We compute the DC and the optical conductivity of graphene for finite values of the chemical potential by taking into account the effect of disorder, due to mid-gap states (unitary scatterers) and charged impurities, and the effect of both optical and acoustic phonons. The disorder due to mid-gap states is treated in the coherent potential approximation (CPA, a self-consistent approach based on the Dyson equation), whereas that due to charged impurities is also treated via the Dyson equation, with the self-energy computed using second order perturbation theory. The effect of the phonons is also included via the Dyson equation, with the self energy computed using first order perturbation theory. The self-energy due to phonons is computed both using the bare electronic Green's function and the full electronic Green's function, although we show that the effect of disorder on the phonon-propagator is negligible. Our results are in qualitative agreement with recent experiments. Quantitative agreement could be obtained if one assumes water molelcules under the graphene substrate. We also comment on the electron-hole asymmetry observed in the DC conductivity of suspended graphene.
We reported the basal-plane thermal conductivity in exfoliated bilayer hexagonal boron nitride h-BN that was measured using suspended prepatterned microstructures. The h-BN sample suitable for thermal measurements was fabricated by dry-transfer method, whose sample quality, due to less polymer residues on surfaces, is believed to be superior to that of PMMA-mediated samples. The measured room temperature thermal conductivity is around 484 Wm-1K-1(+141 Wm-1K-1/ -24 Wm-1K-1) which exceeds that in bulk h-BN, providing experimental observation of the thickness-dependent thermal conductivity in sus…
We observe trion emission from suspended carbon nanotubes where carriers are introduced electrostatically using field-effect transistor structures. The trion peak emerges below the $E_{11}$ emission energy at gate voltages that coincide with the onset of bright exciton quenching. By investigating nanotubes with various chiralities, we verify that the energy separation between the bright exciton peak and the trion peak becomes smaller for larger diameter tubes. Trion binding energies that are significantly larger compared to surfactant-wrapped carbon nanotubes are obtained, and the difference i…
Establishment of a new technique or extension of an existing technique for thermal and thermoelectric measurements to a more challenging system is an important task to explore the thermal and thermoelectric properties of various materials and systems. The bottleneck lies in the challenges in measuring the thermal contact resistance. In this work, we applied electron beam self-heating technique to derive the intrinsic thermal conductivity of suspended Molybdenum Disulfide (MoS2) ribbons and the thermal contact resistance, with which the interfacial thermal resistance between few-layer MoS2 and …
Modifying phonon thermal conductivity in nanomaterials is important not only for fundamental research but also for practical applications. However, the experiments on tailoring the thermal conductivity in nanoscale, especially in two-dimensional materials, are rare due to technical challenges. In this work, we demonstrate in-situ thermal conduction measurement of MoS2 and find that its thermal conductivity can be continuously tuned to a required value from crystalline to amorphous limits. The reduction of thermal conductivity is understood from phonon-defects scatterings that decrease the phon…
We investigate the thermal conductivity of suspended graphene as a function of the density of defects, ND, introduced in a controllable way. Graphene layers are synthesized using chemical vapor deposition, transferred onto a transmission electron microscopy grid, and suspended over ~7.5-micrometer size square holes. Defects are induced by irradiation of graphene with the low-energy electron beam (20 keV) and quantified by the Raman D-to-G peak intensity ratio. As the defect density changes from 2.0x10^10 cm-2 to 1.8x10^11 cm-2 the thermal conductivity decreases from ~(1.8+/-0.2)x10^3 W/mK to ~…
Building smaller transistors with enhanced functionality is critical in extending the limits of Moores law and meeting the demands of the electronics industry. Here we demonstrate transistor operation in a suspended single carbon nanotube (CNT) using feedback-enabled radiation pressure of a near-field focused laser that enabled significant changes in conductivity of the CNT. Further, using in-situ tip-enhanced Raman spectroscopy, we show that the change in conductivity of over five orders in magnitude is accompanied by self-induced defect states within the CNT. The entire structure is less tha…
The tuning of electrical circuit resonance with a variable capacitor, or varactor, finds wide application with the most important being wireless telecommunication. We demonstrate an electromechanical graphene varactor, a variable capacitor wherein the capacitance is tuned by voltage controlled deflection of a dense array of suspended graphene membranes. The low flexural rigidity of graphene monolayers is exploited to achieve low actuation voltage in an ultra-thin structure. Large arrays comprising thousands of suspensions were fabricated to give a tunable capacitance of over 10 pF/mm$^2$, high…
Electroluminescence from individual carbon nanotubes within split-gate devices is investigated. By characterizing the air-suspended nanotubes with photoluminescence spectroscopy, chirality is identified and electroluminescence peaks are assigned. We observe electroluminescence linewidth comparable to photoluminescence, indicating negligible heating and state-mixing effects. Split-gate and bias voltage dependences are consistent with emission from an electrostatically formed $pn$-junction.
Mapping the thermal transport properties of materials at the nanoscale is of critical importance for optimizing heat conduction in nanoscale devices. Several methods to determine the thermal conductivity of materials have been developed, most of them yielding an average value across the sample, thereby disregarding the role of local variations. Here, we present a method for the spatially-resolved assessment of the thermal conductivity of suspended graphene by using a combination of confocal Raman thermometry and a finite-element calculations-based fitting procedure. We demonstrate the working …
Graphene grown by chemical vapour deposition is transferred on top of flat gold nanoislands and characterized by scanning tunnelling microscopy (STM) and atomic force microscopy (AFM). Graphene bubbles are formed with lateral dimensions determined by the size and shape of nanoislands. These graphene bubbles can be squeezed during STM imaging using bias voltages of less than 250 mV and tunnelling currents of 1 nA. Similarly, the graphene suspended over gold nanovoids is deflected 4 - 5 nm by the STM tip when imaging at low bias voltages (U = 30 mV). Nanoindentation measurements performed by AFM…
Wiedemann-Franz Relation and Thermal-transistor Effect in Suspended Graphene
我们提取实验的电子热导率，$K_{e}$，在悬浮的石墨烯，我们掺杂使用背栅电极。我们利用两点直流电子输运在低偏置电压和中间温度（50 - 160 K），电子和晶格温度去耦。热导率与电荷电导率乘以温度成比例，证实了悬浮石墨烯中服从Wiedemann-Franz关系。我们提取Lorenz系数的估计值为1.1至1.7 $\times 10^{-8}$ W $Ω$ K $^{-2}$。$K_e$显示出晶体管效应，并且当电荷载流子密度在$\approx$ 0.5至1.8 $\times 10^{11}$ cm $^{-2}$范围内时，可以用背栅以大于2的因子进行调谐。
Monolayer WS2 has been a competitive candidate in electrical and optoelectronic devices due to its superior optoelectronic properties. To tackle the challenge of thermal management caused by the decreased size and concentrated heat in modern ICs, it is of great significance to accurately characterize the thermal conductivity of the monolayer WS2, especially with substrate supported. In this work, the dual-wavelength flash Raman method is used to experimentally measure the thermal conductivity of the suspended and the Si/SiO2 substrate supported monolayer WS2 at a temperature range of 200 K - 4…
Recent experiments have reported evidence of dominant electron-hole scattering in the electric conductivity of suspended bilayer graphene near charge neutrality. According to these experiments, plots of the electric conductivity as a function of $μ/k_BT$ (chemical potential scaled with temperature) obtained for different temperatures in the range of $12\rm{K}\lesssim T \lesssim 40\rm{K}$ collapse on a single curve independent of $T$. In a recent theory, this observation has been taken as an indication that the main sub-dominant scattering process is not electron-impurity but electron-phonon. H…
The electrical response of two-dimensional electron gas to vibrations of a nanomechanical cantilever containing it is studied. Vibrations of perpendicularly oriented cantilevers are experimentally shown to change oppositely the conductivity near their bases. This indicates the piezoelectric nature of electromechanical coupling. A physical model is developed, which quantitatively explains the experiment. It shows that the main origin of the conductivity change is a rapid change in the mechanical stress on the boundary between suspended and non-suspended areas, rather than the stress itself.
We present a fabrication process for graphene-based devices where a graphene monolayer is suspended above a local metallic gate placed in a trench. As an example we detail the fabrication steps of a graphene field-effect transistor. The devices are built on a bare high-resistivity silicon substrate. At temperatures of 77~K and below, we observe the field-effect modulation of the graphene resistivity by a voltage applied to the gate. This fabrication approach enables new experiments involving graphene-based superconducting qubits and nano-electromechanical resonators. The method is applicable t…
Thermal properties of suspended single-layer graphene membranes are investigated by characterization of their mechanical motion in response to a high-frequency modulated laser. A characteristic delay time $τ$ between the optical intensity and mechanical motion is observed, which is attributed to the time required to raise the temperature of the membrane. We find, however, that the measured time constants are significantly larger than the predicted ones based on values of the specific heat and thermal conductivity. In order to explain the discrepancy between measured and modeled tau, a model is…
We study the optical response of a suspended graphene field-effect transistor in magnetic fields of up to 9 T (quantum Hall regime). With an illumination power of only 3 μW, we measure a photocurrent of up to 400 nA, corresponding to a photo-responsivity of 0.14 A/W, which we believe to be the highest value ever measured in single-layer graphene. We estimate that every absorbed photon creates more than 8 electron-hole pairs, which demonstrates highly effective carrier multiplication. As suggested by the dependence of the photocurrent on gate voltage and magnetic field, we propose a ballistic t…
We study conductivity of strongly disordered amorphous antimony films under high bias voltages. We observe non-linear current-voltage characteristic, where the conductivity value at zero bias is one of two distinct values, being determined by the sign of previously applied voltage. Relaxation curves demonstrate high stability of these conductivity values on a large timescale. Investigations of the antimony film structure allows to determine the percolation character of electron transport in strongly disordered films. We connect the memory effect in conductivity with modification of the percola…
Suspended graphene is difficult to image by scanning probe microscopy due to the inherent van-der-Waals and dielectric forces exerted by the tip which are not counteracted by a substrate. Here, we report scanning tunneling microscopy data of suspended monolayer graphene in constant-current mode revealing a surprising honeycomb structure with amplitude of 50$-$200 pm and lattice constant of 10-40 nm. The apparent lattice constant is reduced by increasing the tunneling current $I$, but does not depend systematically on tunneling voltage $V$ or scan speed $v_{\rm scan}$. The honeycomb lattice of …
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…
We study, both theoretically and experimentally, the features on the current-voltage characteristic of a highly transparent Josephson junction caused by transition of the superconducting leads to the normal state. These features appear due to the suppression of the Andreev excess current. We show that by tracing the dependence of the voltage, at which the transition occurs, on the bath temperature and by analyzing the suppression of the excess current by the bias voltage one can recover the temperature dependence of the heat flow out of the junction. We verify theory predictions by fabricating…
