Engineering high quality graphene superlattices via ion milled ultra-thin etching masks.

Nanofabrication research pursues the miniaturization of patterned feature size. In the current state of the art, micron scale areas can be patterned with features down to ~30 nm pitch using electron beam lithography. Here, we demonstrate a nanofabrication technique which allows patterning periodic structures with a pitch down to 16 nm. It is based on focused ion beam milling of suspended membranes, with minimal proximity effects typical to standard electron beam lithography. The membranes are then transferred and used as hard etching masks. We benchmark our technique by electrostatically inducing a superlattice potential in graphene and observe bandstructure modification in electronic transport. Our technique opens the path towards the realization of very short period superlattices in 2D materials, but with the ability to control lattice symmetries and strength. This can pave the way for a versatile solid-state quantum simulator platform and the study of correlated electron phases.

Nanomechanical Resonators: Toward Atomic Scale.

The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.

Phonon-Induced Pairing in Quantum Dot Quantum Simulator.

Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well-studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context, we study the behavior of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. These findings will motivate further theoretical and experimental efforts to employ nanoelectromechanical systems to simulate strongly correlated systems with electron-phonon interactions.

Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene.

Superconductivity can occur under conditions approaching broken-symmetry parent states1. In bilayer graphene, the twisting of one layer with respect to the other at 'magic' twist angles of around 1 degree leads to the emergence of ultra-flat moiré superlattice minibands. Such bands are a rich and highly tunable source of strong-correlation physics2-5, notably superconductivity, which emerges close to interaction-induced insulating states6,7. Here we report the fabrication of magic-angle twisted bilayer graphene devices with highly uniform twist angles. The reduction in twist-angle disorder reveals the presence of insulating states at all integer occupancies of the fourfold spin-valley degenerate flat conduction and valence bands-that is, at moiré band filling factors ν = 0, ±1, ±2, ±3. At ν ≈ -2, superconductivity is observed below critical temperatures of up to 3 kelvin. We also observe three new superconducting domes at much lower temperatures, close to the ν = 0 and ν = ±1 insulating states. Notably, at ν = ± 1 we find states with non-zero Chern numbers. For ν = -1 the insulating state exhibits a sharp hysteretic resistance enhancement when a perpendicular magnetic field greater than 3.6 tesla is applied, which is consistent with a field-driven phase transition. Our study shows that broken-symmetry states, interaction-driven insulators, orbital magnets, states with non-zero Chern numbers and superconducting domes occur frequently across a wide range of moiré flat band fillings, including close to charge neutrality. This study provides a more detailed view of the phenomenology of magic-angle twisted bilayer graphene, adding to our evolving understanding of its emergent properties.

Electrical Control of Lifetime-Limited Quantum Emitters Using 2D Materials.

Solid-state quantum emitters are a mainstay of quantum nanophotonics as integrated single-photon sources (SPS) and optical nanoprobes. Integrating such emitters with active nanophotonic elements is desirable in order to attain efficient control of their optical properties, but it typically degrades the photostability of the emitter itself. Here, we demonstrate a tunable hybrid device that integrates state of the art lifetime-limited single emitters (line width ∼40 MHz) and 2D materials at subwavelength separation without degradation of the emission properties. Our device's nanoscale dimensions enable ultrabroadband tuning (tuning range >400 GHz) and fast modulation (frequency ∼100 MHz) of the emission energy, which renders it an integrated, ultracompact tunable SPS. Conversely, this offers a novel approach to optical sensing of 2D material properties using a single emitter as a nanoprobe.

Layering Transition in Superfluid Helium Adsorbed on a Carbon Nanotube Mechanical Resonator.

Helium is recognized as a model system for the study of phase transitions. Of particular interest is the superfluid phase in two dimensions. We report measurements on superfluid helium films adsorbed on the surface of a suspended carbon nanotube. We measure the mechanical vibrations of the nanotube to probe the adsorbed helium film. We demonstrate the formation of helium layers up to five atoms thickness. Upon increasing the vapor pressure, we observe layer-by-layer growth with discontinuities in both the number of adsorbed atoms and the speed of the third sound in the adsorbed film. These hitherto unobserved discontinuities point to a series of first-order layering transitions. Our results show that helium multilayers adsorbed on a nanotube are of unprecedented quality compared to previous works. They pave the way to new studies of quantized superfluid vortex dynamics on cylindrical surfaces, of the Berezinskii-Kosterlitz-Thouless phase transition in this new geometry, and perhaps also to supersolidity in crystalline single layers as predicted in quantum Monte Carlo calculations.

Optomechanical Measurement of Thermal Transport in Two-Dimensional MoSe2 Lattices.

Nanomechanical resonators have emerged as sensors with exceptional sensitivities. These sensing capabilities open new possibilities in the studies of the thermodynamic properties in condensed matter. Here, we use mechanical sensing as a novel approach to measure the thermal properties of low-dimensional materials. We measure the temperature dependence of both the thermal conductivity and the specific heat capacity of a transition metal dichalcogenide monolayer down to cryogenic temperature, something that has not been achieved thus far with a single nanoscale object. These measurements show how heat is transported by phonons in two-dimensional systems. Both the thermal conductivity and the specific heat capacity measurements are consistent with predictions based on first-principles.

Environmental Electrometry with Luminescent Carbon Nanotubes.

We demonstrate that localized excitons in luminescent carbon nanotubes can be utilized to study electrostatic fluctuations in the nanotube environment with sensitivity down to the elementary charge. By monitoring the temporal evolution of the cryogenic photoluminescence from individual carbon nanotubes grown on silicon oxide and hexagonal boron nitride, we characterize the dynamics of charge trap defects for both dielectric supports. We find a one order of magnitude reduction in the photoluminescence spectral wandering for nanotubes on extended atomically flat terraces of hexagonal boron nitride. For nanotubes on hexagonal boron nitride with pronounced spectral fluctuations, our analysis suggests proximity to terrace ridges where charge fluctuators agglomerate to exhibit areal densities exceeding those of silicon oxide. Our results establish carbon nanotubes as sensitive probes of environmental charge fluctuations and highlight their potential for applications in electrometric nanodevices with all-optical readout.

Energy-dependent path of dissipation in nanomechanical resonators.

Energy decay plays a central role in a wide range of phenomena, such as optical emission, nuclear fission, and dissipation in quantum systems. Energy decay is usually described as a system leaking energy irreversibly into an environmental bath. Here, we report on energy decay measurements in nanomechanical systems based on multilayer graphene that cannot be explained by the paradigm of a system directly coupled to a bath. As the energy of a vibrational mode freely decays, the rate of energy decay changes abruptly to a lower value. This finding can be explained by a model where the measured mode hybridizes with other modes of the resonator at high energy. Below a threshold energy, modes are decoupled, resulting in comparatively low decay rates and giant quality factors exceeding 1 million. Our work opens up new possibilities to manipulate vibrational states, engineer hybrid states with mechanical modes at completely different frequencies, and to study the collective motion of this highly tunable system.

High Quality Factor Mechanical Resonators Based on WSe2 Monolayers.

Suspended monolayer transition metal dichalcogenides (TMD) are membranes that combine ultralow mass and exceptional optical properties, making them intriguing materials for opto-mechanical applications. However, the low measured quality factor of TMD resonators has been a roadblock so far. Here, we report an ultrasensitive optical readout of monolayer TMD resonators that allows us to reveal their mechanical properties at cryogenic temperatures. We find that the quality factor of monolayer WSe2 resonators greatly increases below room temperature, reaching values as high as 1.6 × 10(4) at liquid nitrogen temperature and 4.7 × 10(4) at liquid helium temperature. This surpasses the quality factor of monolayer graphene resonators with similar surface areas. Upon cooling the resonator, the resonant frequency increases significantly due to the thermal contraction of the WSe2 lattice. These measurements allow us to experimentally study the thermal expansion coefficient of WSe2 monolayers for the first time. High Q-factors are also found in resonators based on MoS2 and MoSe2 monolayers. The high quality-factor found in this work opens new possibilities for coupling mechanical vibrational states to two-dimensional excitons, valley pseudospins, and single quantum emitters and for quantum opto-mechanical experiments based on the Casimir interaction.

Electromechanical control of nitrogen-vacancy defect emission using graphene NEMS.

Despite recent progress in nano-optomechanics, active control of optical fields at the nanoscale has not been achieved with an on-chip nano-electromechanical system (NEMS) thus far. Here we present a new type of hybrid system, consisting of an on-chip graphene NEMS suspended a few tens of nanometres above nitrogen-vacancy centres (NVCs), which are stable single-photon emitters embedded in nanodiamonds. Electromechanical control of the photons emitted by the NVC is provided by electrostatic tuning of the graphene NEMS position, which is transduced to a modulation of NVC emission intensity. The optomechanical coupling between the graphene displacement and the NVC emission is based on near-field dipole-dipole interaction. This class of optomechanical coupling increases strongly for smaller distances, making it suitable for nanoscale devices. These achievements hold promise for selective control of emitter arrays on-chip, optical spectroscopy of individual nano-objects, integrated optomechanical information processing and open new avenues towards quantum optomechanics.

Silicon-Based Chemical Motors: An Efficient Pump for Triggering and Guiding Fluid Motion Using Visible Light.

We report a simple yet highly efficient chemical motor that can be controlled with visible light. The motor made from a noble metal and doped silicon acts as a pump, which is driven through a light-activated catalytic reaction process. We show that the actuation is based on electro-osmosis with the electric field generated by chemical reactions at the metal and silicon surfaces, whereas the contribution of diffusio-osmosis to the actuation is negligible. Surprisingly, the pump can be operated using water as fuel. This is possible because of the large ζ-potential of silicon, which makes the electro-osmotic fluid motion sizable even though the electric field generated by the reaction is weak. The electro-hydrodynamic process is greatly amplified with the addition of reactive species, such as hydrogen peroxide, which generates higher electric fields. Another remarkable finding is the tunability of silicon-based pumps. That is, it is possible to control the speed of the fluid with light. We take advantage of this property to manipulate the spatial distribution of colloidal microparticles in the liquid and to pattern colloidal microparticle structures at specific locations on a wafer surface. Silicon-based pumps hold great promise for controlled mass transport in fluids.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems.

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Sequential tasks performed by catalytic pumps for colloidal crystallization.

Gold-platinum catalytic pumps immersed in a chemical fuel are used to manipulate silica colloids. The manipulation relies on the electric field and the fluid flow generated by the pump. Catalytic pumps perform various tasks, such as the repulsion of colloids, the attraction of colloids, and the guided crystallization of colloids. We demonstrate that catalytic pumps can execute these tasks sequentially over time. Switching from one task to the next is related to the local change of the proton concentration, which modifies the colloid ζ potential and, consequently, the electric force acting on the colloids.

Harnessing vacuum forces for quantum sensing of graphene motion.

Position measurements at the quantum level are vital for many applications but also challenging. Typically, methods based on optical phase shifts are used, but these methods are often weak and difficult to apply to many materials. An important example is graphene, which is an excellent mechanical resonator due to its small mass and an outstanding platform for nanotechnologies, but it is largely transparent. Here, we present a novel detection scheme based upon the strong, dispersive vacuum interactions between a graphene sheet and a quantum emitter. In particular, the mechanical displacement causes strong changes in the vacuum-induced shifts of the transition frequency of the emitter, which can be read out via optical fields. We show that this enables strong quantum squeezing of the graphene position on time scales that are short compared to the mechanical period.

Parametric amplification and self-oscillation in a nanotube mechanical resonator.

A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the line shape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultralow force sensing experiments.

Structured graphene devices for mass transport.

The reversible atomic-mass transport along graphene devices has been achieved. The motion of Al and Au in the form of atoms or clusters is driven by applying an electric field between the metal electrodes that contact the graphene sheet. It is shown that Al moves in the direction of the applied electric field whereas Au tends to diffuse in all directions. The control of the motion of Al is further demonstrated by achieving a 90° turn, using a graphene device patterned in a crossroads configuration. The controlled motion of Al is attributed to the charge transfer from Al onto the graphene so that the Al is effectively charged and can be accelerated by the applied electric field. To get further insight into the actuation mechanism, theoretical simulations of individual Al and Au impurities on a perfect graphene sheet were performed. The direct (electrostatic) force was found to be ∼1 pN and dominant over the wind force. These findings hold promise for practical use in future mass transport in complex circuits.

Damaging graphene with ozone treatment: a chemically tunable metal-insulator transition.

We present a multiscale ab initio study of electronic and transport properties of two-dimensional graphene after epoxide functionalization via ozone treatment. The orbital rehybridization induced by the epoxide groups triggers a strong intervalley scattering and changes dramatically the conduction properties of graphene. By varying the coverage density of epoxide defects from 0.1 to 4%, charge conduction can be tuned from a diffusive to a strongly localized regime, with localization lengths down to a few nanometers long. Experimental results supporting the interpretation as a metal-insulator transition are also provided.

Transport properties of graphene in the high-current limit.

We present a detailed study of the high-current transport properties of graphene devices patterned in a four-point configuration. The current tends to saturate as the voltage across graphene is increased but never reaches the complete saturation as in metallic nanotubes. Measurements are compared to a model based on the Boltzmann equation, which includes electron-scattering processes due to charged and neutral impurities, and graphene optical phonons. The saturation is incomplete because of the competition between disorder and optical phonon scattering.