Theory of the sub-Sharvin charge transport in graphene disks

Abstract

Ballistic graphene samples in a multimode regime show the sub-Sharvin charge transport, characterized by the conductance reduced by a factor of $\pi/4$ comparing to standard Sharvin contacts in two-dimensional electron gas, and the shot-noise power enhanced up to $F\approx{}1/8$ (with $F$ the Fano factor) [Phys. Rev. B 104, 165413 (2021)]. Here we consider the disk-shaped (Corbino) setup in graphene, with inner radius $r_1$ and outer radius $r_2$, finding that the multimode conductance is slightly enhanced for any $r_1<r_2$, reaching $(4\!-\!\pi)\approx{}0.8684$ of the Sharvin value for $r_1\ll{}r_2$. At the same limit, the Fano factor is reduced, approaching $(9\pi-28)/(12-3\pi)\approx{}0.1065<1/8$. Closed-form approximating expressions for any $r_1/r_2$ ratio are derived supposing incoherent scattering of Dirac fermions on asymmetric double barrier and compared with exact numerical results following from the mode-matching method. Sub-Sharvin values are restored in the narrow-disk limit $r_1/r_2\rightarrow{}1$. For experimentally-accessible radii ratios $0.5\leqslant{}r_1/r_2\leqslant{}0.8$ both the conductance and the Fano factor are noticeably closer to the values predicted for the $r_1\ll{}r_2$ limit, yet still differ from standard Sharvin transport characteristics. The system behavior upon tuning the electrostatic potential barrier from a rectangular to parabolic shape is studied numerically, and the crossover from the sub-Sharvin to standard Sharvin transport regime is demonstrated. Implications for a finite section of the disk are also discussed.