Kronig-Penney model on bilayer graphene: spectrum and transmission periodic in the strength of the barriers

TL;DR

This paper investigates the spectral and transmission properties of bilayer graphene with periodic delta-function potential barriers, revealing periodic behavior in barrier strength and the emergence of Dirac points or energy gaps depending on the potential.

Contribution

It introduces a detailed analysis of the Kronig-Penney model in bilayer graphene, highlighting the periodic dependence of spectrum and conductance on barrier strength P, including bound states and band structure modifications.

Findings

Transmission is periodic in P with period π.

Bound states exist along the potential barrier for certain P.

Spectrum exhibits Dirac points or energy gaps depending on P.

Abstract

We show that the transmission through single and double {\delta}-function potential barriers of strength P in bilayer graphene is periodic in P with period {\pi}. For a certain range of P values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behaviour is found for the conductance. The spectrum of a periodic succession of {\delta}-function barriers (Kronig-Penney model) in bilayer graphene is periodic in P with period 2{\pi}. For P smaller than a critical value, the spectrum exhibits two Dirac points while for P larger than this value an energy gap opens. These results are extended to the case of a superlattice of {\delta}-function barriers with P alternating in sign between successive barriers; the corresponding spectrum is periodic in P with period {\pi}.