Excitation Gap of Fractal Quantum Hall States in Graphene
arXiv:1503.07210 · doi:10.1088/0953-8984/28/1/015801
Abstract
In the presence of a magnetic field and an external periodic potential, the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this work, we develop a Hartree-Fock theory to deal with the electron-electron interaction in the Hofstadter's butterfly state in a finite-size graphene with periodic boundary conditions, in which we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation.
4 figures
References in corpus (12)
- The electronic properties of graphene
- STM Spectroscopy of ultra-flat graphene on hexagonal boron nitride
- Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
- Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
- The Fractional Quantum Hall States of Dirac Electrons in Graphene
- Hofstadter butterflies of bilayer graphene
- Controllable, driven phase transitions in the Fractional quantum Hall states in bilayer graphene
- Long range Coulomb interaction in bilayer graphene
- SO(5) symmetry in the quantum Hall effect in graphene
- Skyrme and Wigner crystals in graphene
- Revealing Hofstadter Spectrum for Graphene in a Periodic Potential
- Spin Transitions in Graphene Butterflies at an Integer Filling Factor