Very recently, borophene has been attracting extensive and ongoing interest as the new wonder material with structural polymorphism and superior attributes, showing that the structural imperfection of line defects (LDs) occurs widely at the interface between $ν_{1/5}$ ($χ_3$) and $ν_{1/6}$ ($β_{12}$) boron sheets. Motivated by these experiments, here we present a theoretical study of electron transport through two-terminal disordered borophene nanoribbons (BNRs) with random distribution of LDs. Our results indicate that LDs could strongly affect the electron transport properties of BNRs. In the absence of LDs, both $ν_{1/5}$ and $ν_{1/6}$ BNRs exhibit metallic behavior, in agreement with experiments. While in the presence of LDs, the overall electron transport ability is dramatically decreased, but some resonant peaks of conductance quantum can be found in the transmission spectrum of any disordered BNR with arbitrary arrangement of LDs. These disordered BNRs exhibit metal-insulator transition by varying nanoribbon width with tunable transmission gap in the insulating regime. Furthermore, the bond currents present fringe patterns and two evolution phenomena of resonant peaks are revealed for disordered BNRs with different widths. These results may help for understanding structure-property relationships and designing LD-based nanodevices.
Nanoribbons produced from cutting β_12-Borophene sheet is investigated by density functional theory. The electronic and magnetic properties of Borophene nanoribbons are studied and found that all considered ribbons are metal which is in good agreement with recent experimental results. β_12-Borophene nanoribbons have a lot of diversity due to existence of 5 Boron atoms in a unit cell of the sheet. The magnetic properties of ribbons are strongly dependent on the cutting direction and the edge profile. It is interesting that a ribbon with a specific width can be a normal or ferromagnetic metal wi…
We report a density-functional-theoretic study of the stability and electronic structure of two recently proposed borophene sheets with Pmmn symmetry and nonzero thickness. We then investigate nanoribbons (BNRs) derived from these nanostructures, with particular attention to technologically relevant properties like magnetism and electronic transport. We consider two perpendicular directions for the edges of the stripes as well as different lateral widths. We show that the Pmmn8 sheet, with 8 atoms in its unit cell and generated by two interpenetrating lattices, has a larger binding energy than…
By using non-equilibrium Green's function (NEGF) method and tight-binding (TB) approximation, we investigated a perfect control on spin transport in a zigzag $α^{\prime}$-boron nanoribbon ($α^{\prime}$-BNR) as the must semi-conducting structure of borophene. It has been found that when an $α^{\prime}$-BNR is exposed to an out-of-plane exchange magnetic field, spin splitting occurs for both spin-up and spin-down states in specific ranges of energy. Therefore, the spin polarization of current could be controlled by adjusting the energy of incoming electrons by means of an external back-gate volt…
The experimental observation of the Dirac fermion states in $β_{12}$-borophene sheets and the discovery of their novel topological properties properties have made them a promising candidate for spintronic applications. Here, by combining non-equilibrium Green's function (NEGF) and tight-binding (TB) approximation, we study the charge and spin transport properties through a $β_{12}$-borophene nanoribbon (BNR) with the different edge shapes. We show when a BNR exposed to a nonlocal exchange magnetic field, the spin filtering occurs for both spin-up and spin-down so that the spin direction of tra…
We investigate the transport properties of pristine zigzag-edged borophene nanoribbons (ZBNRs) of different widths, using the fist-principles calculations. We choose ZBNRs with widths of 5 and 6 as odd and even widths. The differences of the quantum transport properties are found, where even-N BNRs and odd-N BNRs have different current-voltage relationships. Moreover, the negative differential resistance (NDR) can be observed within certain bias range in 5-ZBNR, while 6-ZBNR behaves as metal whose current rises with the increase of the voltage. The spin filter effect of 36% can be revealed whe…
Conductance fluctuations produced by the presence of disorder in zigzag and armchair graphene nanoribbons are studied. We show that quantum transport in zigzag nanoribbons takes place via edge states which are exponentially localized, as in the standard Anderson localization problem, whereas for armchair nanoribbons the symmetry of the graphene sublattices produces anomalous localization, or delocalization. We show that these two different electron localizations lead to significant differences of the conductance statistics between zigzag and armchair nanoribbons. In particular, armchair nanori…
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 …
Using the partition-free time-dependent Landauer-B{ü}ttiker formalism for transient current correlations, we study the traversal times taken for electrons to cross graphene nanoribbon (GNR) molecular junctions. We demonstrate electron traversal signatures that vary with disorder and orientation of the GNR. These findings can be related to operational frequencies of GNR-based devices and their consequent rational design.
Random fluctuations of the shot-noise power in disordered graphene nanoribbons are studied. In particular, we calculate the distribution of the shot noise of nanoribbons with zigzag and armchair edge terminations. We show that the shot noise statistics is different for each type of these two graphene structures, which is a consequence of presence of different electron localizations: while in zigzag nanoribbons electronic edge states are Anderson localized, in armchair nanoribbons edge states are absent, but electrons are anomalously localized. Our analytical results are verified by tight bindi…
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 report on (magneto)-transport experiments in chemically derived narrow graphene nanoribbons under high magnetic fields (up to 60 Tesla). Evidences of field-dependent electronic confinement features are given, and allow estimating the possible ribbon edge symmetry. Besides, the measured large positive magnetoconductance indicates a strong suppression of backscattering induced by the magnetic field. Such scenario is supported by quantum simulations which consider different types of underlying disorders (smooth edge disorder and long range Coulomb scatters).
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 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 study the conductivity of disordered zigzag graphene nanoribbons in the incoherent regime by using the Boltzmann equation approach. The band structure of zigzag nanoribbons contains two energy valleys, and each valley has an excess one-way channel. The crucial point is that the numbers of conducting channels for two propagating directions are imbalanced in each valley due to the presence of an excess one-way channel. It was pointed out that as a consequence of this imbalance, a perfectly conducting channel is stabilized in the coherent regime if intervalley scattering is absent. We show tha…
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 …
The spin-dependent transport properties of armchair graphene nanoribbons in the presence of extrinsic spin-orbit coupling induced by a random distribution of Nickel adatoms is studied. By combining a recursive Green's function formalism with density functional theory, we explore the influence of ribbon length and metal adatom concentration on the conductance. At a given length, we observed a significant enhancement of the spin-flip channel around resonances and at energies right above the Fermi level. We also estimate the spin-relaxation length, finding values on the order of tens of micromete…
Electron transport in a disordered graphene nanoribbon with zigzag edges is crucially affected by a perfectly conducting channel (PCC), which is stabilized if intervalley scattering is ignorable. In the presence of such a PCC, the dimensionless conductance g of the system decreases to the quantized value of g = 1 with increasing system length L. In the realistic case where intervalley scattering is weak but not ignorable, the PCC is gradually destabilized with increasing L, and g eventually decays to zero owing to the onset of Anderson localization. Here, we show that such destabilization of t…
We investigate electron and phonon transport through edge disordered zigzag graphene nanoribbons based on the same methodological tool of nonequilibrium Green functions. We show that edge disorder dramatically reduces phonon thermal transport while being only weakly detrimental to electronic conduction. The behavior of the electronic and phononic elastic mean free paths points to the possibility of realizing an electron-crystal coexisting with a phonon-glass. The calculated thermoelectric figure of merit (ZT) values qualify zigzag graphene nanoribbons as a very promising material for thermoele…
We study electronic transport in graphene nanoribbons with rough edges. We first consider a model of weak disorder that corresponds to an armchair ribbon whose width randomly changes by a single unit cell size. We find that in this case, the low-temperature conductivity is governed by an effective one-dimensional hopping between segments of distinct band structure. We then provide numerical evidence and qualitative arguments that similar behavior also occurs in the limit of strong uncorrelated boundary disorder.
We consider gated graphene nanoribbons subject to Berry-Mondragon boundary conditions in the presence of weak impurities. Using field--theoretical methods, we calculate the density of charge carriers (and, thus, the quantum capacitance) as well as the optical and DC conductivities at zero temperature. We discuss in detail their dependence on the gate (chemical) potential, and reveal a non-linear behaviour induced by the quantization of the transversal momentum.
The low-energy spectrum of graphene nanoribbons with armchair edges (armchair nanoribbons) is described as the superposition of two non-equivalent Dirac points of graphene. In spite of the lack of well-separated two valley structures, the single-channel transport subjected to long-ranged impurities is nearly perfectly conducting, where the backward scattering matrix elements in the lowest order vanish as a manifestation of internal phase structures of the wavefunction. For multi-channel energy regime, however, the conventional exponential decay of the averaged conductance occurs. Since the int…
We investigate the conductivity $σ$ of graphene nanoribbons with zigzag edges as a function of Fermi energy $E_F$ in the presence of the impurities with different potential range. The dependence of $σ(E_F)$ displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of $σ(E_F)$ and a wide dip near the Dirac point, due to the special properties of long range potenti…
We investigate the properties of the gap-edge states of half-filled interacting disordered zigzag graphene nanoribbons. We find that the midgap states can display the quantized fractional charge of 1/2. These gap-edge states can be represented by topological kinks with their site probability distribution divided between the opposite zigzag edges with different chiralities. In addition, there are numerous spin-split gap-edge states, similar to those in a Mott-Anderson insulator.
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…
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…
Study on the electronic transport of a large scale two dimensional system by the transfer matrix method (TMM) based on the Schördinger equation suffers from the numerical instability. To address this problem, we propose a renormalized transfer matrix method (RTMM) by setting up a set of linear equations from U times of multiplication of traditional transfer matrix (U=N/S}with N and S being the atom number of length and the transfer step), and smaller S is required for wider systems. Then we solve the above linear equations by Gauss elimination method and further optimize to reduce the computat…
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 present numerical studies of conduction in graphene nanoribbons with different types of disorder. We find that even when defect scattering depresses the conductance to values two orders of magnitude lower than 2e^2/h, equally spaced conductance plateaus occur at moderately low temperatures due to enhanced electron backscattering near subband edge energies if bulk vacancies are present in the ribbon. This work accounts quantitatively for the surprising conductance quantization observed by Lin et al. [Phys. Rev. B 78, 161409 (2008)] in ribbons with such low conductances.
We report the realization of top-gated graphene nanoribbon field effect transistors (GNRFETs) of ~10 nm width on large-area epitaxial graphene exhibiting the opening of a band gap of ~0.14 eV. Contrary to prior observations of disordered transport and severe edge-roughness effects of GNRs, the experimental results presented here clearly show that the transport mechanism in carefully fabricated GNRFETs is conventional band-transport at room temperature, and inter-band tunneling at low temperature. The entire space of temperature, size, and geometry dependent transport properties and electrostat…
We revisit the problem of electron transport in clean and disordered zigzag graphene nanoribbons, and expose numerous hitherto unknown peculiar properties of these systems at zero energy, where both sublattices decouple because of chiral symmetry. For clean ribbons, we give a quantitative description of the unusual power-law dispersion of the central energy bands and of its main consequences, including the strong divergence of the density of states near zero energy, and the vanishing of the transverse localization length of the corresponding edge states. In the presence of off-diagonal disorde…
We numerically compute the density of states (DOS) of interacting disordered zigzag graphene nanoribbon (ZGNR) having midgap states showing $e/2$ fractional edge charges. The computed Hartree-Fock DOS is linear at the critical disorder strength where the gap vanishes. This implies an $I\mbox{-}V$ curve of $I\propto V^2$. Thus, $I\mbox{-}V$ curve measurement may yield evidence of fractional charges in interacting disordered ZGNR. We show that even a weak disorder potential acts as a singular perturbation on zigzag edge electronic states, producing drastic changes in the energy spectrum. Spin-ch…
Numerical calculations have been performed to elucidate unconventional electronic transport properties in disordered nanographene ribbons with zigzag edges (zigzag ribbons). The energy band structure of zigzag ribbons has two valleys that are well separated in momentum space, related to the two Dirac points of the graphene spectrum. The partial flat bands due to edge states make the imbalance between left- and right-going modes in each valley, {\it i.e.} appearance of a single chiral mode. This feature gives rise to a perfectly conducting channel in the disordered system, i.e. the average of c…
We will present brief overview on the electronic and transport properties of graphene nanoribbons focusing on the effect of edge shapes and impurity scattering. The low-energy electronic states of graphene have two non-equivalent massless Dirac spectrum. The relative distance between these two Dirac points in the momentum space and edge states due to the existence of the zigzag type graphene edges are decisive to the electronic and transport properties of graphene nanoribbons. In graphene nanoribbons with zigzag edges, two valleys related to each Dirac spectrum are well separated in momentum s…
Structural manipulation at the nanoscale breaks the intrinsic correlations among different energy carrier transport properties, achieving high thermoelectric performance. However, the coupled multifunctional (phonon and electron) transport in the design of nanomaterials makes the optimization of thermoelectric properties challenging. Machine learning brings convenience to the design of nanostructures with large degree of freedom. Herein, we conducted comprehensive thermoelectric optimization of isotopic armchair graphene nanoribbons (AGNRs) with antidots and interfaces by combining Green's fun…
We developed a unified mesoscopic transport model for graphene nanoribbons, which combines the non-equilibrium Green's function (NEGF) formalism with the real-space π-orbital model. Based on this model, we probe the spatial distributions of electrons under a magnetic field, in order to obtain insights into the various signature Hall effects in disordered armchair graphene nanoribbons (AGNR). In the presence of a uniform perpendicular magnetic field (B\perp-field), a perfect AGNR shows three distinct spatial current profiles at equilibrium, depending on its width. Under non-equilibrium conditio…
We investigate the influence of low-dimensionality and disorder in phonon transport in ultra-narrow armchair graphene nanoribbons (GNRs) using non-equilibrium Greens function (NEGF) simulation techniques. We specifically focus on how different parts of the phonon spectrum are influenced by geometrical confinement and line edge roughness. With the introduction of line edge roughness, the phonon transmission is reduced, but non-uniformly throughout the spectrum. We identify four distinct behaviors within the phonon spectrum in the presence of disorder: i) the low-energy, low-wavevector acoustic …
We unveil the nature of the structural disorder in bottom-up zigzag graphene nanoribbons along with its effect on the magnetism and electronic transport on the basis of scanning probe microscopies and first-principles calculations. We find that edge-missing m-xylene units emerging during the cyclodehydrogenation step of the on-surface synthesis are the most common point defects. These "bite'' defects act as spin-1 paramagnetic centers, severely disrupt the conductance spectrum around the band extrema, and give rise to spin-polarized charge transport. We further show that the electronic conduct…
A theoretical study of the transport properties of zigzag and armchair graphene nanoribbons with a magnetic barrier on top is presented. The magnetic barrier modifies the energy spectrum of the nanoribbons locally, which results in an energy shift of the conductance steps towards higher energies. The magnetic barrier also induces Fabry-Perot type oscillations, provided the edges of the barrier are sufficiently sharp. The lowest propagating state present in zigzag and metallic armchair nanoribbons prevent confinement of the charge carriers by the magnetic barrier. Disordered edges in nanoribbon…
In this paper, we present a mode space method for atomistic non-equilibrium Green's function simulations of armchair graphene nanoribbon FETs that includes electron-phonon scattering. With reference to both conventional and tunnel FET structures, we show that, in the ideal case of a smooth electrostatic potential, the modes can be decoupled in different groups without any loss of accuracy. Thus, inter-subband scattering due to electron-phonon interactions is properly accounted for, while the overall simulation time considerably improves with respect to real-space, with a speed-up factor of 40 …
We have developed an efficient order-N real-space Kubo approach for the calculation of the phonon conductivity which outperforms state-of-the-art alternative implementations based on the Green's function formalism. The method treats efficiently the time-dependent propagation of phonon wave packets in real space, and this dynamics is related to the calculation of the thermal conductance. Without loss of generality, we validate the accuracy of the method by comparing the calculated phonon mean free paths in disordered carbon nanotubes (isotope impurities) with other approaches, and further illus…
Transport in disordered armchair graphene nanoribbons (AGR) with long-range correlation between quantum wire contact is investigated by transfer matrix combined with Landauer's formula. Metal-insulator transition is induced by disorder in neutral AGR. Thereinto, the conductance is one conductance quantum for metallic phase and exponentially decays otherwise when the length of AGR is infinity and far longer than its width. Similar to the case of long-range disorder, the conductance of neutral AGR first increases and then decreases while the conductance of doped AGR monotonically decreases, as t…
We report on a numerical study of quantum transport in disordered two dimensional graphene and graphene nanoribbons. By using the Kubo and the Landauer approaches, transport length scales in the diffusive (mean free path, charge mobilities) and localized regimes (localization lengths) are computed, assuming a short range disorder (Anderson-type). In agreement with localization scaling theory, the electronic systems are found to undergo a conventional Anderson localization in the zero temperature limit. Localization lengths in weakly disordered ribbons are found to differ by two orders of magni…
Guanine-quadruplex, consisting of several stacked guanine-quartets (GQs), has emerged as an important category of novel molecular targets with applications from nanoelectronic devices to anticancer drugs. Incorporation of metal cations into GQ structure is utilized to form stable G-quadruplexes, while no other passage has been reported yet. Here we report the room temperature (RT) molecular self-assembly of extensive metal-free GQ networks on Au(111) surface. Surface defect induced by an implanted molybdenum atom within Au(111) surface is used to nucleate and stabilize the cation-free GQ netwo…
Impurities are unavoidable during the preparation of graphene samples and play an important role in graphene's electronic properties when they are adsorbed on graphene surface. In this work, we study the electronic structures and transport properties of a two-terminal zigzag graphene nanoribbon (ZGNR) device whose scattering region is covered by various adsorbates within the framework of the tight-binding approximation, by taking into account the coupling strength $γ$ between adsorbates and carbon atoms, the adsorbate concentration $n_i$, and the on-site energy disorder of adsorbates. Our resu…
