet in a Kitaev chain
- Electronic transport in a two-dimensional superlattice engineered via self-assembled nanostructures
- Fractal non-Fermi liquids from moiré-Hofstadter phonons
- Lattice Model For The Quantum Anomalous Hall Effect in Moiré Graphene
- Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
- Landau-level spectrum and the effect of spin-orbit coupling in monolayer graphene on transition metal dichalcogenides
- On dielectric screening in twisted double bilayer graphene
- Fractional quantum Hall effects in graphene on a h-BN substrate
- Hofstadter-Toda spectral duality and quantum groups
- Epitaxially Stabilized Oxide Composed of Twisted Triangular-Lattice Layers
- Geometric interference in a high-mobility graphene annulus p-n junction device
- Moiré superlattices of antimonene on a Bi(111) substrate with van Hove singularity and Rashba-type spin polarization
- High mobility transport in isotopically-enriched C and C exfoliated graphene
- Strong localization in a suspended monolayer graphene by intervalley scattering
- Review of the tight-binding method applicable to the properties of moiré superlattices
- Fractal Butterflies of Chiral Fermions in Bilayer Graphene: Phase Transitions and Emergent Properties
- Anomalous universal quantum transport in 2D asymptotic quasiperiodic system
- Magnetic Hofstadter cascade in a twisted semiconductor homobilayer
- Charge density wave with meronlike spin texture induced by a lateral superlattice in a two-dimensional electron gas
- Field-induced insulating states in a graphene superlattice
- Layer-dependent transport properties in the Moiré of strained homobilayer transition metal dichalcogenides
- A capacitance spectroscopy-based platform for realizing gate-defined electronic lattices
- Josephson junction arrays as a platform for topological phases of matter
- Topological phase diagram of twisted bilayer graphene as a function of the twist angle
- Zigzag edge states in graphene in the presence of in-plane electric field
- Spin-polarized superconducting phase in semiconducting system with next-nearest-neighbor hopping on the honeycomb lattice
- Persistent current distributions along a p-n junction in graphene in a magnetic field
- Spin and Valley Polarized Multiple Fermi Surfaces of α-RuCl/Bilayer Graphene Heterostructure
- Multiband ballistic transport and anisotropic commensurability magnetoresistance in antidot lattices of AB-stacked trilayer graphene
- Towards the growth of single-crystal boron nitride monolayer on Cu
- Generation and control of non-local chiral currents in graphene superlattices by orbital Hall effect
- Ferroelectric hysteresis in singly aligned graphene-hBN moiré superlattices
- Moiré patterns and inversion boundaries in graphene/hexagonal boron nitride bilayers
- Quantum and Thermal Fluctuations and Pair-breaking in Planar QED
- Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field
- Time-Resolved Photoemission Spectroscopy of Quantum Materials Using High Harmonic Generation: Probing Electron-Phonon Interactions and Non-Equilibrium Dynamics
- Modification of the magnetic and electronic properties of the graphene-Ni(111) interface via halogens intercalation
- Strong Correlations and Superconductivity in the Supermoiré Lattice
- Magnetic ordering tendencies in hexagonal boron nitride-bilayer graphene moiré structures
- Bloch and Bethe ansatze for the Harper model: A butterfly with a boundary
- Quantization and quantum oscillations of the sublattice charge order in Dirac insulators
- Room-temperature hybrid 2D-3D quantum spin system for enhanced magnetic sensing and many-body dynamics
- Moiré Imaging in Twisted Bilayer Graphene Aligned on Hexagonal Boron Nitride
- Flat-Band Driven Kondo Breakdown and Reentrant Effects in Heavy-Fermion Moiré Superlattices
- Morphology and magneto-transport in exfoliated graphene on ultrathin crystalline \b{eta}-Si3N4(0001)/Si(111)
- Topological invariant and domain connectivity in moiré materials
- Boosting proximity spin orbit coupling in graphene/WSe heterostructures via hydrostatic pressure
- Effective K valley Hamiltonian for TMD bilayers under pressure and application to twisted bilayers with pressure-induced topological phase transitions
- Controlled formation of an isolated miniband in bilayer graphene on an almost commensurate substrate
- Trigonal Quasicrystalline States in Rotated Double Moiré Superlattices
- Dynamic Moiré-like pattern in non-Hermitian Wannier-Stark ladder system
- Killing the Hofstadter butterfly, one bond at a time
- Effects of site asymmetry and valley mixing on Hofstadter-type spectra of bilayer graphene in a square-scatter array potential
- Magnon transmission across mono-layer graphene junction as a probe of electronic structure
- Hofstadter's Cocoon
- Hexagonal boron nitride/bilayer graphene moiré superlattices in the Dirac-material family: energy-band engineering and carrier doping by dual gating
- Lithography defined semiconductor moires with anomalous in-gap quantum Hall states
- Extended Haldane Model in The Dice Lattice: Multiple Flat-Band-Induced topological Transitions Revealed
- Faraday rotations, ellipticity and circular dichroism in the magneto-optical spectrum of moiré superlattices
- Theory of Hofstadter Superconductors
- Universal non-power-law scaling from a chaotic renormalisation group in the Harper-Hofstadter model
- Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux
- Hall field-induced magneto-oscillations near charge neutrality point in graphene
- Connection between the semiconductor--superconductor transition and the spin-polarized superconducting phase in the honeycomb lattice
- Coexisting Massive and Massless Dirac Fermions in Moire'-Reconstructed Bilayer Graphene
- Hofstadter Butterfly in Graphene
- Multiple Hot-Carrier Collection in Photo-Excited Graphene Moire Superlattices
- Critical magnetic flux for Weyl points in the three-dimensional Hofstadter model
- Uniquely identifying quantum Hall phases in charge neutral graphene
- Observation of Anomalous Moiré Patterns
- Non-Abelian Charge Transport in Three-Flavor Gauge Semimetal Model with Braiding Majoranas
- Phase transitions induced by a lateral superlattice potential in a two-dimensional electron gas
- Moiré potential, lattice corrugation, and band gap spatial variation in a twist-free MoS2/MoTe2 heterobilayer
- Mobility-edge-embedded Hofstadter butterfly from a tilt-induced quasiperiodic potential
- Dynamical symmetry breaking, magnetization and induced charge in graphene: Interplay between magnetic and pseudomagnetic fields
- Emergent electronic insulating states in a one-dimensional moiré superlattice
- Few-Mode and Anisotropic Quantum Transport in InSb Nanoribbons Using an All-van der Waals Material-Based Gate
- Paramagnetic singularities of the orbital magnetism in graphene with a moiré potential
- Quantum matter in ultrahigh magnetic fields
- Holographic entanglement renormalisation for fermionic quantum matter