Conductance quantization suppression in the quantum Hall regime

Quantum Transport in Large-Scale Patterned Nitrogen-Doped Graphene

It has recently been demonstrated how the nitrogen dopant concentration in graphene can be controlled spatially on the nano-meter scale using a molecular mask. This technique may be used to create ballistic electron optics-like structures of high/low doping regions; for example, to focus electron beams, harnessing the quantum wave nature of the electronic propagation. Here, we employ large-scale Greens function transport calculations based on a tight-binding approach. We first benchmark different tight-binding models of nitrogen in graphene with parameters based on density functional theory (DFT) and the virtual crystal approximation (VCA). Then, we study theoretically how the random distribution within the masked regions and the discreteness of the nitrogen scattering centers impact the transport behavior of sharp n-p and n-n' interfaces formed by different, realistic nitrogen concentrations. We investigate how constrictions for the current can be realized by patterned high/low doping regions with experimentally feasible nitrogen concentrations. The constrictions can guide the electronic current, while the quantized conductance is significantly washed out due to the nitrogen scattering. The implications for device design is that a p-n junction with nitrogen corrugation should still be viable for current focusing. Furthermore, a guiding channel with less nitrogen in the conducting canal preserves more features of quantized conductance and, therefore, its low-noise regime.

Nanoscale View of Engineered Massive Dirac Quasiparticles in Lithographic Superstructures

Massive Dirac fermions are low-energy electronic excitations characterized by a hyperbolic band dispersion. They play a central role in several emerging physical phenomena such as topological phase transitions, anomalous Hall effects, and superconductivity. This work demonstrates that massive Dirac fermions can be controllably induced by lithographically patterning superstructures of nanoscale holes in a graphene device. Their band dispersion is systematically visualized using angle-resolved photoemission spectroscopy with nanoscale spatial resolution. A linear scaling of effective mass with feature sizes is reported, underlining the Dirac nature of the superstructures. In situ electrostatic doping dramatically enhances the effective hole mass and leads to the direct observation of an electronic band gap that results in a peak-to-peak band separation of 0.64 ± 0.03 eV, which is shown via first-principles calculations to be strongly renormalized by carrier-induced screening. The methodology demonstrates band structure engineering guided by directly viewing structurally and electrically tunable massive Dirac quasiparticles in lithographic superstructures at the nanoscale.

Super-Resolution Nanolithography of Two-Dimensional Materials by Anisotropic Etching

Nanostructuring allows altering of the electronic and photonic properties of two-dimensional (2D) materials. The efficiency, flexibility, and convenience of top-down lithography processes are, however, compromised by nanometer-scale edge roughness and resolution variability issues, which especially affect the performance of 2D materials. Here, we study how dry anisotropic etching of multilayer 2D materials with sulfur hexafluoride (SF₆) may overcome some of these issues, showing results for hexagonal boron nitride (hBN), tungsten disulfide (WS₂), tungsten diselenide (WSe₂), molybdenum disulfide (MoS₂), and molybdenum ditelluride (MoTe₂). Scanning electron microscopy and transmission electron microscopy reveal that etching leads to anisotropic hexagonal features in the studied transition metal dichalcogenides, with the relative degree of anisotropy ranked as: WS₂ > WSe₂ > MoTe₂ ∼ MoS₂. Etched holes are terminated by zigzag edges while etched dots (protrusions) are terminated by armchair edges. This can be explained by Wulff constructions, taking the relative stabilities of the edges and the AA' stacking order into account. Patterns in WS₂ are transferred to an underlying graphite layer, demonstrating a possible use for creating sub-10 nm features. In contrast, multilayer hBN exhibits no lateral anisotropy but shows consistent vertical etch angles, independent of crystal orientation. Using an hBN crystal as the base, ultrasharp corners can be created in lithographic patterns, which are then transferred to a graphite crystal underneath. We find that the anisotropic SF₆ reactive ion etching process makes it possible to downsize nanostructures and obtain smooth edges, sharp corners, and feature sizes significantly below the resolution limit of electron beam lithography. The nanostructured 2D materials can be used themselves or as etch masks to pattern other nanomaterials.

Upstream modes and antidots poison graphene quantum Hall effect

The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to reveal new facets of this remarkable property. However, in conventional Hall bar geometries, topological protection of graphene edge channels is found regrettably less robust than in high mobility semi-conductors. Here, we explore graphene quantum Hall regime at the local scale, using a scanning gate microscope. We reveal the detrimental influence of antidots along the graphene edges, mediating backscattering towards upstream edge channels, hence triggering topological breakdown. Combined with simulations, our experimental results provide further insights into graphene quantum Hall channels vulnerability. In turn, this may ease future developments towards precise manipulation of topologically protected edge channels hosted in various types of two-dimensional crystals.

Long-range nontopological edge currents in charge-neutral graphene

Van der Waals heterostructures display numerous unique electronic properties. Nonlocal measurements, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers, have been widely used in the search for novel transport mechanisms, including dissipationless spin and valley transport^1-9, topological charge-neutral currents^10-12, hydrodynamic flows¹³ and helical edge modes^14-16. Monolayer^1-5,10,15-19, bilayer^9,11,14,20 and few-layer²¹ graphene, transition-metal dichalcogenides^6,7 and moiré superlattices^8,10,12 have been found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated^{3,11,17,22-24}. Graphene, in particular, exhibits giant nonlocality at charge neutrality^1,15-19, a striking behaviour that has attracted competing explanations. Using a superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging²⁵, here we demonstrate that the commonly occurring charge accumulation at graphene edges^23,26-31 leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, although the edge conductance has little effect on the current flow in zero magnetic field, it leads to field-induced decoupling between edge and bulk transport at moderate fields. The resulting giant nonlocality at charge neutrality and away from it produces exotic flow patterns that are sensitive to edge disorder, in which charges can flow against the global electric field. The observed one-dimensional edge transport is generic and nontopological and is expected to support nonlocal transport in many electronic systems, offering insight into the numerous controversies and linking them to long-range guided electronic states at system edges.

Graphenylene-based nanoribbons for novel molecular electronic devices

In the last decade, graphene has been frequently cited as one of the most promising materials for nanoelectronics. However, despite its outstanding mechanical and electronic properties, its use in the production of real nanoelectronic devices usually imposes some practical difficulties. This happens mainly due to the fact that, in its pristine form, graphene is a gapless material. We investigate theoretically the possibility of obtaining rectifying nanodevices using another carbon based two dimensional material, namely the graphenylene. This material has the advantage of being an intrinsic semiconductor, posing as a promising material for nanoelectronics. By doping graphenylene, one could obtain 2-dimensional p-n junctions, which can be useful for the construction of low dimensional electronic devices. We propose 2-dimensional diodes in which a clear rectification effect was demonstrated, with a conducting threshold of approximately 1.5 eV in direct bias and current blocking with opposite bias. During these investigations were found specific configurations that could result in devices with Zener-like behavior. Also, one unexpected effect was identified, which was the existence of transmission dips in electronic conductance plots. This result is discussed as a related feature to what was found in graphene nanoribbon systems under external magnetic fields, even though the external field was not a necessary ingredient to obtain such effect in the present case.

Quantum nanoconstrictions fabricated by cryo-etching in encapsulated graphene

We report on a novel implementation of the cryo-etching method, which enabled us to fabricate low-roughness hBN-encapsulated graphene nanoconstrictions with unprecedented control of the structure edges; the typical edge roughness is on the order of a few nanometers. We characterized the system by atomic force microscopy and used the measured parameters of the edge geometry in numerical simulations of the system conductance, which agree quantitatively with our low temperature transport measurements. The quality of our devices is confirmed by the observation of well defined quantized 2e²/h conductance steps at zero magnetic field. To the best of our knowledge, such an observation reports the clearest conductance quantization in physically etched graphene nanoconstrictions. The fabrication of such high quality systems and the scalability of the cryo-etching method opens a novel promising possibility of producing more complex truly-ballistic devices based on graphene.

Electrostatics of metal-graphene interfaces: sharp p-n junctions for electron-optical applications

Creation of sharp lateral p-n junctions in graphene devices, with transition widths w well below the Fermi wavelength λF of graphene's charge carriers, is vital to study and exploit these electronic systems for electron-optical applications. The achievement of such junctions is, however, not trivial due to the presence of a considerable out-of-plane electric field in lateral p-n junctions, resulting in large widths. Metal-graphene interfaces represent a novel, promising and easy to implement technique to engineer such sharp lateral p-n junctions in graphene field-effect devices, in clear contrast to the much wider (i.e. smooth) junctions achieved via conventional local gating. In this work, we present a systematic and robust investigation of the electrostatic problem of metal-induced lateral p-n junctions in gated graphene devices for electron-optics applications, systems where the width w of the created junctions is not only determined by the metal used but also depends on external factors such as device geometries, dielectric environment and different operational parameters such as carrier density and temperature. Our calculations demonstrate that sharp junctions (w ≪ λF) can be achieved via metal-graphene interfaces at room temperature in devices surrounded by dielectric media with low relative permittivity (<10). In addition, we show how specific details such as the separation distance between metal and graphene and the permittivity of the gap in-between plays a critical role when defining the p-n junction, not only defining its width w but also the energy shift of graphene underneath the metal. These results can be extended to any two-dimensional (2D) electronic system doped by the presence of metal clusters and thus are relevant for understanding interfaces between metals and other 2D materials.

Fabry-Pérot resonances and a crossover to the quantum Hall regime in ballistic graphene quantum point contacts

We report on the observation of quantum transport and interference in a graphene device that is attached with a pair of split gates to form an electrostatically-defined quantum point contact (QPC). In the low magnetic field regime, the resistance exhibited Fabry-Pérot (FP) resonances due to np'n(pn'p) cavities formed by the top gate. In the quantum Hall (QH) regime with a high magnetic field, the edge states governed the phenomena, presenting a unique condition where the edge channels of electrons and holes along a p-n junction acted as a solid-state analogue of a monochromatic light beam. We observed a crossover from the FP to QH regimes in ballistic graphene QPC under a magnetic field with varying temperatures. In particular, the collapse of the QH effect was elucidated as the magnetic field was decreased. Our high-mobility graphene device enabled observation of such quantum coherence effects up to several tens of kelvins. The presented device could serve as one of the key elements in future electronic quantum optic devices.

Oxidation of Suspended Graphene: Etch Dynamics and Stability Beyond 1000 °C

We study the oxidation of clean suspended mono- and few-layer graphene in real time by in situ environmental transmission electron microscopy. At an oxygen pressure below 0.1 mbar, we observe anisotropic oxidation in which armchair-oriented hexagonal holes are formed with a sharp edge roughness below 1 nm. At a higher pressure, we observe an increasingly isotropic oxidation, eventually leading to irregular holes at a pressure of 6 mbar. In addition, we find that few-layer flakes are stable against oxidation at temperatures up to at least 1000 °C in the absence of impurities and electron-beam-induced defects. These findings show, first, that the oxidation behavior of mono- and few-layer graphene depends critically on the intrinsic roughness, cleanliness and any imposed roughness or additional reactivity from a supporting substrate and, second, that the activation energy for oxidation of pristine suspended few-layer graphene is up to 43% higher than previously reported for graphite. In addition, we have developed a cleaning scheme that results in the near-complete removal of hydrocarbon residues over the entire visible sample area. These results have implications for applications of graphene where edge roughness can critically affect the performance of devices and more generally highlight the surprising (meta)stability of the basal plane of suspended bilayer and thicker graphene toward oxidative environments at high temperature.

Valley Subband Splitting in Bilayer Graphene Quantum Point Contacts

We report a study of one-dimensional subband splitting in a bilayer graphene quantum point contact in which quantized conductance in steps of 4e^{2}/h is clearly defined down to the lowest subband. While our source-drain bias spectroscopy measurements reveal an unconventional confinement, we observe a full lifting of the valley degeneracy at high magnetic fields perpendicular to the bilayer graphene plane for the first two lowest subbands where confinement and Coulomb interactions are the strongest and a peculiar merging or mixing of K and K^{'} valleys from two nonadjacent subbands with indices (N,N+2), which are well described by our semiphenomenological model.

A Graphene-Edge Ferroelectric Molecular Switch

We show that polar molecules (water, ammonia, and nitrogen dioxide) adsorbed solely at the exposed edges of an encapsulated graphene sheet exhibit ferroelectricity, collectively orienting and switching reproducibly between two available states in response to an external electric field. This ferroelectric molecular switching introduces drastic modifications to the graphene bulk conductivity and produces a large and ambipolar charge bistability in micrometer-size graphene devices. This system comprises an experimental realization of envisioned memory capacitive ("memcapacitive") devices whose capacitance is a function of their charging history, here conceived via confined and correlated polar molecules at the one-dimensional edge of a two-dimensional crystal.