Quantum oscillations in graphene in the presence of disorder and interactions

Abstract

Quantum oscillations in graphene is discussed. The effect of interactions are addressed by Kohn's theorem regarding de Haas-van Alphen oscillations, which states that electron-electron interactions cannot affect the oscillation frequencies as long as disorder is neglected and the system is sufficiently screened, which should be valid for chemical potentials not very close to the Dirac point. We determine the positions of Landau levels in the presence of potential disorder from exact transfer matrix and finite size diagonalization calculations. The positions are shown to be unshifted even for moderate disorder; stronger disorder, can, however, lead to shifts, but this also appears minimal even for disorder width as large as one-half of the bare hopping matrix element on the graphene lattice. Shubnikov-de Haas oscillations of the conductivity are calculated analytically within a self-consistent Born approximation of impurity scattering. The oscillatory part of the conductivity follows the widely invoked Lifshitz-Kosevich form when certain mass and frequency parameters are properly interpreted.

Appendix A was removed, as the content of it is already contained in Ref. 17. Thanks to M. A. H. Vozmediano

References in corpus (4)

• The electronic properties of graphene
• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• High temperature superconductivity: from complexity to simplicity
• Dissipation and criticality in the lowest Landau level of graphene

Cited by in corpus (5)

• Key issues in theories of high temperature superconductors
• Resolution of two apparent paradoxes concerning quantum oscillations in underdoped high-$T_c$ superconductors
• Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity
• Quantum transport in chemically functionalized graphene at high magnetic field: Defect-Induced Critical States and Breakdown of Electron-Hole Symmetry
• A theorem of Kohn applied to quantum oscillations in Cuprates