Ballistic Transport in Graphene Antidot Lattices

Probing the Anisotropic Fermi Surface in Tetralayer Graphene via Transverse Magnetic Focusing

Bernal-stacked tetralayer graphene (4LG) exhibits intriguing low-energy properties, featuring two massive sub-bands and showcasing diverse features of topologically distinct, anisotropic Fermi surfaces, including Lifshitz transitions and trigonal warping. Here, we study the influence of the band structure on electron dynamics within 4LG using transverse magnetic focusing. Our analysis reveals two distinct focusing peaks corresponding to the two sub-bands. Furthermore, we uncover a pronounced dependence of the focusing spectra on crystal orientations, indicative of an anisotropic Fermi surface. Utilizing the semiclassical model, we attribute this orientation-dependent behavior to the trigonal warping of the band structure. This phenomenon leads to variations in electron trajectories based on crystal orientation. Our findings not only enhance our understanding of the dynamics of electrons in 4LG but also offer a promising method for probing anisotropic Fermi surfaces in other materials.

Atomically precise vacancy-assembled quantum antidots

Patterning antidots, which are regions of potential hills that repel electrons, into well-defined antidot lattices creates fascinating artificial periodic structures, leading to anomalous transport properties and exotic quantum phenomena in two-dimensional systems. Although nanolithography has brought conventional antidots from the semiclassical regime to the quantum regime, achieving precise control over the size of each antidot and its spatial period at the atomic scale has remained challenging. However, attaining such control opens the door to a new paradigm, enabling the creation of quantum antidots with discrete quantum hole states, which, in turn, offer a fertile platform to explore novel quantum phenomena and hot electron dynamics in previously inaccessible regimes. Here we report an atomically precise bottom-up fabrication of a series of atomic-scale quantum antidots through a thermal-induced assembly of a chalcogenide single vacancy in PtTe2. Such quantum antidots consist of highly ordered single-vacancy lattices, spaced by a single Te atom, reaching the ultimate downscaling limit of antidot lattices. Increasing the number of single vacancies in quantum antidots strengthens the cumulative repulsive potential and consequently enhances the collective interference of multiple-pocket scattered quasiparticles inside quantum antidots, creating multilevel quantum hole states with a tunable gap from the telecom to far-infrared regime. Moreover, precisely engineered quantum hole states of quantum antidots are geometry protected and thus survive on oxygen substitutional doping. Therefore, single-vacancy-assembled quantum antidots exhibit unprecedented robustness and property tunability, positioning them as highly promising candidates for advancing quantum information and photocatalysis technologies.

Resonant Scattering in Proximity-Coupled Graphene/Superconducting Mo2 C Heterostructures

The realization of high-quality heterostructures or hybrids of graphene and superconductor is crucial for exploring various novel quantum phenomena and devices engineering. Here, the electronic transport on directly grown high-quality graphene/Mo2 C vertical heterostructures with clean and sharp interface is comprehensively investigated. Owing to the strong interface coupling, the graphene layer feels an effective confinement potential well imposed by two-dimensional (2D) Mo2 C crystal. Employing cross junction device geometry, a series of resonance-like magnetoresistance peaks are observed at low temperatures. The temperature and gate voltage dependences of the observed resonance peaks give evidence for geometric resonance of electron cyclotron orbits with the formed potential well. Moreover, it is found that both the amplitude of resonance peaks and conductance fluctuation exhibit different temperature-dependent behaviors below the superconducting transition temperature of 2D Mo2 C, indicating the correlation of quantum fluctuations and superconductivity. This study offers a promising route toward integrating graphene with 2D superconducting materials, and establishes a new way to investigate the interplay of massless Dirac fermion and superconductivity based on graphene/2D superconductor vertical heterostructures.

Quantum magnetotransport oscillations in graphene nanoribbons coupled to superconductors

Magnetotransport properties of zigzag and armchair graphene nanoribbons that are in contact with superconductors are investigated using a tight-binding model. The cyclotron orbital motion together with the quantum interference under the coexistence of Andreev and normal reflections gives rise to a number of oscillations in characteristic magnetic-field regimes when the superconducting coupling is weak. The oscillations become irregular and/or suppressed as the coupling is made strong. The period of the oscillations differs from that when a nonrelativistic two-dimensional electron gas is employed rather than the graphene sheet. The modifications of the oscillations are attributed to the phase shift associated with the reflection from the graphene-superconductor interface. The presence of a magnetic field suppresses the quantum blocking of Andreev transmission, which occurs for the edge mode of zigzag nanoribbons, in the same way regardless of it being induced by the Andreev retro- or specular reflection.

Electrically tunable graphene metamaterial with strong broadband absorption

The coupling system with dynamic manipulation characteristics is of great importance for the field of active plasmonics and tunable metamaterials. However, the traditional metal-based architectures suffer from a lack of electrical tunability. In this study, a metamaterial composed of perpendicular or parallel graphene-Al₂O₃-graphene stacks is proposed and demonstrated, which allows for the electric modulation of both graphene layers simultaneously. The resultant absorption of hybridized modes can be modulated to more than 50% by applying an external voltage, and the absorption bandwidth can reach 3.55 μm, which is 1.7 times enhanced than the counterpart of single-layer graphene. The modeling results demonstrate that the small relaxation time of graphene is of great importance to realize the broadband absorption. Moreover, the optical behaviors of the tunable metamaterial can be influenced by the incident polarization, the dielectric thickness, and especially by the Fermi energy of graphene. This work is of a crucial role in the design and fabrication of graphene-based broadband optical and optoelectronic devices.

Small-Nanostructure-Size-Limited Phonon Transport within Composite Films Made of Single-Wall Carbon Nanotubes and Reduced Graphene Oxides

Nanocarbon materials have been widely used for nanoelectronics and energy-related applications. In this work, composite films consisting of reduced graphene oxides (rGOs) and single-wall carbon nanotubes (SWCNTs) are synthesized and studied for their in-plane thermal conductivities. Different from pristine carbon nanotubes or graphene with decreased thermal conductivities above 300 K, the in-plane thermal conductivities of these composite films are found to follow the trend of the specific heat of graphene from 100 to 400 K, i.e., monotonously increasing at elevated temperatures. Such a trend can often be found within amorphous solids but has seldom been observed for nanocarbon. This unique temperature dependence of thermal conductivities is attributed to the largely restricted phonon mean free paths within the graphene sheets that mainly contribute to the in-plane thermal transport. The highest in-plane thermal conductivity among samples with different synthesis conditions is 62.8 W/(m·K) at 300 K. Such a high thermal conductivity, combined with its unique temperature dependency, can be ideal for applications such as flexible film-like thermal diodes based on the junction between two materials with a large contrast for their temperature dependence of the thermal conductivity.

Gate-Tunable Two-Dimensional Superlattices in Graphene

We report an efficient technique to induce gate-tunable two-dimensional superlattices in graphene by the combined action of a back gate and a few-layer graphene patterned bottom gate complementary to existing methods. The patterned gates in our approach can be easily fabricated and implemented in van der Waals stacking procedures, allowing flexible use of superlattices with arbitrary geometry. In transport measurements on a superlattice with a lattice constant a = 40 nm, well-pronounced satellite Dirac points and signatures of the Hofstadter butterfly including a nonmonotonic quantum Hall response are observed. Furthermore, the experimental results are accurately reproduced in transport simulations and show good agreement with features in the calculated band structure. Overall, we present a comprehensive picture of graphene-based superlattices, featuring a broad range of miniband effects, both in experiment and in theoretical modeling. The presented technique is suitable for studying more advanced geometries which are not accessible by other methods.

Effects of A Magnetic Field on the Transport and Noise Properties of a Graphene Ribbon with Antidots

We perform a numerical simulation of the effects of an orthogonal magnetic field on charge transport and shot noise in an armchair graphene ribbon with a lattice of antidots. This study relies on our envelope-function based code, in which the presence of antidots is simulated through a nonzero mass term and the magnetic field is introduced with a proper choice of gauge for the vector potential. We observe that by increasing the magnetic field, the energy gap present with no magnetic field progressively disappears, together with features related to commensurability and quantum effects. In particular, we focus on the behavior for high values of the magnetic field: we notice that when it is sufficiently large, the effect of the antidots vanishes and shot noise disappears, as a consequence of the formation of edge states crawling along the boundaries of the structure without experiencing any interaction with the antidots.

Ions and Water Dancing through Atom-Scale Holes: A Perspective toward "Size Zero"

We provide an overview of atom-scale apertures in solid-state membranes, from "pores" and "tubes" to "channels", with characteristic sizes comparable to the sizes of ions and water molecules. In this regime of ∼1 nm diameter pores, water molecules and ions are strongly geometrically confined: the size of water molecules (∼0.3 nm) and the size of "hydrated" ions in water (∼0.7-1 nm) are similar to the pore diameters, physically limiting the ion flow through the hole. The pore sizes are comparable to the classical Debye screening length governing the spatial range of electrostatic interaction, ∼0.3 to 1 nm for 1 to 0.1 M KCl. In such small structures, charges can be unscreened, leading to new effects. We discuss experiments on ∼1 nm diameter nanopores, with a focus on carbon nanotube pores and ion transport studies. Finally, we present an outlook for artificial "size zero" pores in the regime of small diameters and small thicknesses. Beyond mimicking protein channels in nature, solid-state pores may offer additional possibilities where sensing and control are performed at the pore, such as in electrically and optically addressable solid-state materials.

New Generation of Moiré Superlattices in Doubly Aligned hBN/Graphene/hBN Heterostructures

The specific rotational alignment of two-dimensional lattices results in a moiré superlattice with a larger period than the original lattices and allows one to engineer the electronic band structure of such materials. So far, transport signatures of such superlattices have been reported for graphene/hBN and graphene/graphene systems. Here we report moiré superlattices in fully hBN encapsulated graphene with both the top and the bottom hBN aligned to the graphene. In the graphene, two different moiré superlattices form with the top and the bottom hBN, respectively. The overlay of the two superlattices can result in a third superlattice with a period larger than the maximum period (14 nm) in the graphene/hBN system, which we explain in a simple model. This new type of band structure engineering allows one to artificially create an even wider spectrum of electronic properties in two-dimensional materials.

Lithographic band structure engineering of graphene

Two-dimensional materials such as graphene allow direct access to the entirety of atoms constituting the crystal. While this makes shaping by lithography particularly attractive as a tool for band structure engineering through quantum confinement effects, edge disorder and contamination have so far limited progress towards experimental realization. Here, we define a superlattice in graphene encapsulated in hexagonal boron nitride, by etching an array of holes through the heterostructure with minimum feature sizes of 12-15 nm. We observe a magnetotransport regime that is distinctly different from the characteristic Landau fan of graphene, with a sizeable bandgap that can be tuned by a magnetic field. The measurements are accurately described by transport simulations and analytical calculations. Finally, we observe strong indications that the lithographically engineered band structure at the main Dirac point is cloned to a satellite peak that appears due to moiré interactions between the graphene and the encapsulating material.

Commensurability Oscillations in One-Dimensional Graphene Superlattices

We report the experimental observation of commensurability oscillations (COs) in 1D graphene superlattices. The widely tunable periodic potential modulation in hBN-encapsulated graphene is generated via the interplay of nanopatterned few-layer graphene acting as a local bottom gate and a global Si back gate. The longitudinal magnetoresistance shows pronounced COs when the sample is tuned into the unipolar transport regime. We observe up to six CO minima, providing evidence for a long mean free path despite the potential modulation. Comparison to existing theories shows that small-angle scattering is dominant in hBN/graphene/hBN heterostructures. We observe robust COs persisting to temperatures exceeding T=150  K. At high temperatures, we find deviations from the predicted T dependence, which we ascribe to electron-electron scattering.

Band structure engineering of 2D materials using patterned dielectric superlattices

The ability to manipulate electrons in two-dimensional materials with external electric fields provides a route to synthetic band engineering. By imposing artificially designed and spatially periodic superlattice potentials, electronic properties can be further altered beyond the constraints of naturally occurring atomic crystals^1-5. Here, we report a new approach to fabricate high-mobility superlattice devices by integrating surface dielectric patterning with atomically thin van der Waals materials. By separating the device assembly and superlattice fabrication processes, we address the intractable trade-off between device processing and mobility degradation that constrains superlattice engineering in conventional systems. The improved electrostatics of atomically thin materials allows smaller wavelength superlattice patterns relative to previous demonstrations. Moreover, we observe the formation of replica Dirac cones in ballistic graphene devices with sub-40 nm wavelength superlattices and report fractal Hofstadter spectra^6-8 under large magnetic fields from superlattices with designed lattice symmetries that differ from that of the host crystal. Our results establish a robust and versatile technique for band structure engineering of graphene and related van der Waals materials with dynamic tunability.

Interfacial engineering in graphene bandgap

Graphene exhibits superior mechanical strength, high thermal conductivity, strong light-matter interactions, and, in particular, exceptional electronic properties. These merits make graphene an outstanding material for numerous potential applications. However, a graphene-based high-performance transistor, which is the most appealing application, has not yet been produced, which is mainly due to the absence of an intrinsic electronic bandgap in this material. Therefore, bandgap opening in graphene is urgently needed, and great efforts have been made regarding this topic over the past decade. In this review article, we summarise recent theoretical and experimental advances in interfacial engineering to achieve bandgap opening. These developments are divided into two categories: chemical engineering and physical engineering. Chemical engineering is usually destructive to the pristine graphene lattice via chemical functionalization, the introduction of defects, doping, chemical bonds with substrates, and quantum confinement; the latter largely maintains the atomic structure of graphene intact and includes the application of an external field, interactions with substrates, physical adsorption, strain, electron many-body effects and spin-orbit coupling. Although these pioneering works have not met all the requirements for electronic applications of graphene at once, they hold great promise in this direction and may eventually lead to future applications of graphene in semiconductor electronics and beyond.

Structurally Controlled Large-Area 10 nm Pitch Graphene Nanomesh by Focused Helium Ion Beam Milling

Graphene nanomesh (GNM) is formed by patterning graphene with nanometer-scale pores separated by narrow necks. GNMs are of interest due to their potential semiconducting characteristics when quantum confinement in the necks leads to an energy gap opening. GNMs also have potential for use in phonon control and water filtration. Furthermore, physical phenomena, such as spin qubit, are predicted at pitches below 10 nm fabricated with precise structural control. Current GNM patterning techniques suffer from either large dimensions or a lack of structural control. This work establishes reliable GNM patterning with a sub-10 nm pitch and an < 4 nm pore diameter by the direct helium ion beam milling of suspended monolayer graphene. Due to the simplicity of the method, no postpatterning processing is required. Electrical transport measurements reveal an effective energy gap opening of up to ∼450 meV. The reported technique combines the highest resolution with structural control and opens a path toward GNM-based, room-temperature semiconducting applications.

Ballistic geometric resistance resonances in a single surface of a topological insulator

Transport in topological matter has shown a variety of novel phenomena over the past decade. Although numerous transport studies have been conducted on three-dimensional topological insulators (TIs), study of ballistic motion and thus exploration of potential landscapes on a hundred nanometer scale is for the prevalent TI materials almost impossible due to their low carrier mobility. Therefore, it is unknown whether helical Dirac electrons in TIs, bound to interfaces between topologically distinct materials, can be manipulated on the nanometer scale by local gates or locally etched regions. Here we impose a submicron periodic potential onto a single surface of Dirac electrons in high-mobility strained mercury telluride (HgTe), which is a strong TI. Pronounced geometric resistance resonances constitute the clear-cut observation of a ballistic effect in three-dimensional TIs.

Ballistic motion on nanometer scale of topological surface states has rarely been studied. Here, Maier et al. report pronounced geometric resistance resonances of high-mobility Dirac electrons in strained HgTe, suggesting a ballistic effect in three-dimensional topological insulators.

Improved Performance of h-BN Encapsulated Double Gate Graphene Nanomesh Field Effect Transistor for Short Channel Length

This paper presents improved performance of Double Gate Graphene Nanomesh Field Effect Transistor (DG-GNMFET) with h-BN as substrate and gate oxide material. The DC characteristics of 0.95[Formula: see text][Formula: see text]m and 5[Formula: see text]nm channel length devices are studied for SiO2 and h-BN substrate and oxide material. For analyzing the ballistic behavior of electron for 5[Formula: see text]nm channel length, von Neumann boundary condition is considered near source and drain contact region. The simulated results show improved saturation current for h-BN encapsulated structure with two times higher on current value (0.375 for SiO2 and 0.621 for h-BN) as compared to SiO2 encapsulated structure. The obtained result shows h-BN to be a better substrate and oxide material for graphene electronics with improved device characteristics.

On-Surface Synthesis of Porous Carbon Nanoribbons from Polymer Chains

We demonstrate the on-surface synthesis of porous carbon nanoribbons on Ag(111) via a preprogrammed isomerization of conformationally flexible polymer chains followed by dehydrogenation reactions using thermal annealing. The carbon chains are fabricated by polymerization of prochiral 1,3,5-tris(3-bromophenyl)benzene (mTBPB) directly on the surface using an Ullmann-type reaction. At room temperature, mTBPB partially self-assembles in halogen-bonded 2D networks, which transform into organometallic chains and rings after debromination. The chain and ring formation is facilitated by conformational switching from a C_3h to C_s symmetry of mTBPB via rotation of m-phenylene units. The high conformational selectivity toward C_s-conformers is templated by the twofold coordination to Ag adatoms. After thermally induced covalent-linking through aryl-aryl coupling, well-ordered nanoporous chains are created. Finally, the rotation of single phenylene units in combination with dehydrogenation cross-linking reactions within the polymer chains leads to the unexpected formation of porous carbon nanoribbons. We unveil the reaction mechanism in a low-temperature scanning tunneling microscopy study and demonstrate that the rotation of m-phenylene units is a powerful design tool to promote structural control in the synthesis of cyclic covalent organic nanostructures on metal surfaces.

Periodic Arrays of Phosphorene Nanopores as Antidot Lattices with Tunable Properties

A tunable band gap in phosphorene extends its applicability in nanoelectronic and optoelectronic applications. Here, we propose to tune the band gap in phosphorene by patterning antidot lattices, which are periodic arrays of holes or nanopores etched in the material, and by exploiting quantum confinement in the corresponding nanoconstrictions. We fabricated antidot lattices with radii down to 13 nm in few-layer black phosphorus flakes protected by an oxide layer and observed suppression of the in-plane phonon modes relative to the unmodified material via Raman spectroscopy. In contrast to graphene antidots, the Raman peak positions in few-layer BP antidots are unchanged, in agreement with predicted power spectra. We also use DFT calculations to predict the electronic properties of phosphorene antidot lattices and observe a band gap scaling consistent with quantum confinement effects. Deviations are attributed primarily to self-passivating edge morphologies, where each phosphorus atom has the same number of bonds per atom as the pristine material so that no dopants can saturate dangling bonds. Quantum confinement is stronger for the zigzag edge nanoconstrictions between the holes as compared to those with armchair edges, resulting in a roughly bimodal band gap distribution. Interestingly, in two of the antidot structures an unreported self-passivating reconstruction of the zigzag edge endows the systems with a metallic component. The experimental demonstration of antidots and the theoretical results provide motivation to further scale down nanofabrication of antidots in the few-nanometer size regime, where quantum confinement is particularly important.

A two-dimensional Dirac fermion microscope

The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.

Room temperature nanostructured graphene transistor with high on/off ratio

We report the batch fabrication of graphene field-effect-transistors (GFETs) with nanoperforated graphene as channel. The transistors were cut and encapsulated. The encapsulated GFETs display saturation regions that can be tuned by modifying the top gate voltage, and have on/off ratios of at least 2 × 10³ at room temperature and at small drain and gate voltages. In addition, the nanoperforated GFETs display orders of magnitude higher photoresponses than any room-temperature graphene detector configurations that do not involve heterostructures with bandgap materials.