Quantization and quantum oscillations of the sublattice charge order in Dirac insulators

Abstract

We report the quantization, quantum oscillations, and singular behavior of sublattice symmetry-breaking sublattice charge order (SCO) in two-dimensional Dirac insulators at charge neutrality under perpendicular magnetic fields $B$. SCO is induced by staggered sublattice potentials, such as those originating from substrates, strains, hydrogenation, and chemical doping. In small non-quantizing magnetic fields that result in less than a flux quantum threading the system, and small sublattice symmetry breaking potentials, SCO exhibits perturbative singular magnetic field dependence, $\sim |B|$, originating from hopping between neighboring sites of the same sublattice. At intermediate magnetic fields, when the cyclotron gap between the zeroth Landau level and the first Landau level, ${\omega }_c$, is smaller than the sublattice potential, ${\omega }_c\lesssim \Delta$, SCO shows $\text{universally}$ quantized plateaus owing to discrete Landau-level degeneracy. As the magnetic flux increases by one flux quantum, one electron (per spin) is transferred from the sublattice with a higher chemical potential to the sublattice with a lower chemical potential. One electron transfer between sublattices per flux quantum results from the sublattice polarization of the zeroth Landau level in gapped Dirac materials, realizing the topological Thouless pump effect. At stronger magnetic fields, ${\omega }_c\gtrsim \Delta$, corresponding to integer quantum Hall regimes, SCO displays singularities based on the physics of quantum magneto-oscillations. Our findings suggest new ways to experimentally detect the presence of the energy gap in Dirac materials, irrespective of the gap size.

19 pages, 13 figures

References in corpus (55)

• The electronic properties of graphene
• Control of graphene's properties by reversible hydrogenation
• Substrate-induced band gap opening in epitaxial graphene
• New Perspectives for Rashba Spin-Orbit Coupling
• Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
• Substrate-induced bandgap in graphene on hexagonal boron nitride
• Unconventional Integer Quantum Hall effect in graphene
• Valley Dependent Optoelectronics from Inversion Symmetry Breaking
• Molecular Doping of Graphene
• Electronic Properties of Graphene in a Strong Magnetic Field
• Commensurate-incommensurate transition for graphene on hexagonal boron nitride
• Hydrogen on graphene: Electronic structure, total energy, structural distortions, and magnetism from first-principles calculations
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Electronic structure of epitaxial graphene layers on SiC: effect of the substrate
• Electrical Tuning of Valley Magnetic Moment via Symmetry Control
• Imaging Quasiparticle Interference in Bi2Sr2CaCu2O8+d
• Scanning Tunneling Spectroscopy of Graphene on Graphite
• Giant and nonreciprocal second harmonic generation from layered antiferromagnetism in bilayer CrI3
• Electronic properties of graphene-based bilayer systems
• Gate-tunable Topological Valley Transport in Bilayer Graphene
• The Ground State of a Two-Dimensional Electron Liquid in a Weak Magnetic Field
• Engineering symmetry breaking in two-dimensional layered materials
• Electron states of mono- and bilayer graphene on SiC probed by STM
• Scanning tunneling spectroscopy of inhomogeneous electronic structure in monolayer and bilayer graphene on SiC
• Thouless pumping and topology
• Tunable crystal symmetry in graphene-boron nitride heterostructures with coexisting moiré superlattices
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations II: transport properties
• Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet
• Quantum oscillations without a Fermi surface and the anomalous de Haas-van Alphen effect
• Accurate determination of electron-hole asymmetry and next-nearest neighbor hopping in graphene
• The energy resolution function of a tunnel junction
• Spontaneous formation of a non-uniform chiral spin liquid in moat-band lattices
• Absence of Bose condensation on lattices with moat bands
• Spectroscopy of Twisted Bilayer Graphene Correlated Insulators
• Statistical transmutation in Floquet driven optical lattices
• Unexpected z-Direction Ising Antiferromagnetic Order in a frustrated Spin-1/2 $J_1-J_2$ XY Model on the Honeycomb Lattice
• Valley symmetry breaking and gap tuning in graphene by spin doping
• Topological spin ordering via Chern-Simons superconductivity
• Theory of competing Chern-Simons orders and emergent phase transitions
• Crossover from weak localization to Shubnikov-de Haas oscillations in a high mobility 2D electron gas
• Quantum Oscillations in the Magnetisation and Density of States of Insulators
• Spectroscopy of the Fractal Hofstadter Energy Spectrum
• Antiferromagnetic magnons from fractionalized excitations
• Smearing of the 2D Kohn anomaly in a nonquantizing magnetic field: Implications for the interaction effects
• Helical spin liquid in a triangular XXZ magnet from Chern-Simons theory
• Is the composite fermion state of Graphene a doped Chern insulator?
• Chiral spin liquid state of strongly interacting bosons with a moat dispersion: a Monte Carlo simulation
• Magneto-oscillations due to electron-electron interactions in the ac conductivity of a 2D electron gas
• High spatial resolution charge sensing of quantum Hall states
• Deformation of graphene sheet: Interaction of fermions with phonons
• Interaction effects in 2D electron gas in a random magnetic field: Implications for composite fermions and quantum critical point
• Persistent Friedel oscillations in Graphene due to a weak magnetic field
• Zero-bias tunneling anomaly in a clean 2D electron gas caused by smooth density variations