Roughness in graphene is known to contribute to scattering effects which lower carrier mobility. Encapsulating graphene in hexagonal boron nitride (hBN) leads to a significant reduction in roughness and has become the de facto standard method for producing high-quality graphene devices. We have fabricated graphene samples encapsulated by hBN that are suspended over apertures in a substrate and used noncontact electron diffraction measurements in a transmission electron microscope to measure the roughness of encapsulated graphene inside such structures. We furthermore compare the roughness of these samples to suspended bare graphene and suspended graphene on hBN. The suspended heterostructures display a root mean square (rms) roughness down to 12 pm, considerably less than that previously reported for both suspended graphene and graphene on any substrate and identical within experimental error to the rms vibrational amplitudes of carbon atoms in bulk graphite. Our first-principles calculations of the phonon bands in graphene/hBN heterostructures show that the flexural acoustic phonon mode is localized predominantly in the hBN layer. Consequently, the flexural displacement of the atoms in the graphene layer is strongly suppressed when it is supported by hBN, and this effect increases when graphene is fully encapsulated.
Ideal graphene antidot lattices are predicted to show promising band gap behavior (i.e., E G 500 meV) under carefully specified conditions. However, for the structures studied so far this behavior is critically dependent on superlattice geometry and is not robust against experimentally realistic disorders. Here we study a rectangular array of triangular antidots with zigzag edge geometries and show that their band gap behavior qualitatively differs from the standard behavior which is exhibited, e.g., by rectangular arrays of armchair-edged triangles. In the spin unpolarized case, zigzag-edged antidots give rise to large band gaps compared to armchair-edged antidots, irrespective of the rules which govern the existence of gaps in armchair-edged antidot lattices. In addition the zigzag-edged antidots appear more robust than armchair-edged antidots in the presence of geometrical disorder. The inclusion of spin polarization within a mean-field Hubbard approach gives rise to a large overall magnetic moment at each antidot due to the sublattice imbalance imposed by the triangular geometry. Half-metallic behavior arises from the formation of spin-split dispersive states near the Fermi energy, reducing the band gaps compared to the unpolarized case. This behavior is also found to be robust in the presence of disorder. Our results highlight the possibilities of using triangular perforations in graphene to open electronic band gaps in systems with experimentally realistic levels of disorder, and furthermore, of exploiting the strong spin dependence of the system for spintronic applications.
Zigzag edges of the honeycomb structure of graphene exhibit magnetic polarization, making them attractive as building blocks for spintronic devices. Here, we show that devices with zigzag-edged triangular antidots perform essential spintronic functionalities, such as spatial spin splitting or spin filtering of unpolarized incoming currents. Near-perfect performance can be obtained with optimized structures. The device performance is robust against substantial disorder. The gate-voltage dependence of transverse resistance is qualitatively different for spin-polarized and spin-unpolarized devices, and can be used as a diagnostic tool. Importantly, the suggested devices are feasible within current technologies. DOI: 10.1103/PhysRevB.95.121406 Introduction. The weak intrinsic spin-orbit coupling and long spin diffusion lengths suggest graphene as an ideal spintronic material [1][2][3][4][5][6][7][8][9][10]. Spin splitting or filtering in graphene is predicted for half-metallic nanoribbons [2,[11][12][13] [24][25][26], and, in particular, nanostructured zigzag (zz)-edged devices [11][12][13]15,16,[27][28][29][30][31][32][33] are among the proposed graphene-based half metals. Spin filters have been proposed using triangular dots [15,31] or perforations [29] with many similarities, e.g., low-energy localized magnetic states and a net sublattice imbalance. However, perforations, or antidots [34][35][36], have the advantage over dots of being embedded in the graphene sheet which allows a wide range of spin-dependent transport properties. Although signatures of localized magnetic states have been detected [37][38][39], spin manipulation in graphene-based half metals has yet to be realized in experiments.In this Rapid Communication, we investigate the transport properties of graphene devices with embedded zz-edged triangular antidots. Such devices are within the reach of stateof-the-art lithographic methods: Triangular holes in graphene have recently been fabricated [40], and experiments suggest the possibility of zz-etched nanostructures [41,42]. Another possibility is to employ a lithographic mask of patterned hexagonal boron nitride, which naturally etches into zz-edged triangular holes [43,44]. The zz-edged structures support local ferromagnetic moments [3], however, global ferromagnetism is induced when the overall sublattice symmetry of the edges is broken [11][12][13]16,27,28,45]. This occurs for zzedged triangles [15,[29][30][31][32][33]. We have recently discussed the electronic structure of triangular graphene antidot lattices (GALs) [33]-here, we focus on transport through devices
The outset of realistic rendering is a desire to reproduce the appearance of the real world. Rendering techniques therefore operate at a scale corresponding to the size of objects that we observe with our naked eyes. At the same time, rendering techniques must be able to deal with objects of nearly arbitrary shapes and materials. These requirements lead to techniques that oftentimes leave the task of setting the optical properties of the materials to the user. Matching the appearance of real objects by manual adjustment of optical properties is however nearly impossible. We can render objects with a plausible appearance in this way but cannot compare the appearance of a manufactured item to that of its digital twin. This is especially true in the case of translucent objects, where we need more than a goniometric measurement of the optical properties. In this survey, we provide an overview of forward and inverse models for acquiring the optical properties of translucent materials. We map out the efforts in graphics research in this area and describe techniques available in related fields. Our objective is to provide a better understanding of the tools currently available for appearance specification when it comes to digital representations of real translucent objects.
Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion. Here, we introduce a bilayer graphene heterostructure, where single-layer graphene is placed on top of another layer of graphene with a regular lattice of antidots. We dub this class of graphene systems GOAL: graphene on graphene antidot lattice. By varying the structure geometry, band-structure engineering can be performed to obtain linearly dispersing bands (with a high concomitant mobility), which nevertheless can be made gapped with a perpendicular field. We analyze the electronic structure and transport properties of various types of GOALs, and draw general conclusions about their properties to aid their design in experiments.
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