Electrode-Free Anodic Oxidation Nanolithography of Low-Dimensional Materials

Site-controlled growth of In(Ga)As/GaAs quantum dots on patterned substrate

In(Ga)As quantum dot (QD) with uniform size and controlled sites have great potential in optical communications and quantum computing. In this review, we focus on the site-controlled preparation of In(Ga)As quantum dot arrays based on patterned substrates, including the improvements made by the researchers to enhance the quantum dot site-control capability and optical quality. Based on the current research on site-controlled In(Ga)As QDs, it has been possible to grow uniformly ordered In(Ga)As QD arrays, in which the size, morphology, and nucleus location of each quantum dot can be precisely controlled. In addition, the study of deoxidation treatment of patterned substrates has led to the performance enhancement of the prepared QD arrays. Finally, we propose that the future development of site-controlled In(Ga)As QD arrays lies in improving the optical quality and tuning their emission wavelength to the telecommunication band.

Charge Transfer Plasmonics in Bespoke Graphene/α-RuCl3 Cavities

Surface plasmon polaritons (SPPs) provide a window into the nano-optical, electrodynamic response of their host material and its dielectric environment. Graphene/α-RuCl3 serves as an ideal model system for imaging SPPs since the large work function difference between these two layers facilitates charge transfer that hole dopes graphene with n ∼ 1013 cm-2 free carriers. In this work, we study the emergent THz response of graphene/α-RuCl3 heterostructures using our home-built cryogenic scanning near-field optical microscope. Using phase-resolved imaging, we clearly observe long wavelength, heavily damped THz SPPs in a series of variable-size graphene cavities. From this, we extract the plasmonic wavelength and scattering rate in the graphene/α-RuCl3 heterostructures. We determine that the measured plasmon wavelength and electronic scattering rate match our heterostructures' theoretically predicted values. Our results demonstrate that shaping graphene into bespoke cavity structures enables observation and quantification of SPPs in heavily doped graphene that are largely not addressable with other experimental techniques. Moreover, the manifest lack of metallicity observed in the adjacent doped α-RuCl3 layer provides significant constraints on the nature of the interfacial charge transfer in this 2D heterostructure.

Long-lived isospin excitations in magic-angle twisted bilayer graphene

Numerous correlated many-body phases, both conventional and exotic, have been reported in magic-angle twisted bilayer graphene (MATBG)1-24. However, the dynamics associated with these correlated states, crucial for understanding the underlying physics, remain unexplored. Here we combine exciton sensing and optical pump-probe spectroscopy to investigate the dynamics of isospin orders in MATBG with WSe2 substrate across the entire flat band, achieving sub-picosecond resolution. We observe remarkably slow isospin dynamics in a broad filling range around ν = 2 and between ν = -3 and -2, with lifetimes of up to 300 ps that decouple from the much faster cooling of electronic temperature (about 10 ps). This non-thermal behaviour demonstrates the presence of abnormally long-lived modes in the isospin degrees of freedom. This observation, not anticipated by theory, implies the existence of long-range propagating collective modes, strong isospin fluctuations and memory effects and is probably associated with an intervalley coherent or incommensurate Kekulé spiral ground state. We further demonstrate non-equilibrium control of the isospin orders previously found around integer fillings. Specifically, through ultrafast manipulation, it can be transiently shifted away from integer fillings. Our study demonstrates a unique probe of collective excitations in MATBG and paves the way for actively controlling non-equilibrium phenomena in moiré systems.

In situ via Contact to hBN-Encapsulated Air-Sensitive Atomically Thin Semiconductors

Establishing reliable electrical contacts to atomically thin materials is a prerequisite for both fundamental studies and applications yet remains a challenge. In particular, the development of contact techniques for air-sensitive monolayers has lagged behind, despite their unique properties and significant potential for applications. Here, we present a robust method to create contacts to device layers encapsulated within hexagonal boron nitride (hBN). This method uses plasma etching and metal deposition to create 'vias' in the hBN with graphene forming an atomically thin etch-stop. The resulting partially fluorinated graphene (PFG) protects the underlying device layer from air-induced degradation and damage during metal deposition. PFG is resistive in-plane but maintains high out-of-plane conductivity. The work function of the PFG/metal contact is tunable through the degree of fluorination, offering opportunities for contact engineering. Using the in situ via technique, we achieve ambipolar contact to air-sensitive monolayer 2H-molybdenum ditelluride (MoTe2) with more than 1 order of magnitude improvement in on-current density compared to previous literature. The complete encapsulation provides high reproducibility and long-term stability. The technique can be extended to other air-sensitive materials as well as air-stable materials, offering highly competitive device performance.

Low Resistance Contact to P-Type Monolayer WSe2

Advanced microelectronics in the future may require semiconducting channel materials beyond silicon. Two-dimensional (2D) semiconductors, with their atomically thin thickness, hold great promise for future electronic devices. One challenge to achieving high-performance 2D semiconductor field effect transistors (FET) is the high contact resistance at the metal-semiconductor interface. In this study, we develop a charge-transfer doping strategy with WSe2/α-RuCl3 heterostructures to achieve low-resistance ohmic contact for p-type monolayer WSe2 transistors. We show that hole doping as high as 3 × 1013 cm-2 can be achieved in the WSe2/α-RuCl3 heterostructure due to its type-III band alignment, resulting in an ohmic contact with resistance of 4 kΩ μm. Based on that, we demonstrate p-type WSe2 transistors with an on-current of 35 μA·μm-1 and an ION/IOFF ratio exceeding 109 at room temperature.

Mapping charge excitations in generalized Wigner crystals

Transition metal dichalcogenide-based moiré superlattices exhibit strong electron-electron correlations, thus giving rise to strongly correlated quantum phenomena such as generalized Wigner crystal states. Evidence of Wigner crystals in transition metal dichalcogenide moire superlattices has been widely reported from various optical spectroscopy and electrical conductivity measurements, while their microscopic nature has been limited to the basic lattice structure. Theoretical studies predict that unusual quasiparticle excitations across the correlated gap between upper and lower Hubbard bands can arise due to long-range Coulomb interactions in generalized Wigner crystal states. However, the microscopic proof of such quasiparticle excitations is challenging because of the low excitation energy of the Wigner crystal. Here we describe a scanning single-electron charging spectroscopy technique with nanometre spatial resolution and single-electron charge resolution that enables us to directly image electron and hole wavefunctions and to determine the thermodynamic gap of generalized Wigner crystal states in twisted WS2 moiré heterostructures. High-resolution scanning single-electron charging spectroscopy combines scanning tunnelling microscopy with a monolayer graphene sensing layer, thus enabling the generation of individual electron and hole quasiparticles in generalized Wigner crystals. We show that electron and hole quasiparticles have complementary wavefunction distributions and that thermodynamic gaps of ∼50 meV exist for the 1/3 and 2/3 generalized Wigner crystal states in twisted WS2.

Conduction Band Replicas in a 2D Moiré Semiconductor Heterobilayer

Stacking monolayer semiconductors creates moiré patterns, leading to correlated and topological electronic phenomena, but measurements of the electronic structure underpinning these phenomena are scarce. Here, we investigate the properties of the conduction band in moiré heterobilayers of WS2/WSe2 using submicrometer angle-resolved photoemission spectroscopy with electrostatic gating. We find that at all twist angles the conduction band edge is the K-point valley of the WS2, with a band gap of 1.58 ± 0.03 eV. From the resolved conduction band dispersion, we deduce an effective mass of 0.15 ± 0.02 me. Additionally, we observe replicas of the conduction band displaced by reciprocal lattice vectors of the moiré superlattice. We argue that the replicas result from the moiré potential modifying the conduction band states rather than final-state diffraction. Interestingly, the replicas display an intensity pattern with reduced 3-fold symmetry, which we show implicates the pseudo vector potential associated with in-plane strain in moiré band formation.

Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene

Rhombohedral-stacked multilayer graphene hosts a pair of flat bands touching at zero energy, which should give rise to correlated electron phenomena that can be tuned further by an electric field. Moreover, when electron correlation breaks the isospin symmetry, the valley-dependent Berry phase at zero energy may give rise to topologically non-trivial states. Here we measure electron transport through hexagonal boron nitride-encapsulated pentalayer graphene down to 100 mK. We observed a correlated insulating state with resistance at the megaohm level or greater at charge density n = 0 and displacement field D = 0. Tight-binding calculations predict a metallic ground state under these conditions. By increasing D, we observed a Chern insulator state with C = -5 and two other states with C = -3 at a magnetic field of around 1 T. At high D and n, we observed isospin-polarized quarter- and half-metals. Hence, rhombohedral pentalayer graphene exhibits two different types of Fermi-surface instability, one driven by a pair of flat bands touching at zero energy, and one induced by the Stoner mechanism in a single flat band. Our results establish rhombohedral multilayer graphene as a suitable system for exploring intertwined electron correlation and topology phenomena in natural graphitic materials without the need for moiré superlattice engineering.

Fractional quantum anomalous Hall effect in multilayer graphene

The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2-6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7-9. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2 (refs. 10-13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene-hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance [Formula: see text] at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals [Formula: see text] at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14-16. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7-9,17-19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20-22.

Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene

Interactions among charge carriers in graphene can lead to the spontaneous breaking of multiple degeneracies. When increasing the number of graphene layers following rhombohedral stacking, the dominant role of Coulomb interactions becomes pronounced due to the significant reduction in kinetic energy. In this study, we employ phonon-polariton-assisted near-field infrared imaging to determine the stacking orders of tetralayer graphene devices. Through quantum transport measurements, we observe a range of spontaneous broken-symmetry states and their transitions, which can be finely tuned by carrier density n and electric displacement field D. Specifically, we observe a layer-antiferromagnetic insulator at n = D = 0 with a gap of approximately 15 meV. Increasing D allows for a continuous phase transition from a layer-antiferromagnetic insulator to a layer-polarized insulator. By simultaneously tuning n and D, we observe isospin-polarized metals, including spin-valley-polarized and spin-polarized metals. These transitions are associated with changes in the Fermi surface topology and are consistent with the Stoner criteria. Our findings highlight the efficient fabrication of specially stacked multilayer graphene devices and demonstrate that crystalline multilayer graphene is an ideal platform for investigating a wide range of broken symmetries driven by Coulomb interactions.

Orbital multiferroicity in pentalayer rhombohedral graphene

Ferroic orders describe spontaneous polarization of spin, charge and lattice degrees of freedom in materials. Materials exhibiting multiple ferroic orders, known as multiferroics, have important parts in multifunctional electrical and magnetic device applications1-4. Two-dimensional materials with honeycomb lattices offer opportunities to engineer unconventional multiferroicity, in which the ferroic orders are driven purely by the orbital degrees of freedom and not by electron spin. These include ferro-valleytricity corresponding to the electron valley5 and ferro-orbital-magnetism6 supported by quantum geometric effects. These orbital multiferroics could offer strong valley-magnetic couplings and large responses to external fields-enabling device applications such as multiple-state memory elements and electric control of the valley and magnetic states. Here we report orbital multiferroicity in pentalayer rhombohedral graphene using low-temperature magneto-transport measurements. We observed anomalous Hall signals Rxy with an exceptionally large Hall angle (tanΘH > 0.6) and orbital magnetic hysteresis at hole doping. There are four such states with different valley polarizations and orbital magnetizations, forming a valley-magnetic quartet. By sweeping the gate electric field E, we observed a butterfly-shaped hysteresis of Rxy connecting the quartet. This hysteresis indicates a ferro-valleytronic order that couples to the composite field E · B (where B is the magnetic field), but not to the individual fields. Tuning E would switch each ferroic order independently and achieve non-volatile switching of them together. Our observations demonstrate a previously unknown type of multiferroics and point to electrically tunable ultralow-power valleytronic and magnetic devices.

Programming twist angle and strain profiles in 2D materials

Moiré superlattices in twisted two-dimensional materials have generated tremendous excitement as a platform for achieving quantum properties on demand. However, the moiré pattern is highly sensitive to the interlayer atomic registry, and current assembly techniques suffer from imprecise control of the average twist angle, spatial inhomogeneity in the local twist angle, and distortions caused by random strain. We manipulated the moiré patterns in hetero- and homobilayers through in-plane bending of monolayer ribbons, using the tip of an atomic force microscope. This technique achieves continuous variation of twist angles with improved twist-angle homogeneity and reduced random strain, resulting in moiré patterns with tunable wavelength and ultralow disorder. Our results may enable detailed studies of ultralow-disorder moiré systems and the realization of precise strain-engineered devices.

Engineering SYK Interactions in Disordered Graphene Flakes under Realistic Experimental Conditions

We model interactions following the Sachdev-Ye-Kitaev (SYK) framework in disordered graphene flakes up to 300 000 atoms in size (∼100  nm in diameter) subjected to an out-of-plane magnetic field B of 5-20 Tesla within the tight-binding formalism. We investigate two sources of disorder: (i) irregularities at the system boundaries, and (ii) bulk vacancies-for a combination of which we find conditions that could be favorable for the formation of the phase with Sachdev-Ye-Kitaev features under realistic experimental conditions above the liquid helium temperature.

Quantifying the local mechanical properties of twisted double bilayer graphene

Nanomechanical measurements of minimally twisted van der Waals materials remained elusive despite their fundamental importance for device realisation. Here, we use Ultrasonic Force Microscopy (UFM) to locally quantify the variation of out-of-plane Young's modulus in minimally twisted double bilayer graphene (TDBG). We reveal a softening of the Young's modulus by 7% and 17% along single and double domain walls, respectively. Our experimental results are confirmed by force-field relaxation models. This study highlights the strong tunability of nanomechanical properties in engineered twisted materials, and paves the way for future applications of designer 2D nanomechanical systems.

Proximity-induced superconductivity in epitaxial topological insulator/graphene/gallium heterostructures

The introduction of superconductivity to the Dirac surface states of a topological insulator leads to a topological superconductor, which may support topological quantum computing through Majorana zero modes^1,2. The development of a scalable material platform is key to the realization of topological quantum computing^3,4. Here we report on the growth and properties of high-quality (Bi,Sb)₂Te₃/graphene/gallium heterostructures. Our synthetic approach enables atomically sharp layers at both hetero-interfaces, which in turn promotes proximity-induced superconductivity that originates in the gallium film. A lithography-free, van der Waals tunnel junction is developed to perform transport tunnelling spectroscopy. We find a robust, proximity-induced superconducting gap formed in the Dirac surface states in 5-10 quintuple-layer (Bi,Sb)₂Te₃/graphene/gallium heterostructures. The presence of a single Abrikosov vortex, where the Majorana zero modes are expected to reside, manifests in discrete conductance changes. The present material platform opens up opportunities for understanding and harnessing the application potential of topological superconductivity.

Unconventional non-local relaxation dynamics in a twisted trilayer graphene moiré superlattice

The electronic and structural properties of atomically thin materials can be controllably tuned by assembling them with an interlayer twist. During this process, constituent layers spontaneously rearrange themselves in search of a lowest energy configuration. Such relaxation phenomena can lead to unexpected and novel material properties. Here, we study twisted double trilayer graphene (TDTG) using nano-optical and tunneling spectroscopy tools. We reveal a surprising optical and electronic contrast, as well as a stacking energy imbalance emerging between the moiré domains. We attribute this contrast to an unconventional form of lattice relaxation in which an entire graphene layer spontaneously shifts position during assembly, resulting in domains of ABABAB and BCBACA stacking. We analyze the energetics of this transition and demonstrate that it is the result of a non-local relaxation process, in which an energy gain in one domain of the moiré lattice is paid for by a relaxation that occurs in the other.

Gate-Tunable Proximity Effects in Graphene on Layered Magnetic Insulators

The extreme versatility of van der Waals materials originates from their ability to exhibit new electronic properties when assembled in close proximity to dissimilar crystals. For example, although graphene is inherently nonmagnetic, recent work has reported a magnetic proximity effect in graphene interfaced with magnetic substrates, potentially enabling a pathway toward achieving a high-temperature quantum anomalous Hall effect. Here, we investigate heterostructures of graphene and chromium trihalide magnetic insulators (CrI₃, CrBr₃, and CrCl₃). Surprisingly, we are unable to detect a magnetic exchange field in the graphene but instead discover proximity effects featuring unprecedented gate tunability. The graphene becomes highly hole-doped due to charge transfer from the neighboring magnetic insulator and further exhibits a variety of atypical gate-dependent transport features. The charge transfer can additionally be altered upon switching the magnetic states of the nearest CrI₃ layers. Our results provide a roadmap for exploiting proximity effects arising in graphene coupled to magnetic insulators.

Spontaneous Gully-Polarized Quantum Hall States in ABA Trilayer Graphene

Bernal-stacked multilayer graphene is a versatile platform to explore quantum transport phenomena and interaction physics due to its exceptional tunability via electrostatic gating. For instance, upon applying a perpendicular electric field, its band structure exhibits several off-center Dirac points (so-called Dirac gullies) in each valley. Here, the formation of Dirac gullies and the interaction-induced breakdown of gully coherence is explored via magnetotransport measurements in high-quality Bernal-stacked (ABA) trilayer graphene. At zero magnetic field, multiple Lifshitz transitions indicating the formation of Dirac gullies are identified. In the quantum Hall regime, the emergence of Dirac gullies is evident as an increase in Landau level degeneracy. When tuning both electric and magnetic fields, electron-electron interactions can be controllably enhanced until, beyond critical electric and magnetic fields, the gully degeneracy is eventually lifted. The arising correlated ground state is consistent with a previously predicted nematic phase that spontaneously breaks the rotational gully symmetry.

Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene

In conventional superconductors, Cooper pairing occurs between electrons of opposite spin. We observe spin-polarized superconductivity in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by a large applied perpendicular electric field. We observe a cascade of electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within the isospin space defined by the combination of the spin and momentum-space valley degrees of freedom. Although all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite magnetic field B_‖ ≈ 150 milliteslas applied parallel to the two-dimensional sheet. Superconductivity occurs near a symmetry-breaking transition and exists exclusively above the B_‖ limit expected of a paramagnetic superconductor with the observed transition critical temperature T_C ≈ 30 millikelvins, consistent with a spin-triplet order parameter.

Scanning Probe Lithography: State-of-the-Art and Future Perspectives

High-throughput and high-accuracy nanofabrication methods are required for the ever-increasing demand for nanoelectronics, high-density data storage devices, nanophotonics, quantum computing, molecular circuitry, and scaffolds in bioengineering used for cell proliferation applications. The scanning probe lithography (SPL) nanofabrication technique is a critical nanofabrication method with great potential to evolve into a disruptive atomic-scale fabrication technology to meet these demands. Through this timely review, we aspire to provide an overview of the SPL fabrication mechanism and the state-the-art research in this area, and detail the applications and characteristics of this technique, including the effects of thermal aspects and chemical aspects, and the influence of electric and magnetic fields in governing the mechanics of the functionalized tip interacting with the substrate during SPL. Alongside this, the review also sheds light on comparing various fabrication capabilities, throughput, and attainable resolution. Finally, the paper alludes to the fact that a majority of the reported literature suggests that SPL has yet to achieve its full commercial potential and is currently largely a laboratory-based nanofabrication technique used for prototyping of nanostructures and nanodevices.

Tunable Orbital Ferromagnetism at Noninteger Filling of a Moiré Superlattice

The flat bands resulting from moiré superlattices exhibit fascinating correlated electron phenomena such as correlated insulators, ( Nature 2018, 556 (7699), 80-84), ( Nature Physics 2019, 15 (3), 237) superconductivity, ( Nature 2018, 556 (7699), 43-50), ( Nature 2019, 572 (7768), 215-219) and orbital magnetism. ( Science 2019, 365 (6453), 605-608), ( Nature 2020, 579 (7797), 56-61), ( Science 2020, 367 (6480), 900-903) Such magnetism has been observed only at particular integer multiples of n₀, the density corresponding to one electron per moiré superlattice unit cell. Here, we report the experimental observation of ferromagnetism at noninteger filling (NIF) of a flat Chern band in a ABC-TLG/hBN moiré superlattice. This state exhibits prominent ferromagnetic hysteresis behavior with large anomalous Hall resistivity in a broad region of densities centered in the valence miniband at n = -2.3n₀. We observe that, not only the magnitude of the anomalous Hall signal, but also the sign of the hysteretic ferromagnetic response can be modulated by tuning the carrier density and displacement field. Rotating the sample in a fixed magnetic field demonstrates that the ferromagnetism is highly anisotropic and likely purely orbital in character.

Molecular Recognition by Silicon Nanowire Field-Effect Transistor and Single-Molecule Force Spectroscopy

Silicon nanowire (SiNW) field-effect transistors (FETs) have been developed as very sensitive and label-free biomolecular sensors. The detection principle operating in a SiNW biosensor is indirect. The biomolecules are detected by measuring the changes in the current through the transistor. Those changes are produced by the electrical field created by the biomolecule. Here, we have combined nanolithography, chemical functionalization, electrical measurements and molecular recognition methods to correlate the current measured by the SiNW transistor with the presence of specific molecular recognition events on the surface of the SiNW. Oxidation scanning probe lithography (o-SPL) was applied to fabricate sub-12 nm SiNW field-effect transistors. The devices were applied to detect very small concentrations of proteins (500 pM). Atomic force microscopy (AFM) single-molecule force spectroscopy (SMFS) experiments allowed the identification of the protein adsorption sites on the surface of the nanowire. We detected specific interactions between the biotin-functionalized AFM tip and individual avidin molecules adsorbed to the SiNW. The measurements confirmed that electrical current changes measured by the device were associated with the deposition of avidin molecules.

Self-Referenced Refractive Index Biosensing with Graphene Fano Resonance Modes

A hybrid structure composed of periodic monolayer graphene nanoribbons and a dielectric multilayer structure was designed to generate a Fano resonance (FR). The strong interaction between the surface plasmon resonance of graphene and the dielectric waveguide mode results in the FR. The finite element method is utilized to investigate the behaviors of the FR, and it matches well with the theoretical calculations using rigorous coupled wave theory. The results demonstrate that the profile of the FR can be passively tuned by the period of the graphene nanoribbons and actively tuned by the Fermi level of the graphene. The decoupled nature of the FR gives it potential applications as a self-calibrated refractive index biosensor, and the sensitivity can reach as high as 4.615 μm/RIU. Thus, this work provides a new idea for an excellent self-referencing refractive index biosensor.

Superconductivity in rhombohedral trilayer graphene

To access superconductivity via the electric field effect in a clean, two-dimensional device is a central goal of nanoelectronics. Recently, superconductivity has been realized in graphene moiré heterostructures^1-4; however, many of these structures are not mechanically stable, and experiments show signatures of strong disorder. Here we report the observation of superconductivity-manifesting as low or vanishing resistivity at sub-kelvin temperatures-in crystalline rhombohedral trilayer graphene^5,6, a structurally metastable carbon allotrope. Superconductivity occurs in two distinct gate-tuned regions (SC1 and SC2), and is deep in the clean limit defined by the ratio of mean free path and superconducting coherence length. Mapping of the normal state Fermi surfaces by quantum oscillations reveals that both superconductors emerge from an annular Fermi sea, and are proximal to an isospin-symmetry-breaking transition where the Fermi surface degeneracy changes⁷. SC1 emerges from a paramagnetic normal state, whereas SC2 emerges from a spin-polarized, valley-unpolarized half-metal¹⁷ and violates the Pauli limit for in-plane magnetic fields by at least one order of magnitude^8,9. We discuss our results in view of several mechanisms, including conventional phonon-mediated pairing^10,11, pairing due to fluctuations of the proximal isospin order¹², and intrinsic instabilities of the annular Fermi liquid^13,14. Our observation of superconductivity in a clean and structurally simple two-dimensional metal provides a model system to test competing theoretical models of superconductivity without the complication of modelling disorder, while enabling new classes of field-effect controlled electronic devices based on correlated electron phenomena and ballistic electron transport.

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.

Half- and quarter-metals in rhombohedral trilayer graphene

Ferromagnetism is most common in transition metal compounds where electrons occupy highly localized d orbitals. However, ferromagnetic order may also arise in low-density two-dimensional electron systems^1-5. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene⁶ drive spontaneous ferromagnetic polarization of the electron system into one or more spin and valley flavours. Using capacitance and transport measurements, we observe a cascade of transitions tuned to the density and electronic displacement field between phases in which quantum oscillations have fourfold, twofold or onefold degeneracy, associated with a spin- and valley-degenerate normal metal, spin-polarized 'half-metal', and spin- and valley-polarized 'quarter-metal', respectively. For electron doping, the salient features of the data are well captured by a phenomenological Stoner model⁷ that includes valley-anisotropic interactions. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, we introduce a moiré superlattice using a rotationally aligned hexagonal boron nitride substrate^5,8. Remarkably, we find that the isospin order is only weakly perturbed, with the moiré potential catalysing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter-metal states occur at half- or quarter-superlattice band filling. Our results show that rhombohedral graphene is an ideal platform for well-controlled tests of many-body theory, and reveal magnetism in moiré materials^4,5,9,10 to be fundamentally itinerant in nature.

Nanoimaging of Low-Loss Plasmonic Waveguide Modes in a Graphene Nanoribbon

Graphene nanoribbons are predicted to support low-loss and tunable plasmonic waveguide modes with an ultrasmall mode area. Experimental observation of the plasmonic waveguide modes in graphene nanoribbons, however, is challenging because conventional wet lithography has difficulty creating a clean graphene nanoribbon with a low edge roughness. Here, we use a dry lithography method to fabricate ultraclean and low-roughness graphene nanoribbons, which are then encapsulated in hexagonal boron nitride (hBN). We demonstrate low-loss plasmon propagation with a quality factor up to 35 in the ultraclean nanoribbon waveguide using cryogenic infrared nanoscopy. In addition, we observe both the fundamental and the higher-order plasmonic waveguide modes for the first time. All the plasmon waveguide modes can be tuned through electrostatic gating. The observed tunable plasmon waveguide modes in ultraclean graphene nanoribbons agree well with the finite-difference time-domain (FDTD) simulation results. They are promising for reconfigurable photonic circuits and devices at a subwavelength scale.

Moiré metrology of energy landscapes in van der Waals heterostructures

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe2/WSe2. Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.

Dynamics of a micro-electro-mechanical system associated with an atomic force microscope considering squeeze film damping

In the following paper, we present a nonlinear model of an atomic force microscope considering the potential of Lennard-Jones and the nonlinear friction produced by the squeeze film damping effect, between the cantilever and the sample. Specifically, we study the existence and stability of periodic solutions using the lower and upper solution method in the system without friction. The condition for persistence of the homocline orbit was established by Melnikov method when the model has nonlinear friction. In this sense, the analytic and numerical approach is presented to verify the solutions of the model.

Metallic Carbon Nanotube Nanocavities as Ultracompact and Low-loss Fabry-Perot Plasmonic Resonators

Plasmonic resonators enable deep subwavelength manipulation of light matter interactions and have been intensively studied both in fundamental physics as well as for potential technological applications. While various metallic nanostructures have been proposed as plasmonic resonators, their performances are rather limited at mid- and far-infrared wavelengths. Recently, highly confined and low-loss Luttinger liquid plasmons in metallic single-walled carbon nanotubes (SWNTs) have been observed at infrared wavelengths. Here, we tailor metallic SWNTs into ultraclean nanocavities by advanced scanning probe lithography and investigate plasmon modes in these individual nanocavities by infrared nanoimaging. The dependence of mode evolutions on cavity length and excitation wavelength can be captured by a Fabry-Perot resonator model of a plasmon nanowaveguide terminated by highly reflective ends. Plasmonic resonators based on SWNT nanocavities approach the ultimate plasmon confinement limit and open the door to the strong light-matter coupling regime, which may enable various nanophotonic applications.

Optical Patterning of Two-Dimensional Materials

Recent advances in the field of two-dimensional (2D) materials have led to new electronic and photonic devices enabled by their unique properties at atomic thickness. Structuring 2D materials into desired patterns on substrates is often an essential and foremost step for the optimum performance of the functional devices. In this regard, optical patterning of 2D materials has received enormous interest due to its advantages of high-throughput, site-specific, and on-demand fabrication. Recent years have witnessed scientific reports of a variety of optical techniques applicable to patterning 2D materials. In this minireview, we present the state-of-the-art optical patterning of 2D materials, including laser thinning, doping, phase transition, oxidation, and ablation. Several applications based on optically patterned 2D materials will be discussed as well. With further developments, optical patterning is expected to hold the key in pushing the frontiers of manufacturing and applications of 2D materials.