  We simulate quantum transport between a graphene nanoribbon (GNR) and a
single-walled carbon nanotube (CNT) where electrons traverse vacuum gap between
them. The GNR covers CNT over a nanoscale region while their relative rotation
is 90 degrees, thereby forming a four-terminal crossbar where the bias voltage
is applied between CNT and GNR terminals. The CNT and GNR are chosen as either
semiconducting (s) or metallic (m) based on whether their two-terminal
conductance exhibits a gap as a function of the Fermi energy or not,
respectively. We find nonlinear current-voltage (I-V) characteristics in all
three investigated devices---mGNR-sCNT, sGNR-sCNT and mGNR-mCNT
crossbars---which are asymmetric with respect to changing the bias voltage from
positive to negative. Furthermore, the I-V characteristics of mGNR-sCNT
crossbar exhibits negative differential resistance (NDR) with low onset voltage
$V_\mathrm{NDR} \simeq 0.25$ V and peak-to-valley current ratio $\simeq 2.0$.
The overlap region of the crossbars contains only $\simeq 460$ carbon and
hydrogen atoms which paves the way for nanoelectronic devices ultrascaled well
below the smallest horizontal length scale envisioned by the international
technology roadmap for semiconductors. Our analysis is based on the
nonequilibrium Green function formalism combined with density functional theory
(NEGF-DFT), where we also provide an overview of recent extensions of NEGF-DFT
framework (originally developed for two-terminal devices) to multiterminal
devices.
