Orbital quantization in a system of edge Dirac fermions in nanoperforated graphene

The dependence of the electric resistance $R$ of nanoperforated graphene samples on the position of the Fermi level $E_{\text{F}}$, which is varied by the gate voltage $V_g$, has been studied. Nanoperforation has been performed by irradiating graphene samples on a $\mathrm{Si}/\mathrm{SiO}_2$ substrate by heavy (xenon) or light (helium) ions. A series of regular peaks have been revealed on the $R(V_g)$ dependence at low temperatures in zero magnetic field. These peaks are attributed to the passage of $E_{\text{F}}$ through an equidistant set of levels formed by orbitally quantized states of edge Dirac fermions rotating around each nanohole. The results are in agreement with the theory of edge states for massless Dirac fermions.