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We present in situ calorimetry, thermal conductivity, and thermal diffusivity measurements of materials using temperature-sensing optical wireless integrated circuits (OWiCs). These microscopic and untethered optical sensors eliminate input wires and reduce parasitic effects. Each OWiC has a mass of ∼100 ng, a 100-μm-scale footprint, and a thermal response time of microseconds. We demonstrate that they can measure the thermal properties of nearly any material, from aerogels to metals, on samples as small as 100 ng and over thermal diffusivities covering four orders of magnitude. They also function over a broad temperature range, and we present proof-of-concept measurements of the thermodynamic phase transitions in both liquid crystal 5CB and gadolinium.

Biological systems convert chemical energy into mechanical work by using protein catalysts that assume kinetically controlled conformational states. Synthetic chemomechanical systems using chemical catalysis have been reported, but they are slow, require high temperatures to operate, or indirectly perform work by harnessing reaction products in liquids (e.g., heat or protons). Here, we introduce a bioinspired chemical strategy for gas-phase chemomechanical transduction that sequences the elementary steps of catalytic reactions on ultrathin (total = 1 atm). When fueled by hydrogen gas and either oxygen or ozone gas, we show how kinetically controlled surface states of the catalyst can be exploited to achieve fast actuation (600 ms/cycle) at 20 °C. We also show that the approach can integrate photochemically controlled reactions and can be used to drive the reconfiguration of microhinges and complex origami- and kirigami-based microstructures.

Cilial pumping is a powerful strategy used by biological organisms to control and manipulate fluids at the microscale. However, despite numerous recent advances in optically, magnetically and electrically driven actuation, development of an engineered cilial platform with the potential for applications has remained difficult to realize

Significance Programmable self-assembly of smart, digital, and structurally complex materials from simple components remains a long-standing goal of material science. Here, we propose an assembly platform where information is encoded into building blocks using arrays of magnets that induce specific binding. Similar to current state-of-the-art platforms, magnetic encoding can achieve controlled polymerization of lone panels, complementary binding of panel strands, and 3D assembly of panel nets. This platform, however, has several advantages over current methods in that the approach is scale-invariant, has tunable mechanical strength, and has high information capacity for programmable self-assembly. We envision that this approach will lead to the formation of structures that transmit information, act as mechanical elements, or function as machines across length scales., Programmable self-assembly of smart, digital, and structurally complex materials from simple components at size scales from the macro to the nano remains a long-standing goal of material science. Here, we introduce a platform based on magnetic encoding of information to drive programmable self-assembly that works across length scales. Our building blocks consist of panels with different patterns of magnetic dipoles that are capable of specific binding. Because the ratios of the different panel-binding energies are scale-invariant, this approach can, in principle, be applied down to the nanometer scale. Using a centimeter-sized version of these panels, we demonstrate 3 canonical hallmarks of assembly: controlled polymerization of individual building blocks; assembly of 1-dimensional strands made of panels connected by elastic backbones into secondary structures; and hierarchical assembly of 2-dimensional nets into 3-dimensional objects. We envision that magnetic encoding of assembly instructions into primary structures of panels, strands, and nets will lead to the formation of secondary and even tertiary structures that transmit information, act as mechanical elements, or function as machines on scales ranging from the nano to the macro.

The field of miniature mechanical oscillators is rapidly evolving, with emerging applications including signal processing, biological detection1 and fundamental tests of quantum mechanics2. As the dimensions of a mechanical oscillator shrink to the molecular scale, such as in a carbon nanotube resonator3–7, their vibrations become increasingly coupled and strongly interacting8,9 until even weak thermal fluctuations could make the oscillator nonlinear10–13. The mechanics at this scale possesses rich dynamics, unexplored because an efficient way of detecting the motion in real time is lacking. Here we directly measure the thermal vibrations of a carbon nanotube in real time using a high-finesse micrometre-scale silicon nitride optical cavity as a sensitive photonic microscope. With the high displacement sensitivity of 700 fm Hz−1/2 and the fine time resolution of this technique, we were able to discover a realm of dynamics undetected by previous time-averaged measurements and a room-temperature coherence that is nearly three orders of magnitude longer than previously reported. We find that the discrepancy in the coherence stems from long-time non-equilibrium dynamics, analogous to the Fermi–Pasta–Ulam–Tsingou recurrence seen in nonlinear systems14. Our data unveil the emergence of a weakly chaotic mechanical breather15, in which vibrational energy is recurrently shared among several resonance modes—dynamics that we are able to reproduce using a simple numerical model. These experiments open up the study of nonlinear mechanical systems in the Brownian limit (that is, when a system is driven solely by thermal fluctuations) and present an integrated, sensitive, high-bandwidth nanophotonic interface for carbon nanotube resonators. The thermal vibrations of a carbon nanotube are directly measured in real time with high displacement sensitivity and fine time resolution, revealing dynamics undetected by previous time-averaged measurements.

Monolayer graphene aligned with hexagonal boron nitride ($h\text{\ensuremath{-}}\mathrm{BN}$) develops a gap at the charge neutrality point (CNP). This gap has previously been extensively studied by electrical transport through thermal activation measurements. Here, we report the determination of the gap size at the CNP of $\mathrm{graphene}/h\text{\ensuremath{-}}\mathrm{BN}$ superlattice through photocurrent spectroscopy study. We demonstrate two distinct measurement approaches to extract the gap size. A maximum of $\ensuremath{\sim}14\text{ }\text{ }\mathrm{meV}$ gap is observed for devices with a twist angle of less than 1\ifmmode^\circ\else\textdegree\fi{}. This value is significantly smaller than that obtained from thermal activation measurements, yet larger than the theoretically predicted single-particle gap. Our results suggest that lattice relaxation and moderate electron-electron interaction effects may enhance the CNP gap in $\mathrm{graphene}/h\text{\ensuremath{-}}\mathrm{BN}$ superlattice.

In vivo, chronic neural recording is critical to understand the nervous system, while a tetherless, miniaturized recording unit can render such recording minimally invasive. We present a tetherless, injectable micro-scale opto-electronically transduced electrode (MOTE) that is $\sim 60~\mu \text{m}\,\,\times 30~\mu \text{m}\,\,\times 330~\mu \text{m}$ , the smallest neural recording unit to date. The MOTE consists of an AlGaAs micro-scale light emitting diode ( $\mu $ LED) heterogeneously integrated on top of conventional 180nm complementary metal-oxide-semiconductor (CMOS) circuit. The MOTE combines the merits of optics (AlGaAs $\mu $ LED for power and data uplink), and of electronics (CMOS for signal amplification and encoding). The optical powering and communication enable the extreme scaling while the electrical circuits provide a high temporal resolution ( $ ). This paper elaborates on the heterogeneous integration in MOTEs, a topic that has been touted without much demonstration on feasibility or scalability. Based on photolithography, we demonstrate how to build heterogenous systems that are scalable as well as biologically stable– the MOTEs can function in saline water for more than six months, and in a mouse brain for two months (and counting). We also present handling/insertion techniques for users (i.e. biologists) to deploy MOTEs with little or no extra training. [2020-0080]

We have developed a fabrication process that can be used to build millions of microscopic, electronically-integrated robots. Our procedure includes steps for building silicon microelectronics, building components for actuation, encapsulation steps, and a process for releasing the robots into aqueous environments. Each step is carried out massively in parallel, allowing us to build over a million robots on a single 4-inch wafer. Broadly, the new actuators and fabrication protocols presented here offer a generic platform and can be used to make a wide range of silicon-based, functional robotic systems that are too small to be resolved by the naked eye.

Solid-state magnetic field sensors are important for applications in commercial electronics and fundamental materials research. Most magnetic field sensors function in a limited range of temperature and magnetic field, but Hall sensors in principle operate over a broad range of these conditions. Here, we evaluate ultraclean graphene as a material platform for high-performance Hall sensors. We fabricate micrometer-scale devices from graphene encapsulated with hexagonal boron nitride and few-layer graphite. We optimize the magnetic field detection limit under different conditions. At 1 kHz for a 1 μm device, we estimate a detection limit of 700 nT Hz−1/2 at room temperature, 80 nT Hz−1/2 at 4.2 K, and 3 μT Hz−1/2 in 3 T background field at 4.2 K. Our devices perform similarly to the best Hall sensors reported in the literature at room temperature, outperform other Hall sensors at 4.2 K, and demonstrate high performance in a few-Tesla magnetic field at which the sensors exhibit the quantum Hall effect., The development of high-performance magnetic field sensors is important for magnetic sensing and imaging. Here, the authors fabricate Hall sensors from graphene encapsulated in hBN and few-layer graphite, demonstrating high performance over a wide range of temperature and background magnetic field.

Origami design principles are scale invariant and enable direct miniaturization of origami structures provided the sheets used for folding have equal thickness to length ratios. Recently, seminal steps have been taken to fabricate microscale origami using unidirectionally actuated sheets with nanoscale thickness. Here, we extend the full power of origami-inspired fabrication to nanoscale sheets by engineering bidirectional folding with 4 nm thick atomic layer deposition (ALD) SiNx-SiO2 bilayer films. Strain differentials within these bilayers result in bending, producing microscopic radii of curvature. We lithographically pattern these bilayers and localize the bending using rigid panels to fabricate a variety of complex micro-origami devices. Upon release, these devices self-fold according to prescribed patterns. Our approach combines planar semiconductor microfabrication methods with computerized origami design, making it easy to fabricate and deploy such microstructures en masse. These devices represent an important step forward in the fabrication and assembly of deployable micromechanical systems that can interact with and manipulate micro- and nanoscale environments., Comment: This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright American Chemical Society after peer review. To access the final edited and published work see: https://pubs.acs.org/articlesonrequest/AOR-JJHKJZVTJF4JFWSYZ2NW

Significance The smallest objects resolvable by the unaided human eye are approximately 100 μm in size. This limit sets a boundary between the familiar and the microscopic, the visible and invisible worlds. Here we describe the fabrication of tiny wireless sensors, optical wireless integrated circuits (OWICs) for optical wireless integrated circuits. OWICs are truly microscopic in size, visible to the naked eye at best as a tiny, undifferentiated speck, yet they can sense their environment and report the information back to the macroscopic world. They have potential applications in many areas of science and technology, ranging from neuroscience to chemical sensing.

Recording neural activity in live animals in vivo with minimal tissue damage is one of the major barriers to understanding the nervous system. This paper presents the technology for a tetherless opto-electronic neural interface based on 180 nm CMOS circuits, heterogeneously integrated with an AlGaAs diode that functions as both a photovoltaic and light emitting diode. These microscale opto-electrically transduced electrodes (MOTEs) are powered by and communicate through an optical interface, simultaneously enabling high temporal-resolution electrical measurements without a tether or a bulky RF coil. The MOTE presented here is 250 μ m × 57 μ m, consumes 1 μ W of electrical power, and is capable of capturing and encoding neural signals before transmitting the encoded signals. The measured noise floor is as low as 15 μ VRMS at a 15 kHz bandwidth.

Fifty years of Moore’s law scaling in microelectronics have brought remarkable opportunities for the rapidly evolving field of microscopic robotics1–5. Electronic, magnetic and optical systems now offer an unprecedented combination of complexity, small size and low cost6,7, and could be readily appropriated for robots that are smaller than the resolution limit of human vision (less than a hundred micrometres)8–11. However, a major roadblock exists: there is no micrometre-scale actuator system that seamlessly integrates with semiconductor processing and responds to standard electronic control signals. Here we overcome this barrier by developing a new class of voltage-controllable electrochemical actuators that operate at low voltages (200 microvolts), low power (10 nanowatts) and are completely compatible with silicon processing. To demonstrate their potential, we develop lithographic fabrication-and-release protocols to prototype sub-hundred-micrometre walking robots. Every step in this process is performed in parallel, allowing us to produce over one million robots per four-inch wafer. These results are an important advance towards mass-manufactured, silicon-based, functional robots that are too small to be resolved by the naked eye. A new class of voltage-controllable electrochemical actuators that are compatible with silicon processing are used to produce over one million sub-hundred-micrometre walking robots on a single four-inch wafer.

Measuring the behavior of redox-active molecules in space and time is crucial for better understanding of chemical and biological systems and for the development of new technologies. Optical schemes are non-invasive, scalable and can be applied to many different systems, but usually have a slow response compared to electrical detection methods. Furthermore, many fluorescent molecules for redox detection degrade in brightness over long exposure times. Here we show that the photoluminescence of pixel arrays of an atomically thin two-dimensional (2D) material, a monolayer of MoS$_{2}$, can image spatial and temporal changes in redox molecule concentration in real time. Because of the strong dependence of MoS$_{2}$ photoluminescence on doping and sensitivity to surface changes characteristic of 2D materials, changes in the local chemical potential significantly modulate the photoluminescence of MoS$_{2}$, with a sensitivity of 0.9 mV/$\sqrt{Hz}$ on a 5 $\mu$m by 5 $\mu$m pixel, corresponding to better than parts-per-hundred changes in redox molecule concentration down to nanomolar concentrations at 100 ms frame rates. The real-time imaging of electrochemical potentials with a fast response time provides a new strategy for visualizing chemical reactions and biomolecules with a 2D material screen.

A Correction to this paper has been published: https://doi.org/10.1038/s41467-021-20969-z.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Recording neural activity in live animals in vivo with minimal tissue damage is one of the major barriers to understanding the nervous system. This paper presents the technology for a tetherless opto-electronic neural interface based on 180 nm CMOS circuits, heterogeneously integrated with an AlGaAs diode that functions as both a photovoltaic and light emitting diode. These microscale opto-electrically transduced electrodes (MOTEs) are powered by, and communicate through an optical interface, simultaneously enabling high temporal-resolution electrical measurements without a tether or a bulky RF coil. The MOTE presented here is 250 μm × 57 μm, consumes 1 of electrical power, and is capable of capturing and encoding neural signals before transmitting the encoded signals. The measured noise floor is as low as 15 μVrms at a 15 KHz bandwidth.

Tensioned graphene membranes are of interest both for fundamental physics and for applications ranging from water filtration to nanomechanical resonators. It is generally assumed that these membranes have a stretching modulus of about 340 N/m and a negative, temperature-independent thermal expansion coefficient due to transverse phonon modes. In this paper, we study the two-dimensional Young's modulus and thermal expansion of graphene as functions of temperature by using laser interferometry to detect the static displacement of the membrane in a cryostat. Surprisingly, we find that the modulus decreases strongly with increasing temperature, which leads to a positive temperature-dependent thermal expansion coefficient. We show that the thermally rippled membrane theory is not consistent with our data, while the effects of surface contaminants typically present on these membranes may explain the observed behavior. Our experiments undermine long-standing assumptions about tensioned two-dimensional membranes, but are consistent with puzzling behavior observed in previous experiments on graphene resonators.

Origami-inspired fabrication presents an attractive platform for miniaturizing machines: thinner layers of folding material lead to smaller devices, provided that key functional aspects, such as conductivity, stiffness, and flexibility, are persevered. Here, we show origami fabrication at its ultimate limit by using 2D atomic membranes as a folding material. As a prototype, we bond graphene sheets to nanometer-thick layers of glass to make ultrathin bimorph actuators that bend to micrometer radii of curvature in response to small strain differentials. These strains are two orders of magnitude lower than the fracture threshold for the device, thus maintaining conductivity across the structure. By patterning 2-[Formula: see text]m-thick rigid panels on top of bimorphs, we localize bending to the unpatterned regions to produce folds. Although the graphene bimorphs are only nanometers thick, they can lift these panels, the weight equivalent of a 500-nm-thick silicon chip. Using panels and bimorphs, we can scale down existing origami patterns to produce a wide range of machines. These machines change shape in fractions of a second when crossing a tunable pH threshold, showing that they sense their environments, respond, and perform useful functions on time and length scales comparable with microscale biological organisms. With the incorporation of electronic, photonic, and chemical payloads, these basic elements will become a powerful platform for robotics at the micrometer scale.

Heaven is in the Cloud in this new tome. Paul McEuen watches in wonder. Heaven is in the Cloud in this new tome. Paul McEuen watches in wonder.

For centuries, practitioners of origami ('ori', fold; 'kami', paper) and kirigami ('kiru', cut) have fashioned sheets of paper into beautiful and complex three-dimensional structures. Both techniques are scalable, and scientists and engineers are adapting them to different two-dimensional starting materials to create structures from the macro- to the microscale. Here we show that graphene is well suited for kirigami, allowing us to build robust microscale structures with tunable mechanical properties. The material parameter crucial for kirigami is the Föppl-von Kármán number γ: an indication of the ratio between in-plane stiffness and out-of-plane bending stiffness, with high numbers corresponding to membranes that more easily bend and crumple than they stretch and shear. To determine γ, we measure the bending stiffness of graphene monolayers that are 10-100 micrometres in size and obtain a value that is thousands of times higher than the predicted atomic-scale bending stiffness. Interferometric imaging attributes this finding to ripples in the membrane that stiffen the graphene sheets considerably, to the extent that γ is comparable to that of a standard piece of paper. We may therefore apply ideas from kirigami to graphene sheets to build mechanical metamaterials such as stretchable electrodes, springs, and hinges. These results establish graphene kirigami as a simple yet powerful and customizable approach for fashioning one-atom-thick graphene sheets into resilient and movable parts with microscale dimensions.

The field of miniature mechanical oscillators is rapidly evolving, with emerging applications including signal processing, biological detection

Using the valleys in monolayer MoS 2 The electronic structure of the two-dimensional material MoS 2 has two distinct “valleys” of energy that may help to carry information in future electronic devices. Mak et al. observed the so-called valley Hall effect in a monolayer of MoS 2 . The electrons from different valleys moved in opposite directions across the sample, with one valley being overrepresented with respect to the other. The scientists achieved this by shining circularly polarized light on the material, which created an imbalance in the population of the two valleys. The findings may enable practical applications in the newly formed field of valleytronics. Science , this issue p. 1489

Bending and folding techniques such as origami and kirigami enable the scale-invariant design of 3D structures, metamaterials, and robots from 2D starting materials. These design principles are especially valuable for small systems because most micro- and nanofabrication involves lithographic patterning of planar materials. Ultrathin films of inorganic materials serve as an ideal substrate for the fabrication of flexible microsystems because they possess high intrinsic strength, are not susceptible to plasticity, and are easily integrated into microfabrication processes. Here, atomic layer deposition (ALD) is employed to synthesize films down to 2 nm thickness to create membranes, metamaterials, and machines with micrometer-scale dimensions. Two materials are studied as model systems: ultrathin SiO2 and Pt. In this thickness limit, ALD films of these materials behave elastically and can be fabricated with fJ-scale bending stiffnesses. Further, ALD membranes are utilized to design micrometer-scale mechanical metamaterials and magnetically actuated 3D devices. These results establish thin ALD films as a scalable basis for micrometer-scale actuators and robotics.

The overall signal-to-noise ratio per unit dose for X-ray diffraction data from protein crystals can be improved by reducing the mass and density of all material surrounding the crystals. This article demonstrates a path towards the practical ultimate in background reduction by use of atomically thin graphene sheets as a crystal mounting platform for protein crystals. The results show the potential for graphene in protein crystallography and other cases where X-ray scatter from the mounting material must be reduced and specimen dehydration prevented, such as in coherent X-ray diffraction imaging of microscopic objects.

Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultra-clean suspended carbon nanotube to realize this system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their spin and isospin quantum numbers. These states fall into two multiplets according to their exchange symmetries. The formation of a strongly-interacting Wigner molecule is evident from the small energy splitting measured between the two multiplets, that is quenched by an order of magnitude compared to the non-interacting value. Our ability to tune the two-electron state in space and to study it for both electrons and holes provides an unambiguous demonstration of the fundamental Wigner molecule state., Comment: SP and FK contributed equally to this work

A major achievement of the past decade has been the realization of macroscopic quantum systems by exploiting the interactions between optical cavities and mechanical resonators. In these systems, phonons are coherently annihilated or created in exchange for photons. Similar phenomena have recently been observed through phonon-cavity coupling - energy exchange between the modes of a single system mediated by intrinsic material nonlinearity. This has so far been demonstrated primarily for bulk crystalline, high-quality-factor (Q > 105) mechanical systems operated at cryogenic temperatures. Here, we propose graphene as an ideal candidate for the study of such nonlinear mechanics. The large elastic modulus of this material and capability for spatial symmetry breaking via electrostatic forces is expected to generate a wealth of nonlinear phenomena, including tunable intermodal coupling. We have fabricated circular graphene membranes and report strong phonon-cavity effects at room temperature, despite the modest Q factor (∼100) of this system. We observe both amplification into parametric instability (mechanical lasing) and the cooling of Brownian motion in the fundamental mode through excitation of cavity sidebands. Furthermore, we characterize the quenching of these parametric effects at large vibrational amplitudes, offering a window on the all-mechanical analogue of cavity optomechanics, where the observation of such effects has proven elusive.

The cooling of hot electrons in graphene is the critical process underlying the operation of exciting new graphene-based optoelectronic and plasmonic devices, but the nature of this cooling is controversial. We extract the hot electron cooling rate near the Fermi level by using graphene as novel photothermal thermometer that measures the electron temperature ($T(t)$) as it cools dynamically. We find the photocurrent generated from graphene $p-n$ junctions is well described by the energy dissipation rate $C dT/dt=-A(T^3-T_l^3)$, where the heat capacity is $C=\alpha T$ and $T_l$ is the base lattice temperature. These results are in disagreement with predictions of electron-phonon emission in a disorder-free graphene system, but in excellent quantitative agreement with recent predictions of a disorder-enhanced supercollision (SC) cooling mechanism. We find that the SC model provides a complete and unified picture of energy loss near the Fermi level over the wide range of electronic (15 to $\sim$3000 K) and lattice (10 to 295 K) temperatures investigated., Comment: 7pages, 5 figures

We simulated the behavior of suspended carbon nanotube resonators over a broad range of temperatures to explore the physics of semiflexible polymers in underdamped environments. We find that thermal fluctuations induce strong coupling between resonance modes. This effect leads to spectral fluctuations that readily account for the experimentally observed quality factors Q ∼ 100 at 300 K . Using a mean-field approach to describe fluctuations, we analytically calculate Q and frequency shifts in tensioned and buckled carbon nanotubes and find excellent agreement with simulations.

Over the last fifty years, small has emerged as the new big thing. The reduction of information and electronics to nanometer dimensions has revolutionized science, technology, and society. Now scientists and engineers are creating physical machines that operate at the nanoscale. Using approaches ranging from lithographic patterning to the co-opting of biological machinery, new devices are being built that can navigate, sense, and alter the nanoscale world. In the coming decades, these machines will have enormous impact infields ranging from biotechnology to quantum physics, blurring the boundary between technology and life.

Efficient Carbon Nanotube Photodiodes A single photon absorbed in a single-walled carbon nanotube device can generate multiple unbound particles carrying an electric charge. Gabor et al. (p. 1367 ) report that in such a device at low temperatures, excitation with light of increasing energy leads to well-defined stepwise increases in current. Interestingly, because of the unique band structure of carbon nanotubes, this behavior is analogous to particle-antiparticle creation commonly observed in high-energy particle physics. These observations point to the promise of investigations in other nanoscale carbon systems, such as graphene, and could lead to numerous applications, including highly sensitive photon detection and ultra-efficient photovoltaics.

We report on a method to produce free-standing graphene sheets from epitaxial graphene on silicon carbide (SiC) substrate. Doubly clamped nanomechanical resonators with lengths up to 20 microm were patterned using this technique and their resonant motion was actuated and detected optically. Resonance frequencies of the order of tens of megahertz were measured for most devices, indicating that the resonators are much stiffer than expected for beams under no tension. Raman spectroscopy suggests that the graphene is not chemically modified during the release of the devices, demonstrating that the technique is a robust means of fabricating large-area suspended graphene structures.

We demonstrate that a monolayer graphene membrane is impermeable to standard gases including helium. By applying a pressure difference across the membrane, we measure both the elastic constants and the mass of a single layer of graphene. This pressurized graphene membrane is the world's thinnest balloon and provides a unique separation barrier between 2 distinct regions that is only one atom thick.

Nanoelectromechanical systems were fabricated from single- and multilayer graphene sheets by mechanically exfoliating thin sheets from graphite over trenches in silicon oxide. Vibrations with fundamental resonant frequencies in the megahertz range are actuated either optically or electrically and detected optically by interferometry. We demonstrate room-temperature charge sensitivities down to 8 × 10 –4 electrons per root hertz. The thinnest resonator consists of a single suspended layer of atoms and represents the ultimate limit of two-dimensional nanoelectromechanical systems.

The electronic capacitance of a one-dimensional system such as a carbon nanotube is a thermodynamic quantity that contains fundamental information about the ground state1. It is composed of an electrostatic component describing the interactions between electrons and their correlations, and a kinetic term given by the electronic density of states. Here, we use a field-effect transistor geometry to obtain the first direct capacitance measurement of individual carbon nanotubes, as a function of the carrier density. Our measurements detect the electrostatic part of the capacitance as well as the quantum corrections arising from the electronic density of states. We identify the van-Hove singularities that correspond to the one-dimensional electron and hole sub-bands and show that the measured capacitance exhibits clear electron–hole symmetry. Finally, our measurements suggest the existence of a negative capacitance, which has recently been predicted to exist in one dimension as a result of interactions between electrons2,3,4.

We perform low-temperature electrical transport measurements on gated, quasi-2D graphite quantum dots. In devices with low contact resistances, we use longitudinal and Hall resistances to extract carrier densities of 9.2−13 × 1012 cm-2 and mobilities of 200−1900 cm2/V·s. In devices with high resistance contacts, we observe Coulomb blockade phenomena and infer the charging energies and capacitive couplings. These experiments demonstrate that electrons in mesoscopic graphite pieces are delocalized over nearly the whole graphite piece down to low temperatures.

We measured Kondo-assisted tunneling via C 60 molecules in contact with ferromagnetic nickel electrodes. Kondo correlations persisted despite the presence of ferromagnetism, but the Kondo peak in the differential conductance was split by an amount that decreased (even to zero) as the moments in the two electrodes were turned from parallel to antiparallel alignment. The splitting is too large to be explained by a local magnetic field. However, the voltage, temperature, and magnetic field dependence of the signals agree with predictions for an exchange splitting of the Kondo resonance. The Kondo effect leads to negative values of magnetoresistance, with magnitudes much larger than the Julliere estimate.

The remarkable transport properties of carbon nanotubes (CNTs) are determined by their unusual electronic structure1. The electronic states of a carbon nanotube form one-dimensional electron and hole sub-bands, which, in general, are separated by an energy gap2,3. States near the energy gap are predicted4,5 to have an orbital magnetic moment, µorb, that is much larger than the Bohr magneton (the magnetic moment of an electron due to its spin). This large moment is due to the motion of electrons around the circumference of the nanotube, and is thought to play a role in the magnetic susceptibility of CNTs6,7,8,9 and the magnetoresistance observed in large multiwalled CNTs10,11,12. But the coupling between magnetic field and the electronic states of individual nanotubes remains to be quantified experimentally. Here we report electrical measurements of relatively small diameter (2–5 nm) individual CNTs in the presence of an axial magnetic field. We observe field-induced energy shifts of electronic states and the associated changes in sub-band structure, which enable us to confirm quantitatively the predicted values for µorb.

An atomic force microscope was used to study single-electron motion in nanotube quantum dots. By applying a voltage to the microscope tip, the number of electrons occupying the quantum dot could be changed, causing Coulomb oscillations in the nanotube conductance. Spatial maps of these oscillations were used to locate individual dots and to study the electrostatic coupling between the dot and the tip. The electrostatic forces associated with single electrons hopping on and off the quantum dot were also measured. These forces changed the amplitude, frequency, and quality factor of the cantilever oscillation, demonstrating how single-electron motion can interact with a mechanical oscillator.

Single-walled carbon nanotubes (SWNTs) have emerged as a very promising new class of electronic materials. The fabrication and electronic properties of devices based on individual SWNTs are reviewed. Both metallic and semiconducting SWNTs are found to possess electrical characteristics that compare favorably to the best electronic materials available. Manufacturability issues, however, remain a major challenge.

The motion of electrons through quantum dots is strongly modified by single-electron charging and the quantization of energy levels1,2. Much effort has been directed towards extending studies of electron transport to chemical nanostructures, including molecules3,4,5,6,7,8, nanocrystals9,10,11,12,13 and nanotubes14,15,16,17. Here we report the fabrication of single-molecule transistors based on individual C60 molecules connected to gold electrodes. We perform transport measurements that provide evidence for a coupling between the centre-of-mass motion of the C60 molecules and single-electron hopping18—a conduction mechanism that has not been observed previously in quantum dot studies. The coupling is manifest as quantized nano-mechanical oscillations of the C60 molecule against the gold surface, with a frequency of about 1.2 THz. This value is in good agreement with a simple theoretical estimate based on van der Waals and electrostatic interactions between C60 molecules and gold electrodes.

We address the effects of disorder on the conducting properties of metal and semiconducting carbon nanotubes. Experimentally, the mean free path is found to be much larger in metallic tubes than in doped semiconducting tubes. We show that this result can be understood theoretically if the disorder potential is long-ranged. The effects of a pseudospin index that describes the internal sublattice structure of the states lead to a suppression of scattering in metallic tubes, but not in semiconducting tubes. This conclusion is supported by tight-binding calculations., Comment: four pages

Using an atomic force microscope as a local voltmeter, we measure the Hall voltage profile in a 2D electron gas in the quantum Hall (QH) regime. We observe a linear profile in the bulk of the sample in the transition regions between QH plateaus and a distinctly nonlinear profile on the plateaus. In addition, localized voltage drops are observed at the sample edges in the transition regions. We interpret these results in terms of theories of edge and bulk currents in the QH regime., 4 pages, 5 figures