An introduction to the transport properties of graphene combining experimental results and theoretical analysis is presented. In the theoretical description simple intuitive models are used to illustrate important points on the transport properties of graphene. The concept of chirality, stemming from the massless Dirac nature of the low energy physics of the material, is shown to be instrumental in understanding its transport properties: the conductivity minimum, the electronic mobility, the effect of strain, the weak (anti-)localization, and the optical conductivity.
After the first unequivocal demonstration of spin transport in graphene (Tombros et al., 2007), surprisingly at room temperature, it was quickly realized that this novel material was relevant for both fundamental spintronics and future applications. Over the decade since, exciting results have made the field of graphene spintronics blossom, and a second generation of studies has extended to new two-dimensional (2D) compounds. This Colloquium reviews recent theoretical and experimental advances on electronic spin transport in graphene and related 2D materials, focusing on emergent phenomena in …
Spectroscopic studies of electronic phenomena in graphene are reviewed. A variety of methods and techniques are surveyed, from quasiparticle spectroscopies (tunneling, photoemission) to methods probing density and current response (infrared optics, Raman) to scanning probe nanoscopy and ultrafast pump-probe experiments. Vast complimentary information derived from these investigations is shown to highlight unusual properties of Dirac quasiparticles and many-body interaction effects in the physics of graphene.
In this Colloquium recent advances in the field of quantum heat transport are reviewed. This topic has been investigated theoretically for several decades, but only during the past twenty years have experiments on various mesoscopic systems become feasible. A summary of the theoretical basis for describing heat transport in one-dimensional channels is first provided. Then the main experimental investigations of quantized heat conductance due to phonons, photons, electrons, and anyons in such channels are presented. These experiments are important for understanding the fundamental processes tha…
Ion transport through nanopores permeates through many areas of science and technology, from cell behavior to sensing and separation to catalysis and batteries. Two-dimensional materials, such as graphene, molybdenum disulfide (MoS$_2$), and hexagonal boron nitride (hBN), are recent additions to these fields. Low-dimensional materials present new opportunities to develop filtration, sensing, and power technologies, encompassing ion exclusion membranes, DNA sequencing, single molecule detection, osmotic power generation, and beyond. Moreover, the physics of ionic transport through pores and con…
We review the recent progress in understanding the properties of spin-split superconductors under non-equilibrium conditions. Recent experiments and theories demonstrate a rich variety of transport phenomena occurring in devices based on such materials that suggest direct applications in thermoelectricity, low-dissipative spintronics, radiation detection and sensing. We discuss different experimental situations and present a theoretical framework based on quantum kinetic equations. Within this framework we provide an accurate description of the non-equilibrium distribution of charge, spin and …
The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. We begin this review by discussing underpinnings of the topological band theory, which basically involves a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are deli…
The discovery of unusual heat conduction properties of graphene has led to a surge of theoretical and experimental studies of phonon transport in two-dimensional material systems. The rapidly developing graphene thermal field spans from theoretical physics to practical engineering applications. In this invited review we outline different theoretical approaches developed for describing phonon transport in graphene and provide comparison with available experimental thermal conductivity data. A special attention is given to analysis of the recent theoretical results for the phonon thermal conduct…
In this paper we review thermal properties of graphene and multilayer graphene and discuss the optothermal technique developed for the thermal conductivity measurements. We also outline different theoretical approaches used for the description of phonon transport in graphene and provide comparison with available experimental thermal conductivity data.
Graphene nanoribbon (GNR) field-effect transistors (FETs) with widths down to 12 nm have been fabricated by electron beam lithography using a wafer-scale chemical vapor deposition (CVD) process to form the graphene. The GNR FETs show drain-current modulation of approximately 10 at 300 K, increasing to nearly 106 at 4 K. The strong temperature dependence of the minimum current indicates the opening of a bandgap for CVD-grown GNR-FETs. The extracted bandgap is estimated to be around 0.1 eV by differential conductance methods. This work highlights the development of CVD-grown large-area graphene …
Geometry, stability, and thermal transport of graphene nanoquilts folded by hydrogenation are studied using molecular dynamics simulations. The hydrogenated graphene nanoquilts show increased thermodynamic stability and better transport properties than folded graphene structures without hydrogenation. For the two-fold graphene nanoquilt, both geometry and thermal conductivity are very sensitive to the adsorbed hydrogen chains, which is interpreted by the red-shift of PDOS. For the multi-fold nanoquilts, their thermal conductivities can be tuned from 100% to 15% of pristine graphene, by varying…
Engineering the electronic properties of graphene has triggered great interest for potential applications in electronics and opto-electronics. Here we demonstrate the possibility to tune the electronic transport properties of graphene monolayers and multilayers by functionalisation with fluorine. We show that by adjusting the fluorine content different electronic transport regimes can be accessed. For monolayer samples, with increasing the fluorine content, we observe a transition from electronic transport through Mott variable range hopping in two dimensions to Efros - Shklovskii variable ran…
We report first principles investigations of the nonequilibrium transport properties of a Cu(111)|graphene interface. The Cu(111) electrode is found to induce a transmission minimum (TM) located -0.68eV below the Fermi level, a feature originating from the Cu-induced charge transfer resulting in n-type doped graphene with the Dirac point coinciding with the TM. An applied bias voltage shifts the n-graphene TM relative to the pure graphene TM and leads to a distinctive peak in the differential conductance indicating the doping level, a characteristic not observed in pure graphene.
A discovery of the unusual thermal properties of graphene stimulated experimental, theoretical and computational research directed at understanding phonon transport and thermal conduction in two-dimensional material systems. We provide a critical review of recent results in the graphene thermal field focusing on phonon dispersion, specific heat, thermal conductivity, and comparison of different models and computational approaches. The correlation between the phonon spectrum in graphene-based materials and the heat conduction properties is analyzed in details. The effects of the atomic plane ro…
Properties of phonons - quanta of the crystal lattice vibrations - in graphene have attracted strong attention of the physics and engineering communities. Acoustic phonons are the main heat carriers in graphene near room temperature while optical phonons are used for counting the number of atomic planes in Raman experiments with few-layer graphene. It was shown both theoretically and experimentally that transport properties of phonons, i.e. energy dispersion and scattering rates, are substantially different in the quasi two-dimensional system such as graphene compared to basal planes in graphi…
We report on the structural and transport properties of the smallest dislocation loop in graphene, known as a flower defect. First, by means of advanced experimental imaging techniques, we deduce how flower defects are formed during recrystallization of chemical vapor deposited graphene. We propose that the flower defects arise from a bulge type mechanism in which the flower domains are the grains left over by dynamic recrystallisation. Next, in order to evaluate the use of such defects as possible building blocks for all-graphene electronics, we combine multiscale modeling tools to investigat…
Graphene two-dimensional nature combined with today lithography allows to achieve nanoelectronics devices smaller than the Dirac electrons wavelength. Here we show that in these graphene subwavelength nanodevices the electronic quantum transport properties present deep analogies with classical phenomena of subwavelength optics. By introducing the concept of electronic diffraction barrier to represent the effect of constrictions, we can easily describe the rich transport physics in a wealth of nanodevices: from Bethe and Kirchhoff diffraction in graphene slits, to Fabry-Perot interference oscil…
We have measured the impact of calcium adsorbates on the transport property of graphene. Although calcium renders conductivity linearly dependent on the carrier density of graphene as predicted, our experimental results diverge from the existing theoretical calculations. Our data expose the inadequacy of any existing theory to describe the minimum conductivity of graphene and indicate that a more complete testing of the impurity scattering calculations will require improving the experimental capabilities by minimizing the contribution from the substrate-bound charged impurities and developing …
We examine thermal transport in graphene supported on SiO2 using molecular dynamics simulations. Coupling to the substrate reduces the thermal conductivity (TC) of supported graphene by an order of magnitude, due to damping of the flexural acoustic (ZA) phonons. However, increasing the strength of the graphene-substrate interaction enhances the TC of supported graphene, contrary to expectations. The enhancement is due to the coupling of graphene ZA modes to the substrate Rayleigh waves, which linearizes the dispersion and increases the group velocity of the hybridized modes. These findings sug…
We investigate the spin transport and precession in graphene by using the Hanle effect in nonlocal and threeterminal measurement geometries. Identical spin lifetimes, spin diffusion lengths and spin polarizations are observed in graphene devices for both techniques over a wide range of temperatures. The magnitude of the spin signals is well explained by spin transport models. These observations rules out any signal enhancements or additional scattering mechanisms at the interfaces for both geometries. This validates the applicability of both the measurement methods for graphene based spintroni…
We investigate transport in graphene supported on various dielectrics (SiO2, BN, Al2O3, HfO2) through a hydrodynamic model which includes self-heating and thermal coupling to the substrate, scattering with ionized impurities, graphene phonons and dynamically screened interfacial plasmon-phonon (IPP) modes. We uncover that while low-field transport is largely determined by impurity scattering, high-field transport is defined by scattering with dielectric-induced IPP modes, and a smaller contribution of graphene intrinsic phonons. We also find that lattice heating can lead to negative differenti…
We investigate the morphology of quasi-free-standing monolayer graphene (QFMLG) formed at several temperatures by hydrogen intercalation and discuss its relationship with transport properties. Features corresponding to incomplete hydrogen intercalation at the graphene-substrate interface are observed by scanning tunneling microscopy on QFMLG formed at 600 and 800°C. They contribute to carrier scattering as charged impurities. Voids in the SiC substrate and wrinkling of graphene appear at 1000°C, and they decrease the carrier mobility significantly.
The effects of surface chemical doping on spin transport in graphene are investigated by performing non-local measurements in ultrahigh vacuum while depositing gold adsorbates. We demonstrate manipulation of the gate-dependent non-local spin signal as a function of gold coverage. We discover that charged impurity scattering is not the dominant mechanism for spin relaxation in graphene, despite its importance for momentum scattering. Finally, unexpected enhancements of the spin lifetime illustrate the complex nature of spin relaxation in graphene.
A method is suggested to separately determine the surface density of positively and negatively charged impurities that limit the mobility in a graphene monolayer. The method is based on the exact result for the transport cross-section, according to which the massless carriers are scattered more strongly when they are attracted to a charged impurity than when they are repelled from it.
The thermal properties of graphene-based materials are theoretically investigated. The fourth-nearest neighbor force constant method for phonon properties is used in conjunction with both the Landauer ballistic and the non-equilibrium Green's function techniques for transport. Ballistic phonon transport is investigated for different structures including graphene, graphene antidot lattices, and graphene nanoribbons. We demonstrate that this particular methodology is suitable for robust and efficient investigation of phonon transport in graphene-based devices. This methodology is especially usef…
Two-dimensional graphene, carbon nanotubes and graphene nanoribbons represent a novel class of low dimensional materials that could serve as building blocks for future carbon-based nanoelectronics. Although these systems share a similar underlying electronic structure, whose exact details depend on confinement effects, crucial differences emerge when disorder comes into play. In this short review, we consider the transport properties of these materials, with particular emphasis to the case of graphene nanoribbons. After summarizing the electronic and transport properties of defect-free systems…
We investigate the transport of electrons in disordered and pristine graphene devices. Fano shot noise, a standard metric to assess the mechanism for electronic transport in mesoscopic devices, has been shown to produce almost the same magnitude ($\approx 1/3$) in ballistic and diffusive graphene devices and is therefore of limited applicability. We consider a two-terminal geometry where the graphene flake is contacted by narrow metallic leads. We propose that the dependence of the conductance on the position of one of the leads, a conductance profile, can give us insight into the charge flow,…
Devices made from graphene encapsulated in hexagonal boron-nitride exhibit pronounced negative bend resistance and an anomalous Hall effect, which are a direct consequence of room-temperature ballistic transport on a micrometer scale for a wide range of carrier concentrations. The encapsulation makes graphene practically insusceptible to the ambient atmosphere and, simultaneously, allows the use of boron nitride as an ultrathin top gate dielectric.
We develop two types of graphene devices based on nanoelectromechanical systems (NEMS), that allows transport measurement in the presence of in situ strain modulation. Different mobility and conductance responses to strain were observed for single layer and bilayer samples. These types of devices can be extended to other 2D membranes such as MoS2, providing transport, optical or other measurements with in situ strain.
We provide a broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature dependent carrier transport in doped or gated graphene structures. A salient feature of our review is a critical comparison between carrier transport in graphene and in two-dimensional semiconductor systems (e.g. heterostructures, quantum wells, inversion layers) so that the unique features of graphene electronic properties arising from its gap- less, massless, chiral Dirac spectrum are highlighted. Experiment and theory as well as quantum and semi-classical t…
We theoretically consider, comparing with the existing experimental literature, the electrical conductivity of gated monolayer graphene as a function of carrier density, temperature, and disorder in order to assess the prospects of accessing the Dirac point using transport studies in high-quality suspended graphene. We show that the temperature dependence of graphene conductivity around the charge neutrality point provides information about how close the system can approach the Dirac point although competition between long-range and short-range disorder as well as between diffusive and ballist…
We develop a theory for density, disorder, and temperature dependent electrical conductivity of bilayer graphene in the presence of long-range charged impurity scattering as well as an additional short-range disorder of independent origin, establishing that both scattering mechanisms contribute significantly to determining bilayer transport properties. We find that although strong screening properties of bilayer graphene lead to qualitative differences with the corresponding single layer situation, both systems exhibit the linearly density dependent conductivity at high density and the minimum…
All local electronic properties of graphene on a hexagonal boron nitride (hBN) substrate exhibit spatial moiré patterns related to lattice constant and orientation differences between shared triangular Bravais lattices. We apply a previously derived effective Hamiltonian for the $π$-bands of graphene on h-BN to address the carrier-dependence of transport properties, concentrating on the conductivity features at four electrons and four holes per unit cell. These transport features measure the strength of Bragg scattering of $π$-electrons off the moiré pattern, and exhibit a striking particle-ho…
Local curvature, or bending, of a graphene sheet is known to increase the chemical reactivity presenting an opportunity for templated chemical functionalization. Using first principles calculations based on density functional theory (DFT) we investigate the reduction of the reaction barrier for adsorption of atomic hydrogen at linear bends in graphene. We find a significant lowering (15%) for realistic radii of curvature (20 Å), and that adsorption along the linear bend leads to a stable linear kink. We compute the electronic transport properties of individual and multiple kink-lines, and demo…
We study a suspended graphene sheet subject to the electric field of a gate underneath. We compute the elastic deformation of the sheet and the corresponding effective gauge field, which modifies the electronic transport. In a clean system the two-terminal conductance of the sample is reduced below the ballistic limit and is almost totally suppressed at low carrier concentrations in samples under tension. Residual disorder restores a small finite conductivity.
Using high temperature annealing conditions with a graphite cap covering the C-face of an 8deg off-axis 4H-SiC sample, large and homogeneous single epitaxial graphene layers have been grown. Raman spectroscopy shows evidence of the almost free-standing character of these monolayer graphene sheets, which was confirmed by magneto-transport measurements. We find a moderate p-type doping, high carrier mobility and half integer Quantum Hall effect typical of high quality graphene samples. This opens the way to a fully compatible integration of graphene with SiC devices on the wafers that constitute…
We reveal that phononic thermal transport in graphene is not immune to grain boundaries (GBs) aligned along the direction of the temperature gradient. Non-equilibrium molecular dynamics simulations uncover a large reduction in the phononic thermal conductivity ($κ_p$) along linear ultra-narrow GBs comprising periodically-repeating pentagon-heptagon dislocations. Green's function calculations and spectral energy density analysis indicate that $κ_p$ is the complex manifestation of the periodic strain field, which behaves as a reflective diffraction grating with both diffuse and specular phonon r…
We show that the pseudospin being an additional degree of freedom for carriers in graphene can be efficiently controlled by means of the electron-electron interactions which, in turn, can be manipulated by changing the substrate. In particular, an out-of-plane pseudospin component can occur leading to a zero-field Hall current as well as to polarization-sensitive interband optical absorption.
Step junctions are often present in layered materials, i.e. where single-layer regions meet multi-layer regions, yet their effect on thermal transport is not understood to date. Here, we measure heat flow across graphene junctions (GJs) from monolayer to bilayer graphene, as well as bilayer to four-layer graphene for the first time, in both heat flow directions. The thermal conductance of the monolayer-bilayer GJ device ranges from ~0.5 to 9.1x10^8 Wm-2K-1 between 50 K to 300 K. Atomistic simulations of such GJ device reveal that graphene layers are relatively decoupled, and the low thermal co…
Graphene has shown impressive properties for nanoelectronics applications including a high mobility and a width-dependent bandgap. Use of graphene in nanoelectronics would most likey be in the form of graphene nanoribbons (GNRs) where the ribbon width is expected to be less than 20 nm. Many theoretical projections have been made on the impact of edge-scattering on carrier transport in GNRs - most studies point to a degradation of mobility (of GNRs) as well as the on/off ratio (of GNR FETs). This study provides the first clear experimental evidence of the onset of size-effect in patterned GNRs;…
Most materials in available macroscopic quantities are polycrystalline. Graphene, a recently discovered two-dimensional form of carbon with strong potential for replacing silicon in future electronics, is no exception. There is growing evidence of the polycrystalline nature of graphene samples obtained using various techniques. Grain boundaries, intrinsic topological defects of polycrystalline materials, are expected to dramatically alter the electronic transport in graphene. Here, we develop a theory of charge carrier transmission through grain boundaries composed of a periodic array of dislo…
Graphene-based laminates, with ultralong and tortuous nanocapillaries formed by simply stacking graphene flakes together, have great promises in filtration and separation. However, the information on liquid water trans-membrane permeation is lacking, which is the most fundamental problem and of crucial importance in solution-based mass transport. Here, based on isotope labelling, we investigate the liquid water transportation through graphene-based nanocapillaries under no external hydrostatic pressures. Liquid water can afford an unimpeded permeation through graphene-based nanochannels with a…
We report on the observation of inertial-ballistic transport in nanoscale cross junctions fabricated from epitaxial graphene grown on SiC(0001). Ballistic transport is indicated by a negative bend resistance of R12,43 ~ 170 ohm which is measured in a non-local, four-terminal configuration at 4.2 K and which vanishes as the temperature is increased above 80 K.
We develop a hydrodynamic description of transport properties in graphene-based systems which we derive from the quantum kinetic equation. In the interaction-dominated regime, the collinear scattering singularity in the collision integral leads to fast unidirectional thermalization and allows us to describe the system in terms of three macroscopic currents carrying electric charge, energy, and quasiparticle imbalance. Within this "three-mode" approximation we evaluate transport coeffcients in monolayer graphene as well as in double-layer graphene-based structures. The resulting classical magne…
We investigate charge transport in pentacene-graphene nanojunctions employing density functional theory (DFT) electronic structure calculations and the Landauer transport formalism. The results show that the unique electronic properties of graphene strongly influence the transport in the nanojunctions. In particular, edge states in graphene electrodes with zigzag termination result in additional transport channels close to the Fermi energy which deeply affects the conductance at small bias voltages. Investigating different linker groups as well as chemical substitution, we demonstrate how the …
The momentum transport in ultraclean bilayer graphene is characterized by the viscous transport. In quantizing magnetic field the momentum current passes through the guiding centers of cyclotron orbits. In this study we derive the quantized Hall viscosity of bilayer graphene that is the next topological feature after the quantum Hall effect. This can be detected in the non-local magnetoresistivity measurements that varies with the quantized steps of magnetoresistivity.
We study spin transport in normal/ferromagnetic/normal graphene junctions where a gate electrode is attached to the ferromagnetic graphene. We find that due to the exchange field of the ferromagnetic graphene, spin current through the junctions has an oscillatory behavior with respect to the chemical potential in the ferromagnetic graphene, which can be tuned by the gate voltage. Especially, we obtain a controllable spin current reversal by the gate voltage. Our prediction of high controllability of spin transport in ferromagnetic graphene junction may contribute to the development of the spin…
Photon-assisted electron transport in ballistic graphene is analyzed using scattering theory. We show that the presence of an ac signal (applied to a gate electrode in a region of the system) has interesting consequences on electron transport in graphene, where the low energy dynamics is described by the Dirac equation. In particular, such a setup describes a feasible way to probe energy dependent transmission in graphene. This is of substantial interest because the energy dependence of transmission in mesoscopic graphene is the basis of many peculiar transport phenomena proposed in the recent…
Growth of large-scale graphene is still accompanied by imperfections. By means of a four-tip STM/SEM the local structure of graphene grown on SiC(0001) was correlated with scanning electron microscope images and spatially resolved transport measurements. The systematic variation of probe spacings and substrate temperature has clearly revealed two-dimensional transport regimes of Anderson localization as well as of diffusive transport. The detailed analysis of the temperature dependent data demonstrates that the local on-top nano-sized contacts do not induce significant strain to the epitaxial …
We have studied spin-depend electron tunnelling through the Rashba barrier in a monolayer graphene lattice. The transfer matrix method, have been employed to obtain the spin dependent transport properties of the chiral particles. It is shown that graphene sheets in presence of Rashba spin-orbit barrier will act as an electron spin- inverter.
Chemical functionalization of graphene holds promise for various applications ranging from nanoelectronics to catalysis, drug delivery, and nanoassembly. In many applications it is important to be able to transport adsorbates on graphene in real time. We propose to use electromigration to drive the adsorbate transport across the graphene sheet. To assess the efficiency of electromigration, we develop a tight-binding model of electromigration of an adsorbate on graphene and obtain simple analytical expressions for different contributions to the electromigration force. Using experimentally acces…
We present first principles study of thermoelectric transport properties of sandwiched heterostructure of Graphene (G)/hexagonal Boron Nitride (BN)/G, based on Boltzmann transport theory for band electrons using the bandstructure calculated from the Density Functional Theory (DFT) based plane-wave method. Calculations were carried out for three, four and five BN layers sandwiched between Graphene layers with three different arrangements to obtain the Seebeck coefficient and Power factor in $T\sim 25-400$K range. Moreover, using Molecular Dynamics (MD) simulations with very large simulation cel…
The magnetic effects in ferromagnetic graphene basically depend on the principle of exchange interaction when ferromagntism is induced by depositing an insulator layer on graphene. Here we deal with the consequences of non-uniformity in the exchange coupling strength of the ferromagnetic graphene. We discuss how the in- homogeneity in the coordinate and momentum of the exchange vector field can provide interesting results in the conductivity analysis of the ferromagnetic graphene. Our analysis is based on the Kubo formalism of quantum transport.
We report transport measurements through graphene on SrTiO3 substrates as a function of magnetic field B, carrier density n, and temperature T. The large dielectric constant of SrTiO3 screens very effectively long-range electron-electron interactions and potential fluctuations, making Dirac electrons in graphene virtually non-interacting. The absence of interactions results in a unexpected behavior of the longitudinal resistance in the N=0 Landau level, and in a large suppression of the transport gap in nano-ribbons. The "bulk" transport properties of graphene at B=0T, on the contrary, are com…
Graphene is a fascinating material for exploring fundamental science questions as well as a potential building block for novel electronic applications. In order to realize the full potential of this material the fabrication techniques of graphene devices, still in their infancy, need to be refined to better isolate the graphene layer from the environment. We present results from a study on the influence of extrinsic factors on the quality of graphene devices including material defects, lithography, doping by metallic leads and the substrate. The main finding is that trapped Coulomb scatterers …
Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken, by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion. Here, we introduce a novel bilayer graphene heterostructure, where single-layer graphene is placed on top of another layer of graphene with a regular lattice of antidots. We dub this class of graphene systems GOAL: graphene on graphene antidot lattice. By varying the structure geometry, band structure engineering can be performed to obtain linearly dispersi…
Graphene nanoribbons provide an opportunity to integrate phase-coherent transport phenomena with nanoelectromechanical systems (NEMS). Due to the strain induced by a deflection in a graphene nanoribbon resonator, coherent electron transport and mechanical deformations couple. As the electrons in graphene have a Fermi wavelength λ~ a_0 = 1.4 Å, this coupling can be used for sensitive displacement detection in both armchair and zigzag graphene nanoribbon NEMS. Here it is shown that for ordered as well as disordered ribbon systems of length L, a strain ε~ (w/L)^2 due to a deflection w leads to a …
