The transmission $T$ and conductance $G$ through one or multiple one-dimensional, $\delta$-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 $\delta$-function barrier $V\left(x,y\right)/\hslash v_F=P\delta \left(x\right)$. 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 $P=2\pi n$ and $n$ integer. For a KP superlattice with alternating sign of the height of the barriers the Dirac point becomes a Dirac line for $P=\left(n+1/2\right)\pi$.

• Received 23 October 2009

DOI:https://doi.org/10.1103/PhysRevB.80.205415