The differential conductance in a suspended few layered graphene sample is fou nd to exhibit a series of quasi-periodic sharp dips as a function of bias at l ow temperature. We show that they can be understood within a simple model of dyn amical Coulomb blockade where energy exchanges take place between the charge carriers transmitted trough the sample and a dissipative electromagnetic envir onment with a resonant phonon mode strongly coupled to the electrons.
Single-electron transistors embedded in a suspended nanobeam or carbon nanotube may exhibit effects originating from the coupling of the electronic degrees of freedom to the mechanical oscillations of the suspended structure. Here, we investigate theoretically the consequences of a capacitive electromechanical interaction when the supporting beam is brought close to the Euler buckling instability by a lateral compressive strain. Our central result is that the low-bias current blockade, originating from the electromechanical coupling for the classical resonator, is strongly enhanced near the Eu…
Suspended graphene nano-ribbons formed during current annealing of suspended graphene flakes have been investigated experimentally. Transport measurements show the opening of a transport gap around charge neutrality due to the formation of "Coulomb islands", coexisting with quantum Hall conductance plateaus appearing at moderate values of magnetic field $B$. Upon increasing $B$, the transport gap is rapidly suppressed, and is taken over by a much larger energy gap due to electronic correlations. Our observations show that suspended nano-ribbons allow the investigation of phenomena that could n…
Transport measurements allow sensitive detection of nanomechanical motion of suspended carbon nanotubes. It has been predicted that when the electro-mechanical coupling is sufficiently large a bistability with a current blockade appears. Unambiguous observation of this transition by current measurements may be difficult. Instead, we investigate the mechanical response of the system, namely the displacement spectral function; the linear response to a driving; and the ring-down behavior. We find that by increasing the electro-mechanical coupling the peak in the spectral function broadens and shi…
Low-temperature transport spectroscopy measurements on a suspended few-hole carbon nanotube quantum dot are presented, showing a gate-dependent harmonic excitation spectrum which, strikingly, occurs in the Coulomb blockade regime. The quantized excitation energy corresponds to the scale expected for longitudinal vibrations of the nanotube. The electronic transport processes are identified as cotunnel-assisted sequential tunneling, resulting from non-equilibrium occupation of the mechanical mode. They appear only above a high-bias threshold at the scale of electronic nanotube excitations. We di…
Understanding the influence of vibrational motion of the atoms on electronic transitions in molecules constitutes a cornerstone of quantum physics, as epitomized by the Franck-Condon principle of spectroscopy. Recent advances in building molecular-electronics devices and nanoelectromechanical systems open a new arena for studying the interaction between mechanical and electronic degrees of freedom in transport at the single-molecule level. The tunneling of electrons through molecules or suspended quantum dots has been shown to excite vibrational modes, or vibrons. Beyond this effect, theory pr…
Suspended carbon nanotubes are known to support self-driven oscillations due to electromechanical feedback under certain conditions, including low temperatures and high mechanical quality factors. Prior reports identified signatures of such oscillations in Kondo or high-bias transport regimes. Here, we observe self-driven oscillations that give rise to significant conduction in normally Coulomb-blockaded low-bias transport. Using a master equation model, the self-driving is shown to result from strongly energy-dependent electron tunneling, and the dependencies of transport features on bias, ga…
An electron-phonon cavity consisting of a quantum dot embedded in a free-standing GaAs/AlGaAs membrane is characterized in Coulomb blockade measurements at low temperatures. We find a complete suppression of single electron tunneling around zero bias leading to the formation of an energy gap in the transport spectrum. The observed effect is induced by the excitation of a localized phonon mode confined in the cavity. This phonon blockade of transport is lifted at magnetic fields where higher electronic states with nonzero angular momentum are brought into resonance with the phonon energy.
We report on suspended single-layer graphene deposition by a transfer-printing approach based on polydimethylsiloxane stamps. The transfer printing method allows the exfoliation of graphite flakes from a bulk graphite sample and their residue-free deposition on a silicon dioxide substrate. This deposition system creates a blistered graphene surface due to strain induced by the transfer process itself. Single-layer-graphene deposition and its "blistering" on the substrate are demonstrated by a combination of Raman spectroscopy, scanning electron microscopy and atomic-force microscopy measuremen…
We have performed low-temperature STM measurements on single-wall carbon nanotubes that are freely suspended over a trench. The nanotubes were grown by CVD on a Pt substrate with predefined trenches etched into it. Atomic resolution was obtained on the freestanding portions of the nanotubes. Spatially resolved spectroscopy on the suspended portion of both metallic and semiconducting nanotubes was also achieved, showing a Coulomb-staircase behavior superimposed on the local density of states. The spacing of the Coulomb blockade peaks changed with tip position reflecting a changing tip-tube capa…
Influence of forced mechanical vibrations of a suspended single-electron transistor on electron tunneling through the quantum dot limited by the Coulomb blockade is investigated. It is shown that mechanical oscillations of the quantum dot lead to the Coulomb blockade breakdown, shown in sharp resonant peaks in the transistor conductance dependence on the excitation frequency at values corresponding to the mechanical oscillations eigen modes. Physical mechanism of the observed effect is considered. It is presumably connected with oscillations of the mutual electrical capacitances between the qu…
We study hot carrier transport under magnetic fields up to 15 T in suspended graphitic multilayers through differential conductance (dI/dV) spectroscopy. Distinct high-energy dI/dV anomalies have been observed and shown to be related to intrinsic phonon-emission processes in graphite. The evolution of such dI/dV anomalies under magnetic fields is further understood as a consequence of inter-Landau level cyclotron-phonon resonance scattering. The observed magneto-phonon effects not only shed light on the physical mechanisms responsible for high-current transport in graphitic systems, but also o…
We carried out measurements on nanoelectromechanical systems based on multilayer graphene sheets suspended over trenches in silicon oxide. The motion of the suspended sheets was electrostatically driven at resonance using applied radio-frequency voltages. The mechanical vibrations were detected using a novel form of scanning probe microscopy, which allowed identification and spatial imaging of the shape of the mechanical eigenmodes. In as many as half the resonators measured, we observed a new class of exotic nanoscale vibration eigenmodes not predicted by the elastic beam theory, where the am…
Quantum confined devices that manipulate single electrons in graphene are emerging as attractive candidates for nanoelectronics applications. Previous experiments have employed etched graphene nanostructures, but edge and substrate disorder severely limit device functionality. Here we present a technique that builds quantum confined structures in suspended bilayer graphene with tunnel barriers defined by external electric fields that break layer inversion symmetry, thereby eliminating both edge and substrate disorder. We report clean quantum dot formation in two regimes: at zero magnetic field…
We make use of micro-magneto Raman scattering spectroscopy to probe magneto-phonon resonances (MPR) in suspended mono- to penta-layer graphene. MPR correspond to avoided crossings between zone-center optical phonons (G-mode) and optically-active inter Landau level (LL) transitions and provide a tool to perform LL spectroscopy at a fixed energy ($\approx 197~\rm{meV}$) set by the G-mode phonon. Using a single-particle effective bilayer model, we readily extract the velocity parameter associated with each MPR. A single velocity parameter slightly above the bulk graphite value suffices to fit all…
We present a simple and fast method for thickness characterization of suspended graphene flakes that is based on transmission electron microscopy (TEM) techniques. For this method, the dynamical theory of electron diffraction (Bloch-wave approach in two-beam case approximation) was used to obtain an analytical expression for the intensity of the transmitted electron beam I0(t), as function of the specimen thickness t for thin samples (t<< λ; where λ is the absorption constant for graphite). We show that in thin graphite crystals the transmitted intensity is a linear function of the thickness. …
The answer to the title question is yes and the sheets exhibit diffraction peaks but may not have long range crystalline order. This is not a trivial question and answer and is immersing in the very active field now days of the study of properties of graphite and specially of graphene. This note is motivated in fact by a recent paper by Meyer et al (1) on the structure of suspended graphene sheets.
We study the intrinsic transport properties of suspended graphene devices at high fields (>1 V/um) and high temperatures (>1000 K). Across 15 samples, we find peak (average) saturation velocity of 3.6x10^7 cm/s (1.7x10^7 cm/s), and peak (average) thermal conductivity of 530 W/m/K (310 W/m/K), at 1000 K. The saturation velocity is 2-4 times and the thermal conductivity 10-17 times greater than in silicon at such elevated temperatures. However, the thermal conductivity shows a steeper decrease at high temperature than in graphite, consistent with stronger effects of second-order three-phonon sca…
Thermal conductivity $κ$ of both suspended and supported graphene has been studied by using molecular dynamics simulations. Obvious length dependence is observed in $κ$ of suspended single-layer graphene (SLG), while $κ$ of supported SLG is insensitive to the length. The simulation result of room temperature $κ$ of supported SLG is in good agreement with experimental value. In contrast to the decrease in $κ$ induced by inter-layer interaction in suspended few-layer graphene (FLG), $κ$ of supported FLG is found to increase rapidly with the layer thickness, reaching about 90% of that of bulk gra…
Charge noise is critical in the performance of gate-controlled quantum dots (QDs). Here we show the 1/f noise for a microscopic graphene QD is substantially larger than that for a macroscopic graphene field-effect transistor (FET), increasing linearly with temperature. To understand its origin, we suspended the graphene QD above the substrate. In contrast to large area graphene FETs, we find that a suspended graphene QD has an almost-identical noise level as an unsuspended one. Tracking noise levels around the Coulomb blockade peak as a function of gate voltage yields potential fluctuations of…
Natural and resonant oscillations of suspended circular graphene and hexagonal boron nitride (h-BN) membranes (single-layer sheets lying on a flat substrate having a circular hole of radius $R$) have been simulated using full-atomic models. Substrates formed by flat surfaces of graphite and h-BN crystal, hexagonal ice, silicon carbide 6H-SiC and nickel surface (111) have been used. The presence of the substrate leads to the forming of a gap at the bottom of the frequency spectrum of transversal vibrations of the sheet. The frequencies of natural oscillations of the membrane (oscillations local…
We have measured the mechanical properties of few-layer graphene and graphite flakes that are suspended over circular holes. The spatial profile of the flake's spring constant is measured with an atomic force microscope. The bending rigidity of and the tension in the membranes are extracted by fitting a continuum model to the data. For flakes down to eight graphene layers, both parameters show a strong thickness-dependence. We predict fundamental resonance frequencies of these nanodrums in the GHz range based on the measured bending rigidity and tension.
Layered materials have uncommonly anisotropic thermal properties due to their strong in-plane covalent bonds and weak out-of-plane van der Waals interactions. Here we examine heat flow in graphene (graphite), h-BN, MoS2, and WS2 monolayers and bulk films, from diffusive to ballistic limits. We determine the ballistic thermal conductance limit (Gball) both in-plane and out-of-plane, based on full phonon dispersions from first-principles calculations. An overall phonon mean free path (λ) is expressed in terms of Gball and the diffusive thermal conductivity, consistent with kinetic theory if prop…
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. Our work demonstrates a new 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 electron beam lithography. The membranes are then transferred and used as hard etching masks. We benchmark our technique by engineering a superlattice…
