Quantum oscillations of magnetization in the tight-binding electrons on honeycomb lattice

Abstract

We show that the new quantum oscillations of the magnetization can occur when the Fermi surface consists of points (massless Dirac points) or even when the chemical potential is in a energy gap by studying the tight-binding electrons on a honeycomb lattice in a uniform magnetic field. The quantum oscillations of the magnetization as a function of the inverse magnetic field are known as the de Haas-van Alphen (dHvA) oscillations and the frequency is proportional to the area of the Fermi surface. The dominant period of the new oscillations corresponds to the area of the first Brillouin zone and its phase is zero. The origin of the new quantum oscillations is the characteristic magnetic field dependence of the energy known as the Hofstadter butterfly and the Harper broadening of Landau levels. The new oscillations are not caused by the crossing of the chemical potential and Landau levels, which is the case in the dHvA oscillations. The new oscillations can be observed experimentally in systems with large supercell such as graphene antidot lattice or ultra cold atoms in optical lattice at an external magnetic field of a few Tesla when the area of the supercell is ten thousand times larger than that of graphene.

arXiv comment6 pages, 8 Postscript figures

References in corpus (14)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Phase analysis of quantum oscillations in graphite
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations
• Quantum Hall effect and the topological number in graphene
• Quantum Hall effect in multilayered massless Dirac fermion systems with tilted cones
• de Haas-van Alphen Effect in the Two-Dimensional and the Quasi-Two-Dimensional Systems
• Semiclassical analysis and the magnetization of the Hofstadter model
• Periodic Landau gauge and Quantum Hall effect in twisted bilayer graphene
• Hofstadter butterflies and magnetically induced band gap quenching in graphene antidot lattices
• Probing the Hofstadter butterfly with the quantum oscillation of magnetization

Cited by in corpus (15)

• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices
• Theory of Quantum Oscillations of Magnetization in Kondo Insulators
• Intrinsic bulk quantum oscillations in a bulk unconventional insulator SmB${}_6$
• Enhanced quantum oscillations in Kondo insulators
• Particle-Hole Asymmetry in Gapped Topological Insulator Surface States
• Three-quarter Dirac points, Landau levels and magnetization in $\alpha$-(BEDT-TTF)${}_2$I${}_3$
• Magnetic oscillations in a model of graphene
• Magnetization of the Metallic Surface States in Topological Insulators
• Inversion and magnetic quantum oscillations in symmetric periodic Anderson model
• Saddle point anomaly of Landau levels in graphenelike structures
• Magnetizations and de Haas-van Alphen oscillations in massive Dirac fermions
• Quantized Hall conductance in graphene by nonperturbative magnetic-field-containing relativistic tight-binding approximation method
• Orthonormal wave functions for periodic fermionic states under an applied magnetic field
• Anomalous Landau levels and quantum oscillation in rotation-invariant insulators