Density inhomogeneity driven percolation metal-insulator transition and dimensional crossover in graphene nanoribbons

Phase Engineering of 2D Materials

Polymorphic 2D materials allow structural and electronic phase engineering, which can be used to realize energy-efficient, cost-effective, and scalable device applications. The phase engineering covers not only conventional structural and metal-insulator transitions but also magnetic states, strongly correlated band structures, and topological phases in rich 2D materials. The methods used for the local phase engineering of 2D materials include various optical, geometrical, and chemical processes as well as traditional thermodynamic approaches. In this Review, we survey the precise manipulation of local phases and phase patterning of 2D materials, particularly with ideal and versatile phase interfaces for electronic and energy device applications. Polymorphic 2D materials and diverse quantum materials with their layered, vertical, and lateral geometries are discussed with an emphasis on the role and use of their phase interfaces. Various phase interfaces have demonstrated superior and unique performance in electronic and energy devices. The phase patterning leads to novel homo- and heterojunction structures of 2D materials with low-dimensional phase boundaries, which highlights their potential for technological breakthroughs in future electronic, quantum, and energy devices. Accordingly, we encourage researchers to investigate and exploit phase patterning in emerging 2D materials.

Charge Transport in UV-Oxidized Graphene and Its Dependence on the Extent of Oxidation

Graphene oxides with different degrees of oxidation are prepared by controlling UV irradiation on graphene, and the charge transport and the evolution of the transport gap are investigated according to the extent of oxidation. With increasing oxygenous defect density nD, a transition from ballistic to diffusive conduction occurs at nD≃1012 cm-2 and the transport gap grows in proportion to nD. Considering the potential fluctuation related to the e-h puddle, the bandgap of graphene oxide is deduced to be Eg≃30nD(1012cm-2) meV. The temperature dependence of conductivity showed metal-insulator transitions at nD≃0.3×1012 cm-2, consistent with Ioffe-Regel criterion. For graphene oxides at nD≥4.9×1012 cm-2, analysis indicated charge transport occurred via 2D variable range hopping conduction between localized sp2 domain. Our work elucidates the transport mechanism at different extents of oxidation and supports the possibility of adjusting the bandgap with oxygen content.

Percolative switching in transition metal dichalcogenide field-effect transistors at room temperature

We have addressed the microscopic transport mechanism at the switching or 'on-off' transition in transition metal dichalcogenide (TMDC) field-effect transistors (FETs), which has been a controversial topic in TMDC electronics, especially at room temperature. With simultaneous measurement of channel conductivity and its slow time-dependent fluctuation (or noise) in ultrathin WSe2 and MoS2 FETs on insulating SiO2 substrates where noise arises from McWhorter-type carrier number fluctuations, we establish that the switching in conventional backgated TMDC FETs is a classical percolation transition in a medium of inhomogeneous carrier density distribution. From the experimentally observed exponents in the scaling of noise magnitude with conductivity, we observe unambiguous signatures of percolation in a random resistor network, particularly, in WSe2 FETs close to switching, which crosses over to continuum percolation at a higher doping level. We demonstrate a powerful experimental probe to the microscopic nature of near-threshold electrical transport in TMDC FETs, irrespective of the material detail, device geometry, or carrier mobility, which can be extended to other classes of 2D material-based devices as well.

Continuous and reversible tuning of the disorder-driven superconductor-insulator transition in bilayer graphene

The influence of static disorder on a quantum phase transition (QPT) is a fundamental issue in condensed matter physics. As a prototypical example of a disorder-tuned QPT, the superconductor–insulator transition (SIT) has been investigated intensively over the past three decades, but as yet without a general consensus on its nature. A key element is good control of disorder. Here, we present an experimental study of the SIT based on precise in-situ tuning of disorder in dual-gated bilayer graphene proximity-coupled to two superconducting electrodes through electrical and reversible control of the band gap and the charge carrier density. In the presence of a static disorder potential, Andreev-paired carriers formed close to the Fermi level in bilayer graphene constitute a randomly distributed network of proximity-induced superconducting puddles. The landscape of the network was easily tuned by electrical gating to induce percolative clusters at the onset of superconductivity. This is evidenced by scaling behavior consistent with the classical percolation in transport measurements. At lower temperatures, the solely electrical tuning of the disorder-induced landscape enables us to observe, for the first time, a crossover from classical to quantum percolation in a single device, which elucidates how thermal dephasing engages in separating the two regimes.

Probing the electron states and metal-insulator transition mechanisms in molybdenum disulphide vertical heterostructures

The metal-insulator transition is one of the remarkable electrical properties of atomically thin molybdenum disulphide. Although the theory of electron-electron interactions has been used in modelling the metal-insulator transition in molybdenum disulphide, the underlying mechanism and detailed transition process still remain largely unexplored. Here we demonstrate that the vertical metal-insulator-semiconductor heterostructures built from atomically thin molybdenum disulphide are ideal capacitor structures for probing the electron states. The vertical configuration offers the added advantage of eliminating the influence of large impedance at the band tails and allows the observation of fully excited electron states near the surface of molybdenum disulphide over a wide excitation frequency and temperature range. By combining capacitance and transport measurements, we have observed a percolation-type metal-insulator transition, driven by density inhomogeneities of electron states, in monolayer and multilayer molybdenum disulphide. In addition, the valence band of thin molybdenum disulphide layers and their intrinsic properties are accessed.

Electronic transport in graphene with aggregated hydrogen adatoms

Hydrogen adatoms and other species covalently bound to graphene act as resonant scattering centers affecting the electronic transport properties and inducing Anderson localization. We show that attractive interactions between adatoms on graphene and their diffusion mobility strongly modify the spatial distribution, thus fully eliminating isolated adatoms and increasing the population of larger size adatom aggregates. Such spatial correlation is found to strongly influence the electronic transport properties of disordered graphene. Our scaling analysis shows that such aggregation of adatoms increases conductance by up to several orders of magnitude and results in significant extension of the Anderson localization length in the strong localization regime. We introduce a simple definition of the effective adatom concentration x*, which describes the transport properties of both random and correlated distributions of hydrogen adatoms on graphene across a broad range of concentrations.

Graphene nanoribbon devices at high bias

We present the electron transport in graphene nanoribbons (GNRs) at high electric bias conduction. When graphene is patterned into a few tens of nanometer width of a ribbon shape, the carriers are confined to a quasi-one-dimensional (1D) system. Combining with the disorders in the system, this quantum confinement can lead into a transport gap in the energy spectrum of the GNRs. Similar to CNTs, this gap depends on the width of the GNR. In this review, we examine the electronic properties of lithographically fabricated GNRs, focusing on the high bias transport characteristics of GNRs as a function of density tuned by a gate voltage. We investigate the transport behavior of devices biased up to a few volts, a regime more relevant for electronics applications. We find that the high bias transport behavior in this limit can be described by hot electron scattered by the surface phonon emission, leading to a carrier velocity saturation. We also showed an enhanced current saturation effect in the GNRs with an efficient gate coupling. This effect results from the introduction of the charge neutrality point into the channel, and is similar to pinch-off in MOSFET devices. We also observe that heating effects in graphene at high bias are significant.

Conduction tuning of graphene based on defect-induced localization

The conduction properties of graphene were tuned by tailoring the lattice by using an accelerated helium ion beam to embed low-density defects in the lattice. The density of the embedded defects was estimated to be 2-3 orders of magnitude lower than that of carbon atoms, and they functionalized a graphene sheet in a more stable manner than chemical surface modifications can do. Current modulation through back gate biasing was demonstrated at room temperature with a current on-off ratio of 2 orders of magnitude, and the activation energy of the thermally activated transport regime was evaluated. The exponential dependence of the current on the length of the functionalized region in graphene suggested that conduction tuning is possible through strong localization of carriers at sites induced by a sparsely distributed random potential modulation.

Effect of dimensionality on the localization behavior in hydrogenated graphene systems

Recently, several experiments have shown that graphene exhibits a metal-to-insulator transition by hydrogenation. Here we theoretically study the transport properties of hydrogenated graphene and graphene nanoribbons (GNRs), focusing on the conductance fluctuation behavior in the localized regime. Using a simple model for the conductance distribution in the quasi-localized regime where the conventional theory fails, we derive the modified single parameter scaling (SPS) relations for quasi-one-dimensional (Q1D) GNRs as well as two-dimensional (2D) graphene. We show that, as the dimensional crossover occurs from 2D to Q1D, the shape of the conductance distribution evolves from a positively skewed distribution to a log-normal distribution. We predict that GNRs with widths much larger than the localization lengths do not behave as a Q1D system. Our results provide fundamental insights into the dimensionality change not only in graphene, but also in general mesoscopic systems in the localized regime.

Magnetic response of conductance peak structure in junction-confined graphene nanoribbons

We have numerically investigated the magnetic response of the conductance peak structures in the transport gap of graphene nanoribbons. It is shown that the magnetic field induces a number of new conductance peaks within the transport gap of graphene nanoribbons confined by structural junctions. In addition, the magnetic field causes a shift of the conductance peak position and broadening of the peak width. This behaviour is due to the disappearance of zero conductance dips at the junction as a result of breaking time-reversal symmetry. Such behaviour is, however, not observed in the electronic transport of graphene nanoribbons confined by potential barriers, i.e. p-n-junctions. Thus, the magnetic response of conductance peaks may be used to distinguish the origin of the conductance peak structure within the transport gap observed in the experiments.

Metal-to-insulator transition and electron-hole puddle formation in disordered graphene nanoribbons

The experimentally observed metal-to-insulator transition in hydrogenated graphene is numerically confirmed for actual sized graphene samples and realistic impurity concentrations. The eigenstates of our tight-binding model with substitutional disorder corroborate the formation of electron-hole puddles with characteristic length scales comparable to the ones found in experiments. The puddles cause charge inhomogeneities and tend to suppress Anderson localization. Even though, monitoring the charge carrier quantum dynamics and performing a finite-size scaling of the local density of states distribution, we find strong evidence for the existence of localized states in graphene nanoribbons with short-range but also correlated long-range disorder.

Electrical characterization of graphene synthesized by chemical vapor deposition using Ni substrate

In this work, the electrical characterization of graphene films grown by chemical vapor deposition (CVD) on a Ni thin film is carried out and a simple relation between the gate-dependent electrical transport and the thickness of the films is presented. Arrays of two-terminal devices with an average graphene film thickness of 6.9 nm were obtained using standard fabrication techniques. A simple two-band model is used to describe the graphene films, with a band overlap parameter E(0) = 17 meV determined by the dependence of conductivity on temperature. Statistical electrical measurement data are presented for 126 devices, with an extracted average background conductivity σ = 0.91 mS, average carrier mobility μ = 1300 cm(2) V(-1) s(-1) and residual resistivity ρ = 1.65 kΩ. The ratio of mobility to conductivity is calculated to be inversely proportional to the graphene film thickness and this calculation is statistically verified for the ensemble of 126 devices. This result is a new method of graphene film thickness determination and is useful for films which cannot have their thickness measured by AFM or optical interference, but which are electrically contacted and gated. This general approach provides a framework for comparing graphene devices made using different fabrication methods and graphene growth techniques, even without prior knowledge of their uniformity or thickness.

Inhomogenous electronic structure, transport gap, and percolation threshold in disordered bilayer graphene

The inhomogenous real-space electronic structure of gapless and gapped disordered bilayer graphene is calculated in the presence of quenched charge impurities. For gapped bilayer graphene, we find that for current experimental conditions the amplitude of the fluctuations of the screened disorder potential is of the order of (or often larger than) the intrinsic gap Δ induced by the application of a perpendicular electric field. We calculate the crossover chemical potential Δ(cr), separating the insulating regime from a percolative regime in which less than half of the area of the bilayer graphene sample is insulating. We find that most of the current experiments are in the percolative regime with Δ(cr)≪Δ. The huge suppression of Δ(cr) compared with Δ provides a possible explanation for the large difference between the theoretical band gap Δ and the experimentally extracted transport gap.

Room-temperature high on/off ratio in suspended graphene nanoribbon field-effect transistors

We have fabricated suspended few-layer (1-3 layers) graphene nanoribbon field-effect transistors from unzipped multi-wall carbon nanotubes. Electrical transport measurements show that current annealing effectively removes the impurities on the suspended graphene nanoribbons, uncovering the intrinsic ambipolar transfer characteristic of graphene. Further increasing the annealing current creates a narrow constriction in the ribbon, leading to the formation of a large bandgap and subsequent high on/off ratio (which can exceed 10(4)). Such fabricated devices are thermally and mechanically stable: repeated thermal cycling has little effect on their electrical properties. This work shows for the first time that ambipolar field-effect characteristics and high on/off ratios at room temperature can be achieved in relatively wide graphene nanoribbons (15-50 nm) by controlled current annealing.

Electronic properties of graphene nanostructures

In this review, recent developments in the fabrication and understanding of the electronic properties of graphene nanostructures are discussed. After a brief overview of the structure of graphene and the two-dimensional transport properties, the focus is put on graphene constrictions, quantum dots and double quantum dots. For constrictions with a width below 100 nm, the current through the constriction is strongly suppressed for a certain back gate voltage range, related to the so-called transport gap. This transport gap is due to the formation of localized puddles in the constriction, and its size depends strongly on the constriction width. Such constrictions can be used to confine charge carriers in quantum dots, leading to Coulomb blockade effects.

The effects of disorder and interactions on the Anderson transition in doped graphene

We undertake an exact numerical study of the effects of disorder on the Anderson localization of electronic states in graphene. Analyzing the scaling behaviors of inverse participation ratio and geometrically averaged density of states, we find that the Anderson metal-insulator transition can be introduced by the presence of quenched random disorder. In contrast with the conventional picture of localization, four mobility edges can be observed for the honeycomb lattice with specific disorder strength and impurity concentration. Considering the screening effects of interactions on disorder potentials, the experimental findings of the scale enlargements of puddles can be explained by reviewing the effects of both interactions and disorder.

Nanoanalysis of graphene layers using scanning probe techniques

Graphene is an almost ideal two-dimensional system. Unlike other two-dimensional electron gas systems realized in silicon or gallium arsenide, the electron wave functions are very close to the surrounding environment. While this causes problems in trying to passivate the surface without reducing the mobility, it does allow direct electrical access to the two-dimensional surface states using scanning probe techniques. In this review, we look at recent advances in the nanoanalytics of the surface and edges of graphene using scanning probe techniques.

High-on/off-ratio graphene nanoconstriction field-effect transistor

A method is reported to pattern monolayer graphene nanoconstriction field-effect transistors (NCFETs) with critical dimensions below 10 nm. NCFET fabrication is enabled by the use of feedback-controlled electromigration (FCE) to form a constriction in a gold etch mask that is first patterned using conventional lithographic techniques. The use of FCE allows the etch mask to be patterned on size scales below the limit of conventional nanolithography. The opening of a confinement-induced energy gap is observed as the NCFET width is reduced, as evidenced by a sharp increase in the NCFET on/off ratio. The on/off ratios obtained with this procedure can be larger than 1000 at room temperature for the narrowest devices; this is the first report of such large room-temperature on/off ratios for patterned graphene FETs.

Charge transport in dual gated bilayer graphene with Corbino geometry

The resistance of dual-gated bilayer graphene is measured as a function of temperature and gating electric fields in the Corbino geometry which precludes edge transport. The temperature-dependent resistance is quantitatively described by a two-channel conductance model including parallel thermal activation and variable range hopping channels, which gives the electric-field-dependent band gap whose magnitude is found to be in good agreement with infrared absorption experiments. Low-temperature transport is similar to that seen in previous studies of dual-gated bilayer graphene with edges, suggesting that edge transport does not play an important role.

Electronic transport in dual-gated bilayer graphene at large displacement fields

We study the electronic transport properties of dual-gated bilayer graphene devices. We focus on the regime of low temperatures and high electric displacement fields, where we observe a clear exponential dependence of the resistance as a function of displacement field and density, accompanied by a strong nonlinear behavior in the transport characteristics. The effective transport gap is typically 2 orders of magnitude smaller than the optical band gaps reported by infrared spectroscopy studies. Detailed temperature dependence measurements shed light on the different transport mechanisms in different temperature regimes.

Very large magnetoresistance in graphene nanoribbons

Graphene has unique electronic properties, and graphene nanoribbons are of particular interest because they exhibit a conduction bandgap that arises due to size confinement and edge effects. Theoretical studies have suggested that graphene nanoribbons could have interesting magneto-electronic properties, with a very large predicted magnetoresistance. Here, we report the experimental observation of a significant enhancement in the conductance of a graphene nanoribbon field-effect transistor by a perpendicular magnetic field. A negative magnetoresistance of nearly 100% was observed at low temperatures, with over 50% magnetoresistance remaining at room temperature. This magnetoresistance can be tuned by varying the gate or source-drain bias. We also find that the charge transport in the nanoribbons is not significantly modified by an in-plane magnetic field. The large observed values of magnetoresistance may be attributed to the reduction of quantum confinement through the formation of cyclotron orbits and the delocalization effect under the perpendicular magnetic field.

Peierls-type instability and tunable band gap in functionalized graphene

Functionalizing graphene was recently shown to have a dramatic effect on the electronic properties of this material. Here we investigate spatial ordering of adatoms driven by the RKKY-type interactions. In the ordered state, which arises via a Peierls-instability-type mechanism, the adatoms reside mainly on one of the two graphene sublattices. Bragg scattering of electron waves induced by sublattice symmetry breaking results in a band gap opening, whereby Dirac fermions acquire a finite mass. The band gap is found to be immune to the adatoms' positional disorder, with only an exponentially small number of localized states residing in the gap. The gapped state is stabilized in a wide range of electron doping. Our findings show that controlled adsorption of adatoms or molecules provides a route to engineering a tunable band gap in graphene.

Transport and elastic scattering times as probes of the nature of impurity scattering in single-layer and bilayer graphene

Transport and elastic scattering times, tau{tr} and tau{e}, are experimentally determined from the carrier density dependence of the magnetoconductance of monolayer and bilayer graphene. Both times and their dependences on carrier density are found to be very different in the monolayer and the bilayer. However, their ratio tau{tr}/tau{e} is found to be close to 1.8 in the two systems and nearly independent of the carrier density. These measurements give insight on the nature (neutral or charged) and range of the scatterers. Comparison with theoretical predictions suggests that the main scattering mechanism in our samples is due to strong (resonant) scatterers of a range shorter than the Fermi wavelength, likely candidates being vacancies, voids, adatoms or short-range ripples.

Electron transport in disordered graphene nanoribbons

We report an electron transport study of lithographically fabricated graphene nanoribbons (GNRs) of various widths and lengths. At the charge neutrality point, a length-independent transport gap forms whose size is inversely proportional to the GNR width. In this gap, electrons are localized, and charge transport exhibits a transition between thermally activated behavior at higher temperatures and variable range hopping at lower temperatures. By varying the geometric capacitance, we find that charging effects constitute a significant portion of the activation energy.

Random-gap model for graphene and graphene bilayers

The effect of a randomly fluctuating gap, created by a random staggered potential, is studied in a monolayer and a bilayer of graphene. The density of states, the one-particle scattering rate, and the transport properties (diffusion coefficient and conductivity) are calculated at the neutrality point. All of these quantities vanish at a critical value of the average staggered potential, signaling a continuous transition to an insulating behavior. Transport quantities are directly linked to the one-particle scattering rate. Although the behavior is qualitatively the same in mono- and bilayers, the effect of disorder is much stronger in the latter.

Localization and the Kosterlitz-Thouless transition in disordered graphene

We investigate disordered graphene with strong long-range impurities. Contrary to the common belief that delocalization should persist in such a system against any disorder, as the system is expected to be equivalent to a disordered two-dimensional Dirac fermionic system, we find that states near the Dirac points are localized for sufficiently strong disorder (therefore inevitable intervalley scattering) and the transition between the localized and delocalized states is of Kosterlitz-Thouless type. Our results show that the transition originates from bounding and unbounding of local current vortices.

The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons

Graphene shows promise as a future material for nanoelectronics owing to its compatibility with industry-standard lithographic processing, electron mobilities up to 150 times greater than Si and a thermal conductivity twice that of diamond. The electronic structure of graphene nanoribbons (GNRs) and quantum dots (GQDs) has been predicted to depend sensitively on the crystallographic orientation of their edges; however, the influence of edge structure has not been verified experimentally. Here, we use tunnelling spectroscopy to show that the electronic structure of GNRs and GQDs with 2-20 nm lateral dimensions varies on the basis of the graphene edge lattice symmetry. Predominantly zigzag-edge GQDs with 7-8 nm average dimensions are metallic owing to the presence of zigzag edge states. GNRs with a higher fraction of zigzag edges exhibit a smaller energy gap than a predominantly armchair-edge ribbon of similar width, and the magnitudes of the measured GNR energy gaps agree with recent theoretical calculations.

Energy gaps in etched graphene nanoribbons

Transport measurements on an etched graphene nanoribbon are presented. It is shown that two distinct voltage scales can be experimentally extracted that characterize the parameter region of suppressed conductance at low charge density in the ribbon. One of them is related to the charging energy of localized states, the other to the strength of the disorder potential. The lever arms of gates vary by up to 30% for different localized states which must therefore be spread in position along the ribbon. A single-electron transistor is used to prove the addition of individual electrons to the localized states. In our sample the characteristic charging energy is of the order of 10 meV, the characteristic strength of the disorder potential of the order of 100 meV.