Touching points in the energy band structure of bilayer graphene superlattices

Abstract

Energy band structure of the bilayer graphene superlattices with zero-averaged periodic $\delta$-function potentials are studied within the four-band continuum model. Using the transfer matrix method, studies are mainly focused on examining the touching points between adjacent minibands. For the zero-energy touching points the dispersion relation derived shows the Dirac-like double-cone shape with the group velocity which is periodic in the potential strength $P$ with the period of $\pi$ and becomes anisotropic at relatively large $P$. From the finite-energy touching points we have identified those located at zero wave-number. It was shown that for these finite-energy touching points the dispersion is direction-dependent in the sense that it is linear or parabolic in the direction parallel or perpendicular to the superlattice direction, respectively. We have also calculated the density of states and the conductivity that demonstrate a manifestation of the touching points of interest.

Submitted to JPCM

References in corpus (8)

• The electronic properties of graphene
• The electronic properties of bilayer graphene
• Anisotropic behaviors of massless Dirac fermions in graphene under periodic potential
• New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
• Cyclotron resonance in bilayer graphene
• Landau Levels and Quantum Hall Effect in Graphene Superlattices
• Measurement of the electronic compressibility of bilayer graphene
• Electron-electron interactions in graphene bilayers

Cited by in corpus (1)

• Zero and Finite Energy Dirac Points in the Energy Band Structure of Magnetic Bilayer Graphene Superlattices