Touching points in the energy band structure of bilayer graphene superlattices

TL;DR

This paper investigates the energy band structure of bilayer graphene superlattices with periodic delta potentials, revealing Dirac-like touching points and their effects on electronic properties such as density of states and conductivity.

Contribution

It provides a detailed analysis of touching points in the miniband structure of bilayer graphene superlattices, including their dispersion relations and anisotropic behaviors, using the transfer matrix method.

Findings

Zero-energy touching points exhibit Dirac-like dispersion with periodic group velocity.

Finite-energy touching points are located at zero wave-number with direction-dependent dispersion.

Density of states and conductivity are influenced by the presence of touching points.

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.