Quantum transport in topological surface states of Bi$_2$Te$_3$ nanoribbons
Daniel Rosenbach, Nico Oellers, Abdur Rehman Jalil, Martin Mikulics, Jonas Kölzer, Erik Zimmermann, Gregor Mussler, Stephany Bunte, Detlev Grützmacher, Hans Lüth, Thomas Schäpers
Quasi-1D nanowires of topological insulators are emerging candidate structures in superconductor hybrid architectures for the realization of Majorana fermion based quantum computation schemes. It is however technically difficult to both fabricate as well as identify the 1D limit of topological insulator nanowires. Here, we investigated selectively-grown Bi$_2$Te$_3$ topological insulator nanoribbons and nano Hall bars at cryogenic temperatures for their topological properties. The Hall bars are defined in deep-etched Si$_3$N$_4$/SiO$_2$ nano-trenches on a silicon (111) substrate followed by a selective area growth process via molecular beam epitaxy. The selective area growth is beneficial to the device quality, as no subsequent fabrication needs to be performed to shape the nanoribbons. Transmission line measurements are performed to evaluate contact resistances of Ti/Au contacts applied as well as the specific resistance of the Bi$_2$Te$_3$ binary topological insulator. In the diffusive transport regime of these unintentionally $n$-doped Bi$_2$Te$_3$ topological insulator nano Hall bars, we identify distinguishable electron trajectories by analyzing angle-dependent universal conductance fluctuation spectra. When the sample is tilted from a perpendicular to a parallel magnetic field orientation, these high frequent universal conductance fluctuations merge with low frequent Aharonov-Bohm type oscillations originating from the topologically protected surface states encircling the nanoribbon cross section. For 500 nm wide Hall bars we also identify low frequent Shubnikov-de Haas oscillations in the perpendicular field orientation, that reveal a topological high-mobility 2D transport channel, partially decoupled from the bulk of the material.
Armchair biphenylene nanoribbons are investigated by using density functional theory. The nanoribbon that contains one biphenylene subunit in a unit cell is a semiconductor with a direct band gap larger than 1 eV, while that containing four biphenylene subunits is a metal. The semiconducting nanoribbon has high electron mobility of 57174 cm2V-1s-1, superior to armchair graphene nanoribbons. Negative differential resistance behavior is observed in two electronic devices composed of the semiconducting and metallic nanoribbons. The on/off ratios are in the order of 10^3. All these indicate that a…
A WSe2 monolayer of 1T' phase is a large band gap quantum spin Hall insulator, supporting dissipationless charge and spin transports through the topologically protected edge states. In this work, we explore the nanoribbon forms of 1T' phase WSe2 by first-principles density functional calculations and the many-body perturbation GW and Bethe-Salpeter equation method. We found that the 1T' WSe2 nanoribbon can show topological edge states with a ribbon width of ~4-6 nm. Those edge bands show crossing through the Fermi level an odd number of times, with one kind of spin-polarization connecting the …
The robustness of topological materials against disorder and defects is presumed but has not been demonstrated explicitly in realistic systems. In this work, we use state-of-the-art density functional theory and recursive nonequilibrium Green's functions methods to study the effect of disorder in the electronic transport of long nanoribbons, up to 157 nm, as a function of vacancy concentration. In narrow nanoribbons, even for small vacancy concentrations, defect-like localized states give rise to hybridization between the edge states erasing topological protection and enabling backscattering e…
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 …
Effects of electron-electron and spin-orbit interactions on the ground-state magnetic configuration and on the corresponding thermoelectric and spin thermoelectric properties in zigzag nanoribbons of two-dimensional hexagonal crystals are analyzed theoretically. Thermoelectric properties of quasi-stable magnetic states are also considered. Of particular interest is the influence of Coulomb and spin-orbit interactions on the topological edge states and on the transition between the topological insulator and conventional gap insulator states. It is shown that the interplay of both interactions h…
We study numerically the effects of edge and bulk disorder on the conductance of graphene nanoribbons. We compute the conductance suppression due to localization induced by edge scattering. We find that even for weak edge roughness, conductance steps are suppressed and transport gaps appear. These gaps are approximately inversely proportional to the nanoribbon width. On/off conductance ratios grow exponentially with the nanoribbon length. Our results impose severe limitations to the use of graphene in ballistic nanowires.
We theoretically study the electrical, thermal and thermoelectric transport properties of graphene nanoribbons under torsional deformations. The modelling follows a nonequilibrium Green's function approach in the ballistic transport regime, describing the electrical and phononic properties through \textit{ab-initio} density functional theory and empirical interatomic potentials, respectively. We consider two different types of deformations, a continuous twist of a given angle applied to the nanoribbon, and two consecutive twists applied in opposite angular directions. The numerical results are…
We study spin-orbit torques and charge pumping in magnetic quasi-one dimensional zigzag nanoribbons with hexagonal lattice, in the presence of large intrinsic spin-orbit coupling. Such a system experiences topological phase transition from a trivial band insulator to a quantum spin Hall insulator either by tuning the magnetization direction or the intrinsic spin-orbit coupling. We find that spin-charge conversion efficiency (i.e. spin-orbit torque and charge pumping) is dramatically enhanced at the topological transition, displaying a substantial angular anisotropy.
We investigate the electronic transport properties of a folded graphene nanoribbon with monolayer nanoribbon contacts. We consider two possible foldings: either the nanoribbon can be folded onto itself in the shape of a hairpin with the nanoribbon leads at a $0^\circ$ angle, or the monolayer contacts have different directions, forming a $60^\circ$ angle. The system is described by a single $π$-band nearest-neighbor tight-binding Hamiltonian taking into account curvature effects. We have found that for the case of a nanoribbon folded over itself the conductance oscillates from almost zero and a…
The characteristics of energy band spectrum of armchair graphene nanoribbons in presence of line defect are analyzed within a simple non-interacting tight-binding framework. In metallic nanoribbons an energy gap may or may not appear in the band spectrum depending on the location of the defect line, while in semiconducting ribbons the gaps are customized, yielding the potential applicabilities of graphene nanoribbons in nanoscale electronic devices. With a more general model, we also investigate two-terminal electron transport using Green's function formalism.
We investigate the role played by electron traps on adiabatic charge transport for graphene nanoribbons in the presence of an acoustically induced longitudinal surface acoustic wave (SAW) potential. Due to the weak longitudinal SAW-induced potential as well as the strong transverse confinement by a nanoribbon, minibandsof sliding tunnel-coupled quantum dots are formed so that by varying the chemical potential to pass through the minigaps, quantized adiabatic charge transport may be obtained. We analyze the way that the minigaps may be closed, thereby destroying the likelihood of current quanti…
We report the study of a novel linear magneto-resistance (MR) under perpendicular magnetic fields in Bi2Se3 nanoribbons. Through angular dependence magneto-transport experiments, we show that this linear MR is purely due to two-dimensional (2D) transport, in agreement with the recently discovered linear MR from 2D topological surface state in bulk Bi2Te3, and the linear MR of other gapless semiconductors and graphene. We further show that the linear MR of Bi2Se3 nanoribbons persists to room temperature, underscoring the potential of exploiting topological insulator nanomaterials for room tempe…
Graphene nanoribbons with zigzag terminated edges have a magnetic ground state characterized by edge ferromagnetism and antiferromagnetic inter edge coupling. This broken symmetry state is degenerate in the spin orientation and we show that, associated with this degeneracy, the system has topological solitons. The solitons appear at the interface between degenerate ground states. These solitons are the relevant charge excitations in the system. When charge is added to the nanoribbon, the system energetically prefers to create magnetic domains and accommodate the extra electrons in the interfac…
We report an electron transport study of lithographically fabricated graphene nanoribbons of various widths and lengths at different temperatures. At the charge neutrality point, a length-independent transport gap forms whose size is inversely proportional to the width. In this gap, electron is localized, and charge transport exhibits a transition between simple thermally activated behavior at higher temperatures and a variable range hopping at lower temperatures. By varying the geometric capacitance through the addition of top gates, we find that charging effects constitute a significant port…
We have studied quantum transport in Graphene Nanoribbon Tunnel Field-Effect Transistors. Unlike other studies on similar structures, we have included dissipative processes induced by inelastic electron-phonon scattering and edge roughness in the nanoribbon self-consistently within a non-equilibrium transport simulation. Our results show that the dissipative scattering imposes a limit to the minimum OFF current and a minimum subthreshold swing that can be obtained even for long channel lengths where direct source-drain tunneling is inhibited. The edge roughness, in presence of dissipative scat…
We study charge transport in a graphene zigzag nanoribbon driven by an external time-periodic kicking potential. Using the exact solution of the time-dependent Dirac equation with a delta-kick potential acting in each period, we study the time evolution of the quasienergy levels and the time-dependent optical conductivity. By variation of the kicking parameters, the conductivity becomes widely tunable.
We study the electronic structure and transport properties of zigzag and armchair monolayer molybdenum disulfide nanoribbons using an 11-band tight-binding model that accurately reproduces the material's bulk band structure near the band gap. We study the electronic properties of pristine zigzag and armchair nanoribbons, paying particular attention to the edges states that appear within the MoS$_2$ bulk gap. By analyzing both their orbital composition and their local density of states, we find that in zigzag-terminated nanoribbons these states can be localized at a single edge for certain ener…
We combine density-functional theory and the nonequilibrium Green's function method to study the thermal conductance of graphene nanoribbons with armchair and zigzag edges. Zigzag ribbons have higher thermal conductance than armchair ribbons of comparable widths due to an anisotropy in phonon dispersion for graphene nanoribbons: low-frequency bands in zigzag ribbons are more dispersive than those in armchair ribbons. The edges with and without hydrogen-passivation modify the atomic structure and ultimately influence the phonon thermal transport differently for the two ribbon types.
We investigate transport through nanoribbons in the presence of disorder scattering. We show that size quantization patterns are only present when SU(2) pseudospin symmetry is preserved. Symmetry breaking disorder renders transverse quantization invisible, which may provide an explanation for the necessity of suspending graphene nanoconstrictions to obtain size quantization signatures in very recent experiments. Employing a quasi-classical Monte-Carlo simulation, we are able to reproduce and explain key qualitative features of the full quantum-mechanical calculations.
Topological insulator (TI) nanoribbons with proximity-induced superconductivity are a promising platform for Majorana bound states (MBSs). In this work, we consider a detailed modeling approach for a TI nanoribbon in contact with a superconductor via its top surface, which induces a superconducting gap in its surface-state spectrum. The system displays a rich phase diagram with different numbers of end-localized MBSs as a function of chemical potential and magnetic flux piercing the cross section of the ribbon. These MBSs can be robust or fragile upon consideration of electrostatic disorder. W…
We describe designs for the realization of topological Majorana qubits in terms of proximitized topological insulator nanoribbons pierced by a uniform axial magnetic field. This platform holds promise for particularly robust Majorana bound states, with easily manipulable inter-state couplings. We propose proof-of-principle experiments for initializing, manipulating, and reading out Majorana box qubits defined in floating devices dominated by charging effects. We argue that the platform offers design advantages which make it particularly suitable for extension to qubit network structures realiz…
The electronic nonlinear transport through ultra narrow graphene nanoribbons (sub-$10nm$) is studied. A stable region of negative differential resistance (NDR) appears in the I-V characteristic curve of {\it odd} zigzag graphene nanoribbons (ZGNRs) in both positive and negative polarity. This NDR originates from a transport gap inducing by a selection rule which blocks electron transition between disconnecting energy bands of ZGNR. Based on this transition rule, on/off ratio of the current increases exponentially with the ribbon length up to $10^5$. In addition, charging effects and also spati…
We investigate transport properties of the junctions in which the graphene nanoribbon with the zigzag shaped edges consisting of the $N$ legs is sandwiched by the two normal metals by means of recursive Green's function method. The conductance and the transmission probabilities are found to have the remarkable properties depending on the parity of $N$. The singular behaviors close to E=0 with $E$ being the Fermi energy are demonstrated. The channel filtering is shown to occur in the case with $N=$ even.
Electronic transport with a line (or a few lines) of Anderson type disorder in a zigzag graphene nanoribbon is investigated in presence of Rashba spin-orbit interaction. Such line disorders give rise to peculiar behavior in both charge as well as spin-polarized transmission in the following sense. In the weak disorder regime, the charge transport data show Anderson localization up to a certain disorder strength, beyond which the extended states emerge and start dominating over the localized states. These results are the hallmark signature of a selectively disordered (as opposed to bulk disorde…
The energy spectrum and electronic density of states (DOS) of zigzag graphene nanoribbons with edges reconstructed with topological defects are investigated within the tight-binding method. In case of the Stone-Wales zz (57) edge the low-energy spectrum is markedly changed in comparison to the pristine zz edge. We found that the electronic DOS at the Fermi level is different from zero at any width of graphene nanoribbons. In contrast, for ribbons with heptagons only at one side and pentagons at another one the energy gap at the Fermi level is open and the DOS is equal to zero. The reason is th…
We have experimentally investigated quantum interference corrections to the conductivity of graphene nanoribbons at temperatures down to 20 mK studying both weak localization (WL) and universal conductance fluctuations (UCF). Since in individual nanoribbons at millikelvin temperatures the UCFs strongly mask the weak localization feature we employ both gate averaging and ensemble averaging to suppress the UCFs. This allows us to extract the phase coherence length from both WL and UCF at all temperatures. Above 1 K, the phase coherence length is suppressed due to Nyquist scattering whereas at lo…
We study the electronic and transport properties of heterostructures formed by armchair graphene nanoribbons with intersections of finite length. We describe the system by a tight-binding model and calculate the density of states and the conductance within the Green's function formalism based on real-space renormalization techniques. We show the apparition of interface states and bound states in the continuum which present a strong dependence of the heterostructure geometry. We investigate the effects on the conductance of an external perturbation applied on the edges atoms of the intersection…
We report the composition and gate voltage induced tuning of transport properties in chemically synthesized Bi2(Te1-xSex)3 nanoribbons. It is found that increasing Se concentration effectively suppresses the bulk carrier transport and induces semiconducting behavior in the temperature dependent resistance of Bi2(Te1-xSex)3 nanoribbons when x is greater than ~10%. In Bi2(Te1-xSex)3 nanoribbons with x ~20%, gate voltage enables ambipolar modulation of resistance (or conductance) in samples with thickness around or larger than 100nm, indicating significantly enhanced contribution in transport fro…
The magnetic and spin transport properties of a carbon chain between two armchair graphene nanoribbon (AGNR) electrodes were studied using tight-binding Hamiltonian, mean-field Hubbard model and Landauer-Butikker formalism. The results showed that only odd-numbered carbon chains show intrinsic magnetic moments in chain-graphene junctions. It was also found that the electronic, magnetic and spin transport properties of carbon chain-graphene junctions strongly depend on the position and the length of the carbon chains between AGNR electrodes. Interestingly, we found a fully spin-polarized transm…
We present electronic transport measurements on etched graphene nanoribbons on silicon dioxide before and after a short hydrouoric acid (HF) treatment. We report on changes in the transport properties, in particular, in terms of a decreasing transport gap and a reduced doping level after HF dipping. Interestingly, the effective energy gap is nearly unaffected by the HF treatment. Additional measurements on a graphene nanoribbon with lateral graphene gates support strong indications that the HF significantly modifies the edges of the investigated nanoribbons leading to a significantly reduced d…
We report on quantum transport measurements on etched graphene nanoribbons encapsulated in hexagonal boron nitride (hBN). At zero magnetic field our devices behave qualitatively very similar to what has been reported for graphene nanoribbons on $\text{SiO}_2$ or hBN, but exhibit a considerable smaller transport gap. At magnetic fields of around $3~$T the transport behavior changes considerably and is dominated by a much larger energy gap induced by electron-electron interactions completely suppressing transport. This energy gap increases with a slope on the order of $3-4~ $meV/T reaching value…
We study the transport of charge carriers through finite graphene structures. The use of numerical exact kernel polynomial and Green function techniques allows us to treat actual sized samples beyond the Dirac-cone approximation. Particularly we investigate disordered nanoribbons, normal-conductor/graphene interfaces and normal-conductor/graphene/normal-conductor junctions with a focus on the behavior of the local density of states, single-particle spectral function, optical conductivity and conductance. We demonstrate that the contacts and bulk disorder will have a major impact on the electro…
By combining density functional theory and nonequilibrium Green's function, we study the electronic and transport properties of monolayer black phosphorus nanoribbons (PNRs). First, we investigate the band-gap of PNRs and its modulation by the ribbon width and an external transverse electric feld. Our calculations indicate a giant Stark effect in PNRs, which can switch on transport channels of semiconducting PNRs under low bias, inducing an insulator-metal-transition. Next, we study the transport channels in PNRs via the calculations of the current density and local electron transmission pathw…
Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi2Se3 material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi2Se3 nanomaterials with a variety of morpholog…
Many applications for topological insulators (TIs) as well as new phenomena require devices with reduced dimensions. While much progress has been made to realize thin films of TIs with low bulk carrier density, nanostructures have not yet been reported with similar properties, despite the fact that size confinement should help reduce contributions from bulk carriers. Here we demonstrate that Bi2Se3 nanoribbons, grown by a simple catalyst-free physical-vapour deposition, have inherently low bulk carrier densities, and can be further made bulk-free by size confinement, thus revealing the high mo…
The formation of a superlattice in graphene can serve as a way to modify its electronic bandstructure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekulé bond ordering in graphene deposited on top of a Copper substrate, leading to the breaking of the valley degeneracy while preserving the highly desirable feature of linearity and gapless character of its band dispersion. In this paper we study the effects of a Kekulé distortion in zigzag graphene nanoribbons in both, the subband spectrum and on its electronic transport properties. We extend our…
Graphene nanoribbons and constrictions are envisaged as fundamental components of future carbon-based nanoelectronic and spintronic devices. At nanoscale, electronic effects in these devices depend heavily on the dimensions of the active channel and the nature of edges. Hence, controlling both these parameters is crucial to understand the physics in such systems. This review is about the recent progress in the fabrication of graphene nanoribbons and constrictions in terms of low temperature quantum transport. In particular, recent advancements using encapsulated graphene allowing for quantized…
We explore nanoribbons from topological two-dimensional stanene as channel material in tunnel field effect transistors. This novel technological option offers the possibility to build pure one-dimensional (1D) channel devices (comprised of a 1D chain of atoms) due to localized states in correspondence of the nanoribbon edges. The investigation is based on first-principle calculations and multi-scale transport simulations to assess devices performance against industry requirements and their robustness with respect to technological issues like line edge roughness, detrimental for nanoribbons. We…
Spin-orbital interactions (SOI) in silicene results in the quantum spin Hall effect, while the Hubbard-induced Coulomb interaction in zigzag nanoribbons often generates a band gap with the anti-ferromagnetic (AF) spin orders on two edges. In this paper we systematically study these two joint contributions to the zigzag silicene-like nanoribbons (zSiNR). Some topological and magnetic phase transitions are investigated with different material parameters and external fields. We find when the ribbon width or the SOI value exceeds some critical value, the SOI may overcome the Coulomb interaction an…
In this work, electrical and spin properties of armchair silicene nanoribbon (ASiNR) in the presence of charged impurity is studied. The non-equilibrium Green's function along with multi-orbital tight-binding is applied to obtain transmission probability. different type of spin transmission probability in the ASiNR on a substrate is investigated. The charged impurities are located in the underlying substrate. Spin-flip along the channel is calculated by using spin transmission probability. Spin diffusion length in ASiNR for differently charged impurities is obtained and compared with the mean …
We investigate the density and temperature-dependent conductance of graphene nanoribbons with varying aspect ratio. Transport is dominated by a chain of quantum dots forming spontaneously due to disorder. Depending on ribbon length, electron density, and temperature, single or multiple quan- tum dots dominate the conductance. Between conductance resonances cotunneling transport at the lowest temperatures turns into activated transport at higher temperatures. The density-dependent activation energy resembles the Coulomb gap in a quantitative manner. Individual resonances show signatures of mult…
Chemically synthesized "cove"-type graphene nanoribbons (cGNRs) of different widths were brought into dispersion and drop-cast onto exfoliated hexagonal boron nitride (hBN) on a Si/SiO2 chip. With AFM we observed that the cGNRs form ordered domains aligned along the crystallographic axes of the hBN. Using electron beam lithography and metallization, we contacted the cGNRs with NiCr/Au, or Pd contacts and measured their I-V-characteristics. The transport through the ribbons was dominated by the Schottky behavior of the contacts between the metal and the ribbon.
We simulate electron transport through graphene nanoribbons of experimentally realizable size (length L up to 2 micrometer, width W approximately 40 nm) in the presence of scattering at rough edges. Our numerical approach is based on a modular recursive Green's function technique that features sub-linear scaling with L of the computational effort. We identify the influence of the broken A-B sublattice (or chiral) symmetry and of K-K' scattering by Fourier spectroscopy of individual scattering states. For long ribbons we find Anderson-localized scattering states with a well-defined exponential …
Finite graphene nanoribbon (GNR) heterostructures host intriguing topological in-gap states (Rizzo, D. J. et al.~\textit{Nature} \textbf{2018}, \textit{560}, 204]). These states may be localized either at the bulk edges, or at the ends of the structure. Here we show that correlation effects (not included in previous density functional simulations) play a key role in these systems: they result in increased magnetic moments at the ribbon edges accompanied by a significant energy renormalization of the topological end states -- even in the presence of a metallic substrate. Our computed results ar…
We study electronic quantum transport in graphene nanoribbon (GNR) networks on mesoscopic length scales. We focus on zigzag GNRs and investigate the conductance properties of statistical networks. To this end we use a density-functional-based tight-binding model to determine the electronic structure and quantum transport theory to calculate electronic transport properties. We then introduce a new efficient network decimation algorithm that reduces the complexity in generic three-diemnsional GNR networks. We compare our results to semi-classical calculations based on the nodal analysis approach…
Using the tight-binding (TB) approximation with inclusion of the spin-orbit interaction, we predict a topological phase transition in the electronic band structure of phosphorene in the presence of axial strains. We derive a low-energy TB Hamiltonian that includes the spin-orbit interaction for bulk phosphorene. Applying a compressive biaxial in-plane strain and perpendicular tensile strain in ranges where the structure is still stable leads to a topological phase transition. We also examine the influence of strain on zigzag phosphorene nanoribbons (zPNRs) and the formation of the correspondin…
We calculate the local current density in pristine armchair graphene nanoribbons (AGNRs) with varying width, $N_\mathrm{C}$, employing a density-functional-theory-based ab initio transport formalism. We observe very pronounced current patterns (streamlines) with threefold periodicity in $N_\mathrm{C}$. They arise as a consequence of quantum confinement in the transverse flow direction. Neighboring streamlines are separated by stripes of almost vanishing flow. As a consequence, the response of the current to functionalizing adsorbates is very sensitive to their placement: adsorbates located wit…
Ultra-thin topological insulator nanostructures, in which coupling between top and bottom surface states takes place, are of great intellectual and practical importance. Due to the weak Van der Waals interaction between adjacent quintuple layers (QLs), the layered bismuth selenide (Bi2Se3), a single Dirac-cone topological insulator with a large bulk gap, can be exfoliated down to a few QLs. In this paper, we report the first controlled mechanical exfoliation of Bi2Se3 nanoribbons (> 50 QLs) by an atomic force microscope (AFM) tip down to a single QL. Microwave impedance microscopy is employed …
Based on first-principles approaches, we study the ballistic phonon transport properties of finite monatomic carbon chains stretched between graphene nanoribbons, an $sp$-$sp^2$ hybrid carbon nanostructure that has recently seen significant experimental advances in its synthesis. We find that the lattice thermal conductance anomalously increases with tensile strain for the even-numbered carbon chains that adopt the alternating bond-length polyyne configuration. On the other hand, in the odd-numbered carbon chain cases, which assume the equal bond-length cumulene configuration, phonon conductan…
We study dc and ac transport along armchair graphene nanoribbons using the ${\bf k\cdot p}$ spectrum and eigenfunctions and general linear-response expressions for the conductivities. Then we contrast the results with those for transport along ordinary waveguides. In all cases we assess the influence of elastic scattering by impurities, describe it quantitatively with a Drude-type contribution to the current previously not reported, and evaluate the corresponding relaxation time for long- and short-range impurity potentials. We show that this contribution dominates the response at very low fre…
We study the transport property for armchair-edge graphene nanoribbons (AGNRs) with an adatom coupling to a semi-infinite quantum wire. Using the nonequilibrium Green's function approach with tight-binding approximation, we demonstrate that the tunneling current through the system is sensitively dependent on both the AGNR width and adatom location. Interestingly, when the adatom locates onto a carbon atom in the 3$j$th chain from the edge of a metallic AGNR, the system shows a transmission gap accompanied by a threshold voltage in $I-V$ curve like a semiconducting AGNR. This effect may be usef…
Inspired by recent experiments where electron transport was measured across graphene nanoribbons (GNR) suspended between a metal surface and the tip of a scanning tunneling microscope [Koch \textit{et al}., Nat. Nanotechnol. {\bf 7}, 713 (2012)], we present detailed first-principles simulations of inelastic electron tunneling spectroscopy (IETS) of long pristine and defected armchair and zigzag nanoribbons under a range of charge carrier conditions. For the armchair ribbons we find two robust IETS signals around 169 and 196 mV corresponding to the D- and G-modes of Raman spectroscopy as well a…
The presence of strong disorder in graphene nanoribbons yields low-mobility diffusive transport at high charge densities, whereas a transport gap occurs at low densities. Here, we investigate the longitudinal and transverse magnetoresistance of a narrow (60 nm) nanoribbon in a six-terminal Hall bar geometry. At B= 11 T, quantum Hall plateaux appear at $σ_{xy}=\pm2e^2/h$, $\pm6e^2/h$ and $\pm10e^2/h$, for which the Landau level spacing is larger than the Landau level broadening. Interestingly, the transport gap does not disappear in the quantum Hall regime, when the zero-energy Landau level is …
Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide evidence that armchair ribbons of width $3m+2$ with integer $m$ are metallic and otherwise semiconducting, whereas zigzag ribbons are metallic independent of their width. The contact geometry, defining to which atoms at the ribbon edges the source and drain leads are attached, has strong effects on the transport. If leads are attached only to the inner atom…
We have investigated electronic transport in graphene nanoribbon devices with additional bar-shaped extensions ("wings") at each side of the device. We find that the Coulomb-blockade dominated transport found in conventional ribbons is strongly modified by the presence of the extensions. States localized far away from the central ribbon contribute significantly to transport. We discuss these findings within the picture of multiple coupled quantum dots. Finally, we compare the experimental results with tight-binding simulations which reproduce the experiment both qualitatively and quantitativel…
