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We present a method to simulate ballistic quantum transport in one-dimensional nanostructures, such as extremely scaled transistors, with a channel of nanowires or nanoribbons. In contrast to most popular approaches, we develop our method employing an accurate plane-wave basis at the atomic scale while retaining the numerical efficiency of a localized (tight-binding) basis at larger scales. At the core of our method is a finite-element expansion, where the finite element basis is enriched by a set of Bloch waves at high-symmetry points in the Brillouin zone of the crystal. We demonstrate the accuracy and efficiency of our method with the self-consistent simulation of ballistic transport in graphene nanoribbon FETs. 

One-dimensional (1D) materials present the ultimate limit of extremely scaled devices by virtue of their spatial dimensions and the excellent electrostatic gate control in the transistors based on these materials. Among 1D materials, graphene nanoribbon (a-GNR) prove to be very promising due to high carrier mobility and the prospect of reproducible fabrication process [1]. Two popular approaches to study atomistically the electronic properties expand the wavefunction on either a plane-wave basis set, or through the linear combination of localized atomic orbitals. The use of localized orbitals, especially in the tight-binding (TB) approximation, enables highly scalable numerical implementations. Through continuous improvements in methods and computational capabilities, atomistically describing electronic transport in devices containing more than thousands of atoms has become feasible. Plane waves, while not as scalable, are very popular as the basis of accurate ab-initio software [2]. However, for modeling of transport through larger devices, the computational burden prohibits the direct use of a plane wave basis [3]. Here, we demonstrate a study of the transport characteristics of nanoribbon-based devices using a hybrid approach that combines the benefits of plane waves while retaining the efficiency provided by the TB approximation.