Abstract
Ideal Sharvin contact in a multimode regime shows the conductance $G\ensuremath{\approx}{G}_{\mathrm{Sharvin}}={g}_{0}{k}_{F}W/\ensuremath{\pi}$ (with ${g}_{0}$ the conductance quantum, ${k}_{F}$ the Fermi momentum, and $W$ the contact width) accompanied by strongly suppressed shot noise quantified by small Fano factor $F\ensuremath{\approx}0$. For ballistic graphene away from the charge-neutrality point, sub-Sharvin transport occurs, characterized by suppressed conductance $G\ensuremath{\approx}(\ensuremath{\pi}/4)\phantom{\rule{0.16em}{0ex}}{G}_{\mathrm{Sharvin}}$ and enhanced shot noise $F\ensuremath{\approx}1/8$. All these results can be derived from a basic model of quantum scattering, involving assumptions of infinite height and a perfectly rectangular shape of the potential barrier in the sample. Here we have carried out the numerical analysis of the scattering on a family of smooth barriers of finite height interpolating between parabolic and rectangular shapes. We find that, tuning the barrier shape, one can modify the asymmetry between electron- and hole-doped systems. For electronic dopings, the system crosses from the Sharvin to sub-Sharvin transport regime (indicated by both the conductance and the Fano factor) as the potential becomes closer to the rectangular shape. In contrast, for hole dopings, the conductivity is strongly suppressed when the barrier is parabolic and slowly converges to $G\ensuremath{\approx}(\ensuremath{\pi}/4)\phantom{\rule{0.16em}{0ex}}{G}_{\mathrm{Sharvin}}$ as the potential evolves toward a rectangular shape. In such a case, the Sharvin transport regime is inaccessible, shot noise is generically enhanced (with much slower convergence to $F\ensuremath{\approx}1/8$) compared to the electron-doped case, and aperiodic oscillations of both $G$ and $F$ are prominent due to the formation of quasibound states.
Highlights
Soon after the isolation of monolayer graphene [1], experimental and theoretical physicists have reexamined classical effects from mesoscopic physics [2,3,4,5,6,7,8,9,10]
Similar problems were addressed previously [32,34,35,36], but here we focus on the effects of the potential profile, which is gradually tuned from a parabolic to a rectangular shape, on the selected transport properties
We have identified sub-Sharvin transport regime in ballistic graphene, which manifests itself via the suppressed conductivity, G ≈ (π /4) GSharvin, and the enhanced shot noise, F ≈ 1/8, compared to standard quantum point contacts
Summary
Soon after the isolation of monolayer graphene [1], experimental and theoretical physicists have reexamined classical effects from mesoscopic physics [2,3,4,5,6,7,8,9,10]. In ballistic graphene ribbons [5] or constrictions [6] showing conductance quantization, electrical conductance approaches the fundamental upper bound given by the Sharvin formula [11,12]. A few years ago, ultraclean graphene samples exhibiting a viscous charge flow due to electron-electron interactions [13] allowed us to detect the conductance exceeding the Sharvin bound [14,15]. Since the spectrum of excitations in graphene consists of two conical bands and is described by a two-dimensional analog of the relativistic Dirac equation [16,17,18], several novel effects can be identified even at low temperatures, where interactions become negligible and ballistic (or LandauerBüttiker) transport regime is restored [19,20,21,22,23,24,25].
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