Dirac electrons in a Kronig-Penney potential: Dispersion relation and transmission periodic in the strength of the barriers

Abstract

The transmission $T$ and conductance $G$ through one or multiple one-dimensional, $\ensuremath{\delta}$-function barriers of two-dimensional fermions with a linear energy spectrum are studied. $T$ and $G$ are periodic functions of the strength $P$ of the $\ensuremath{\delta}$-function barrier $V(x,y)/\ensuremath{\hbar}{v}_{F}=P\ensuremath{\delta}(x)$. The dispersion relation of a Kronig-Penney (KP) model of a superlattice is also a periodic function of $P$ and causes collimation of an incident electron beam for $P=2\ensuremath{\pi}n$ and $n$ integer. For a KP superlattice with alternating sign of the height of the barriers the Dirac point becomes a Dirac line for $P=(n+1/2)\ensuremath{\pi}$.