Theory of the sub-Sharvin charge transport in graphene disks

Adam Rycerz; Piotr Witkowski

doi:10.1103/PhysRevB.106.155428

paper

Theory of the sub-Sharvin charge transport in graphene disks

arXiv:2207.08239 · doi:10.1103/PhysRevB.106.155428

Abstract

Ballistic graphene samples in a multimode regime show the sub-Sharvin charge transport, characterized by the conductance reduced by a factor of $π /4$ 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 $(4 - π) \approx 0.8684$ of the Sharvin value for $r_{1} ≪ r_{2}$ . At the same limit, the Fano factor is reduced, approaching $(9 π - 28) / (12 - 3 π) \approx 0.1065 < 1/8$ . 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 $r_{1} / r_{2} \to 1$ . For experimentally-accessible radii ratios $0.5 ⩽ r_{1} / r_{2} ⩽ 0.8$ both the conductance and the Fano factor are noticeably closer to the values predicted for the $r_{1} ≪ r_{2}$ 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.

Refs. added; new Sec. V on transport via a finite disk section

Theory of the sub-Sharvin charge transport in graphene disks

Abstract

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