Conditions for Conductance Quantization in Mesoscopic Dirac Systems on the Examples of Graphene Nanoconstrictions

Ballistic transport through an impurity-free section of the Corbino disk in graphene is investigated by means of the Landauer-B"{u}ttiker formalism in the mesoscopic limit. In the linear-responce regime the conductance is quantized in steps close to integer multiples of $4e^2\mathrm{/}h$, yet Fabry-Perot oscillations are strongly suppressed. The quantization arises for small opening angles $\theta \lesssim \pi \mathrm{/}3$ and large radii ratios $R_2\mathrm{/}{R}_1\gtrsim 10$. We find that the condition for emergence of the $n$-th conductance step can be written as $\sqrt{n}\theta \mathrm{/}\pi \ll 1$. A brief comparison with the conductance spectra of graphene nanoribbons with parallel edges is also provided.