The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport measurements at high carrier densities indicate rather high mobilities, many questions pertaining to disorder remain unanswered. In particular, it has been argued theoretically, that when the average carrier density is zero, the inescapable presence of disorder will lead to electron and hole puddles with equal probability. In this work, we use a scanning single electron transistor to image the carrier density landscape of graphene in the vicinity of the neutrality point. Our results clearly show the electron-hole puddles expected theoretically. In addition, our measurement technique enables to determine locally the density of states in graphene. In contrast to previously studied massive two dimensional electron systems, the kinetic contribution to the density of states accounts quantitatively for the measured signal. Our results suggests that exchange and correlation effects are either weak or have canceling contributions.
We study theoretically an influence of the near-interfacial insulator traps and electron-hole puddles on the small-signal capacitance and conductance characteristics of the gated graphene structures. Based on the self-consistent electrostatic consideration and taking into account the interface trap capacitance the explicit analytic expressions for charge carrier density and the quantum capacitance as functions of the gate voltage were obtained. This allows to extract the interface trap capacitance and density of interface states from the gate capacitance measurements. It has shown that self-co…
The topological insulator BiSbTeSe$_2$ corresponds to a compensated semiconductor in which strong Coulomb disorder gives rise to the formation of charge puddles, i.e., local accumulations of charge carriers, both in the bulk and on the surface. Bulk puddles are formed if the fluctuations of the Coulomb potential are as large as half of the band gap. The gapless surface, in contrast, is sensitive to small fluctuations but the potential is strongly suppressed due to the additional screening channel provided by metallic surface carriers. To study the quantitative relationship between the properti…
It is widely believed that carrier-density inhomogeneities ("electron-hole puddles") in single-layer graphene on a substrate like quartz are due to charged impurities located close to the graphene sheet. Here we demonstrate by using a Kohn-Sham-Dirac density-functional scheme that corrugations in a real sample are sufficient to determine electron-hole puddles on length scales that are larger than the spatial resolution of state-of-the-art scanning tunneling microscopy.
The charge carrier density in graphene on a dielectric substrate such as SiO$_2$ displays inhomogeneities, the so-called charge puddles. Because of the linear dispersion relation in monolayer graphene, the puddles are predicted to grow near charge neutrality, a markedly distinct property from conventional two-dimensional electron gases. By performing scanning tunneling microscopy/spectroscopy on a mesoscopic graphene device, we directly observe the puddles' growth, both in spatial extent and in amplitude, as the Dirac point is approached. Self-consistent screening theory provides a unified des…
When graphene is close to charge neutrality, its energy landscape is highly inhomogeneous, forming a sea of electron-like and hole-like puddles, which determine the properties of graphene at low carrier density. However, the details of the puddle formation have remained elusive. We demonstrate numerically that in sharp contrast to monolayer graphene, the normalized autocorrelation function for the puddle landscape in bilayer graphene depends only on the distance between the graphene and the source of the long-ranged impurity potential. By comparing with available experimental data, we find qua…
Using scanning tunneling microscopy, we have imaged local charge density fluctuations in monolayer graphene. By placing a small gold nanoparticle on the end of the STM tip, a charge sensor is created. By raster scanning the tip over the surface and using Coulomb blockade spectroscopy, we map the local charge on the graphene. We observe a series of electron and hole doped puddles with a characteristic length scale of about 20 nm. Theoretical calculations for the correlation length of the puddles based on the number of impurities are in agreement with our measurements.
A near-field scanning optical microscope is used to locally induce photocurrent in a graphene transistor with high spatial resolution. By analyzing the spatially resolved photo-response, we find that in the n-type conduction regime a p-n-p structure forms along the graphene device due to the doping of the graphene by the metal contacts. The modification of the electronic structure is not limited only underneath the metal electrodes, but extends 0.2-0.3 um into the graphene channel. The asymmetric conduction behavior of electrons and holes that is commonly observed in graphene transistors is di…
We suggest a simple model of disorder in graphene assuming that there are randomly distributed positive and negative centers with equal concentration $N/2$ in the bulk of silicon oxide substrate. We show that at zero gate voltage such disorder creates two-dimensional concentration $n_0 \sim N^{2/3}$ of electrons and holes in graphene. Electrons and holes reside in alternating in space puddles of the size $R_0 \sim N^{-1/3}$. A typical puddle has only one or two carriers in agreement with recent scanning single electron transistor experiment.
The mechanisms underlying the intrinsic photoresponse of few-layer (FL) molybdenum disulphide (MoS2) field-effect transistors are investigated via scanning photocurrent microscopy. We attribute the locally enhanced photocurrent to band-bending assisted separation of photoexcited carriers at the MoS2/Au interface. The wavelength-dependent photocurrents of few layer MoS2 transistors qualitatively follow the optical absorption spectra of MoS2, providing direct evidence of interband photoexcitation. Time and spectrally resolved photocurrent measurements at varying external electric fields and carr…
We perform scanning photocurrent microscopy on WS2 ionic liquid-gated field effect transistors exhibiting high-quality ambipolar transport. By properly biasing the gate electrode we can invert the sign of the photocurrent showing that the minority photocarriers are either electrons or holes. Both in the electron- and the hole-doping regimes the photocurrent decays exponentially as a function of the distance between the illumination spot and the nearest contact, in agreement with a two-terminal Schottky-barrier device model. This allows us to compare the value and the doping dependence of the d…
An Al-AlO_x-Al single-electron transistor (SET) acting as the gate of a narrow (~ 100 nm) metal-oxide-semiconductor field-effect transistor (MOSFET) can induce a vertically aligned Si SET at the Si/SiO_2 interface near the MOSFET channel conductance threshold. By using such a vertically coupled Al and Si SET system, we have detected a single-charge defect which is tunnel-coupled to the Si SET. By solving a simple electrostatic model, the fractions of each coupling capacitance associated with the defect are extracted. The results reveal that the defect is not a large puddle or metal island, but…
A single-electron transistor has been realized in a Ga[Al]As heterostructure by oxidizing lines in the GaAs cap layer with an atomic force microscope. The oxide lines define the boundaries of the quantum dot, the in-plane gate electrodes, and the contacts of the dot to source and drain. Both the number of electrons in the dot as well as its coupling to the leads can be tuned with an additional, homogeneous top gate electrode. Pronounced Coulomb blockade oscillations are observed as a function of voltages applied to different gates. We find that, for positive top-gate voltages, the lithographic…
Surfaces of three-dimensional topological insulators have emerged as one of the most remarkable states of condensed quantum matter1-5 where exotic electronic phases of Dirac particles should arise1,6-8. Here we report a discovery of surface superconductivity in a topological material (Sb2Te3) with resistive transition at a temperature of ~9 K induced through a minor tuning of growth chemistry that depletes bulk conduction channels. The depletion shifts Fermi energy towards the Dirac point as witnessed by about two orders of magnitude reduction of carrier density and by very large (~25,000 cm^2…
We have investigated the low frequency (f) flicker (also called 1/f) noise of single-layer graphene devices on h-BN (placed on SiO2/Si) along with those on SiO2/Si. We observe that the devices fabricated on h-BN have on average one order of magnitude lower noise amplitude compared with devices fabricated on SiO2/Si. We associate this noise reduction to the lower densities of impurities and trap sites in h-BN than in SiO2. Furthermore, the gate voltage dependent noise amplitude shows a broad maximum at Dirac point for devices on h-BN, in contrast to the M-shaped behavior showing a minimum at Di…
Disordered Fermi-Dirac distributions are used to model, within a straightforward and essentially phenomenological Boltzmann equation approach, the electron/hole transport across graphene puddles. We establish, with striking experimental support, a functional relationship between the graphene minimum conductivity, the mobility in the Boltzmann regime, and the steepness of the conductivity parabolic profile usually observed through gate-voltage scanning around the charge neutral point.
We show that silicon nitride can provide uniform coverage of graphene in field-effect transistors while preserving the channel mobility. This insulator allowed us to study the maximum channel resistance at the Dirac (neutrality) point as a function of the strength of a perpendicular electric field in top-gated devices with different numbers of graphene layers. Using a simple model to account for surface potential variations (electron-hole puddles) near the Dirac point we estimate the field-induced band-gap or band-overlap in the different layers.
At any metal-carbon nanotube interface there is charge transfer and the induced interfacial field determines the position of the carbon nanotube band structure relative to the metal Fermi-level. In the case of a single-wall carbon nanotube (SWNT) supported on a gold substrate, we show that the charge transfers induce a local electrostatic potential perturbation which gives rise to the observed Fermi-level shift in scanning tunneling spectroscopy (STS) measurements. We also discuss the relevance of this study to recent experiments on carbon nanotube transistors and argue that the Fermi-level al…
Two-dimensional (2D) materials have become a new territory for exploring novel properties and functionalities because of their superior tunability. The unprecedented tunability of 2D materials is also accompanied by many and equally great challenges, as they are susceptible to defects and disorders. The presence of defects and disorders induces the inhomogeneity of electronic states, often making it difficult to directly probe the intrinsic properties of materials. Therefore, many efforts have been devoted to improve the electronic homogeneity, for example, by reducing the density of defects a…
The influence of defects on electron transport in single-wall carbon nanotube field effect transistors (CNFETs) is probed by combined scanning gate microscopy (SGM) and scanning impedance microscopy (SIM). SGM reveals a localized field effect at discrete defects along the CNFET length. The depletion surface potential of individual defects is quantified from the SGM-imaged radius of the defect as a function of tip bias voltage. This provides a measure of the Fermi level at the defect with zero tip voltage, which is as small as 20 meV for the strongest defects. The effect of defects on transport…
Transistors, regardless of their size, rely on electrical gates to control the conductance between source and drain contacts. In atomic-scale transistors, this conductance is exquisitely sensitive to single electrons hopping via individual orbitals. Single-electron transport in molecular transistors has been previously studied using top-down approaches to gating, such as lithography and break junctions. But atomically precise control of the gate - which is crucial to transistor action at the smallest size scales - is not possible with these approaches. Here, we used individual charged atoms, m…
The relativistic nature of Dirac electrons and holes in graphene profoundly affects the way they interact with impurities. Signatures of the relativistic behavior have been observed recently in scanning tunneling measurements on individual impurities, but the conductance measurements in this regime are typically dominated by electron and hole puddles. Here we present measurements of quantum interference noise and magnetoresistance in graphene pn junctions. Unlike the conductance, the quantum interference noise can provide access to the scattering at the Dirac point:it is sensitive to the motio…
Top-gated, few-layer graphene field-effect transistors (FETs) fabricated on thermally-decomposed semi-insulating 4H-SiC substrates are demonstrated. Physical vapor deposited SiO2 is used as the gate dielectric. A two-dimensional hexagonal arrangement of carbon atoms with the correct lattice vectors, observed by high-resolution scanning tunneling microscopy, confirms the formation of multiple graphene layers on top of the SiC substrates. The observation of n-type and p-type transition further verifies Dirac Fermions unique transport properties in graphene layers. The measured electron and hole …
Solid-liquid phase transitions are fundamental physical processes, but atomically-resolved microscopy has yet to capture both the solid and liquid dynamics for such a transition. We have developed a new technique for controlling the melting and freezing of 2D molecular layers on a graphene field-effect transistor (FET) that allows us to image phase transition dynamics via atomically-resolved scanning tunneling microscopy. Back-gate voltages applied to a F4TCNQ-decorated graphene FET induce reversible transitions between a charge-neutral solid phase and a negatively charged liquid phase. Nonequ…
The spatial arrangement of adsorbates deposited onto a clean surface in vacuum typically cannot be reversibly tuned. Here we use scanning tunneling microscopy to demonstrate that molecules deposited onto graphene field-effect transistors exhibit reversible, electrically-tunable surface concentration. Continuous gate-tunable control over the surface concentration of charged F4TCNQ molecules was achieved on a graphene FET at T = 4.5K. This capability enables precisely controlled impurity doping of graphene devices and also provides a new method for determining molecular energy level alignment ba…
We report on the first measurement of the Seebeck coefficient in a tunnel-contacted and gate-tunable individual single-quantum dot junction in the Kondo regime, fabricated using the electromigration technique. This fundamental thermoelectric parameter is obtained by directly monitoring the magnitude of the voltage induced in response to a temperature difference across the junction, while keeping a zero net tunneling current through the device. In contrast to bulk materials and single molecules probed in a scanning tunneling microscopy (STM) configuration, investigating the thermopower in nanos…
We demonstrate a graphene-MoS2 architecture integrating multiple field-effect transistors and we independently probe and correlate the conducting properties of van der Waals coupled graphene-MoS2 contacts with the ones of the MoS2 channels. Devices are fabricated starting from high-quality single-crystal monolayers grown by chemical vapor deposition and characterized by scanning Raman and photoluminescence spectroscopies. Transconductance curves of MoS2 are compared with the current-voltage characteristics of graphene contact stripes, revealing a significant suppression of transport on the n-s…
A few-layer palladium diselenide (PdSe2) field effect transistor is studied under external stimuli such as electrical and optical fields, electron irradiation and gas pressure. We observe ambipolar conduction and hysteresis in the transfer curves of the PdSe2 material unprotected and as-exfoliated. We tune the ambipolar conduction and its hysteretic behavior in the air and pure nitrogen environments. The prevailing p-type transport observed at room pressure is reversibly turned into dominant n-type conduction by reducing the pressure, which can simultaneously suppress the hysteresis. The press…
We report about the fabrication and analysis of the properties of Cr/CrO_x/Cr tunnel junctions and SET transistors, prepared by different variants of direct-writing multilayer technique. In all cases, the CrO_x tunnel barriers were formed in air under ambient conditions. From the experiments on single junctions, values for the effective barrier height and thickness were derived. For the Cr/CrO_x/Cr SET transistors we achieved minimal junction areas of 17 x 60 nm^2 using a scanning transmission electron microscope for the e-beam exposure on Si_3N_4 membrane substrate. We discuss the electrical …
We measure the channel potential of a graphene transistor using a scanning photocurrent imaging technique. We show that at a certain gate bias, the impact of the metal on the channel potential profile extends into the channel for more than 1/3 of the total channel length from both source and drain sides, hence most of the channel is affected by the metal. The potential barrier between the metal controlled graphene and bulk graphene channel is also measured at various gate biases. As the gate bias exceeds the Dirac point voltage, VDirac, the original p-type graphene channel turns into a p-n-p c…
We present a theory of a single-electron transistor exchange-coupled to a localized spin. We show how to gain detailed quantitative knowledge about the attached spin such as spin size, exchange coupling strength, Landé g-factor, and spin decay time $T_1$ by utilizing a robust blockade phenomenon of DC magnetotransport with accompanying noise enhancement. Our studies are of particular relevance to spin-resolved scanning single-electron transistor microscopy, electronic transport through nanomagnets, and the effect of hyperfine interaction on transport electrons by surrounding nuclear spins.
Electrical characterization of few-layer MoS2 based field effect transistors with Ti/Au electrodes is performed in the vacuum chamber of a scanning electron microscope in order to study the effects of electron beam irradiation on the transport properties of the device. A negative threshold voltage shift and a carrier mobility enhancement is observed and explained in terms of positive charges trapped in the SiO2 gate oxide, during the irradiation. The transistor channel current is increased up to three order of magnitudes after the exposure to an irradiation dose of 100e-/nm2. Finally, a comple…
The past decade has seen rapid growth in the research area of graphene and its application to novel electronics. With Moore's law beginning to plateau, the need for post-silicon technology in industry is becoming more apparent. Moreover, existing technology is insufficient for implementing terahertz detectors and receivers, which are required for a number of applications including medical imaging and security scanning. Graphene is considered to be a key potential candidate for replacing silicon in existing CMOS technology as well as realizing field effect transistors for terahertz detection, d…
We use scanning photocurrent microscopy (SPCM) to investigate individual suspended semiconducting carbon nanotube devices where the potential profile is engineered by means of local gates. In situ tunable p-n junctions can be generated at any position along the nanotube axis. Combining SPCM with transport measurements allows a detailed microscopic study of the evolution of the band profiles as a function of the gates voltage. Here we study the emergence of a p-n and a n-p junctions out of a n-type transistor channel using two local gates. In both cases the I-V curves recorded for gate configur…
We have performed scanning gate microscopy (SGM) on graphene field effect transistors (GFET), using a biased metallic nanowire coated with a dielectric layer as a contact mode tip and local top gate. Electrical transport through graphene at various back gate voltages is monitored as a function of tip voltage and tip position. Near the Dirac point, the dependence of graphene resistance on tip voltage shows a significant variation with tip position. SGM imaging reveals mesoscopic domains of electron-doped and hole-doped regions. Our measurements indicate a substantial spatial fluctuation (on the…
Developing van der Waals (vdW) homojunction devices requires materials with narrow bandgaps and simultaneously high hole and electron mobilities for bipolar transport, as well as methods to image and study spatial variations in carrier type and associated conductivity with nanometer spatial resolution. Here we demonstrate the general capability of near-field scanning microwave microscopy (SMM) to image and study the local carrier type and associated conductivity in operando by studying ambiploar field effect transistors (FETs) of the 1D vdW material tellurium in 2D form. To quantitatively unde…
Most popular atomically thin carbon material, called graphene, has got no band gap and this particular property of graphene makes it less useful from the aspect of nanoscale transistor devices. The band gap can be introduced in the graphene if it is synthesized through chemical route. First, Graphene Oxide (GO) is made which further go under reduction and turns into Reduced Graphene Oxide (RGO). Band structure investigation of monolayer sheets of reduced graphene oxide (RGO) by Scanning Tunneling Spectroscopy (STS) has been investigated here. The GO sheets are 1-1.2 nm thick and become more th…
We present atomistic calculations of quantum coherent electron transport through fulleropyrrolidine terminated molecules bridging a graphene nanogap. We predict that three difficult problems in molecular electronics with single molecules may be solved by utilizing graphene contacts: (1) a back gate modulating the Fermi level in the graphene leads facilitate control of the device conductance in a transistor effect with high on/off current ratio; (2) the size mismatch between leads and molecule is avoided, in contrast to the traditional metal contacts; (3) as a consequence, distinct features in …
We have used scanning tunneling microscopy (STM) to investigate two types of hydrogen defect structures on monolayer graphene supported by hexagonal boron nitride (h-BN) in a gated field-effect transistor configuration. The first H-defect type is created by bombarding graphene with 1-keV ionized hydrogen and is identified as two hydrogen atoms bonded to a graphene vacancy via comparison of experimental data to first-principles calculations. The second type of H defect is identified as dimerized hydrogen and is created by depositing atomic hydrogen having only thermal energy onto a graphene sur…
The interplay between strong electron-electron interactions and band topology can lead to novel electronic states that spontaneously break symmetries. The discovery of flat bands in magic-angle twisted bilayer graphene (MATBG) with nontrivial topology has provided a unique platform in which to search for new symmetry-broken phases. Recent scanning tunneling microscopy and transport experiments have revealed a sequence of topological insulating phases in MATBG with Chern numbers $C=\pm 3, \, \pm 2, \, \pm 1$ near moiré band filling factors $ν= \pm 1, \, \pm 2, \, \pm 3$, corresponding to a simp…
The interrelation between spin and charge in semiconductors leads to interesting effects, e.g., the Rashba-type spin-orbit splitting or the exchange enhancement. These properties are proposed to be used in applications such as spin transistors or spin qubits. Probing them on the local scale with the ultimate spatial resolution of the scanning tunneling microscope addresses their susceptibility to disorder directly. Here we review the results obtained on two-dimensional semiconductor systems (2DES). We describe the preparation and characterization of an adequate 2DES which can be probed by scan…
We report on measurements of the quantum capacitance in graphene as a function of charge carrier density. A resonant LC-circuit giving high sensitivity to small capacitance changes is employed. The density of states, which is directly proportional to the quantum capacitance, is found to be significantly larger than zero at and around the charge neutrality point. This finding is interpreted to be a result of potential fluctuations with amplitudes of the order of 100 meV in good agreement with scanning single-electron transistor measurements on bulk graphene and transport studies on nanoribbons.
Usually, graphene is used in its horizontal directions to design novel concept devices. Here, we report a single electron tunneling diode based on quantum tunneling through a vertical graphene two-barrier junction. The junction is formed by positioning a scanning tunnelling microscopy (STM) tip above a graphene nanoribbon that was deposited on a graphite surface. Because of the asymmetry of the two-barrier junction, the electrons can unidirectional transfer from the tip to the graphene nanoribbon but not from the graphene to the tip. This result opens intriguing opportunities for designing new…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the electronic transport properties due to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder potential. Transport experiments that probe the extended states in the transition regions between quantum Hall phases h…
Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point. However, accessing the physics of the low density region at the Dirac point has been difficult because of the presence of disorder which leaves the graphene with local microscopic electron and hole puddles, resulting in a finite density of carriers even at the charge neutrality point. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges a…
Particle localization is an essential ingredient in quantum Hall physics [1,2]. In conventional high mobility two-dimensional electron systems Coulomb interactions were shown to compete with disorder and to play a central role in particle localization [3]. Here we address the nature of localization in graphene where the carrier mobility, quantifying the disorder, is two to four orders of magnitude smaller [4,5,6,7,8,9,10]. We image the electronic density of states and the localized state spectrum of a graphene flake in the quantum Hall regime with a scanning single electron transistor [11]. Ou…
We develop a theory for the compressibility of the surface states of 3D topological insulators and propose that surface probes of the compressibility via scanning single electron transistor microscopy will be a straightforward way to access the topological states without interference from the bulk states. We describe the single-particle nature of the surface states taking into account an accurate Hamiltonian for the bands and then include the contribution from electron--electron interactions and discuss the implications of the ultra-violet cutoff, including the universality of the exchange con…
Plasma enhanced chemical vapor deposition (PECVD) techniques have been shown to be an efficient method to achieve single-step synthesis of high-quality monolayer graphene (MLG) without the need of active heating. Here we report PECVD-growth of single-crystalline hexagonal bilayer graphene (BLG) flakes and mm-size BLG films with the interlayer twist angle controlled by the growth parameters. The twist angle has been determined by three experimental approaches, including direct measurement of the relative orientation of crystalline edges between two stacked monolayers by scanning electron micros…
Graphene/silicon (G/Si) heterojunction based devices have been demonstrated as high responsivity photodetectors that are potentially compatible with semiconductor technology. Such G/Si Schottky junction diodes are typically in parallel with gated G/silicon dioxide (SiO$_2$)/Si areas, where the graphene is contacted. Here, we utilize scanning photocurrent measurements to investigate the spatial distribution and explain the physical origin of photocurrent generation in these devices. We observe distinctly higher photocurrents underneath the isolating region of graphene on SiO$_2$ adjacent to the…
Interface phonon modes that are generated by several atomic layers at the heterointerface play a major role in the interface thermal conductance for nanoscale high-power devices such as nitride-based high-electron-mobility transistors and light emitting diodes. Here we measure the local phonon spectra across AlN/Si and AlN/Al interfaces using atomically resolved vibrational electron energy-loss spectroscopy in a scanning transmission electron microscope. At the AlN/Si interface, we observe various localized phonon modes, of which the extended and interfacial modes act as bridges to connect the…
Dominating electron-electron scattering enables viscous electron flow exhibiting hydrodynamic current density patterns such as Poiseuille profiles or vortices. The viscous regime has recently been observed in graphene by non-local transport experiments and mapping of the Poiseuille profile. Here, we probe the current-induced surface potential maps of graphene field effect transistors with moderate mobility using scanning probe microscopy at room temperature. We discover micron-sized large areas appearing close to charge neutrality that show current induced electric fields opposing the external…
Interactions among electrons can give rise to striking collective phenomena when the kinetic energy of charge carriers is suppressed. One example is the fractional quantum Hall effect, in which correlations between electrons moving in two dimensions under the influence of a strong magnetic field generate excitations with fractional charge. Graphene provides a platform to study unique many-body effects due to its massless chiral charge carriers and the fourfold degeneracy that arises from their spin and valley degrees of freedom. Here we report local electronic compressibility measurements of a…
