Coherent electronic transport through graphene constrictions: subwavelength regime and optical analogy

Impact of valley degeneracy on the thermoelectric properties of zig-zag graphene nanoribbons with staggered sublattice potentials and transverse electric fields

This study investigates the band inversion of flat bands in zig-zag graphene nanoribbons (ZGNRs) using a tight-binding model. The band inversion results from symmetry breaking in the transverse direction, achievable through deposition on specific substrates such as separated silicon carbide or hexagonal boron nitride sheets. Upon band inversion, ZGNRs exhibit electronic structures characterized by valley degeneracy and band gap properties, which can be modulated by transverse electric fields. To explore the impact of this level degeneracy on thermoelectric properties, we employ Green's function techniques to calculate thermoelectric quantities in ZGNR segments with staggered sublattice potentials and transverse electric fields. Two carrier transport scenarios are considered: the chemical potential is positioned above and below the highest occupied molecular orbital. We analyze thermionic-assisted transport (TAT) and direct ballistic transport (DBT). Level degeneracy enhances the electric power factors of ZGNRs by increasing electrical conductance, while the Seebeck coefficient remains robust in the TAT scenario. Conversely, in DBT, the enhancement of the power factor primarily stems from improvements in the Seebeck coefficient at elevated temperatures.

Thermoelectric properties of armchair graphene nanoribbons with array characteristics

The thermoelectric properties of armchair graphene nanoribbons (AGNRs) with array characteristics are investigated theoretically using the tight-binding model and Green's function technique. The AGNR structures with array characteristics are created by embedding a narrow boron nitride nanoribbon (BNNR) into a wider AGNR, resulting in two narrow AGNRs. This system is denoted as w-AGNR/n-BNNR, where 'w' and 'n' represent the widths of the wider AGNR and narrow BNNR, respectively. We elucidate the coupling effect between two narrow symmetrical AGNRs on the electronic structure of w-AGNR/i-BNNR. A notable discovery is that the power factor of the 15-AGNR/5-BNNR with the minimum width surpasses the quantum limitation of power factor for 1D ideal systems. The energy level degeneracy observed in the first subbands of w-AGNR/n-BNNR structures proves to be highly advantageous in enhancing the electrical power outputs of graphene nanoribbon devices.

Semi-Empirical Pseudopotential Method for Graphene and Graphene Nanoribbons

We implemented a semi-empirical pseudopotential (SEP) method for calculating the band structures of graphene and graphene nanoribbons. The basis functions adopted are two-dimensional plane waves multiplied by several B-spline functions along the perpendicular direction. The SEP includes both local and non-local terms, which were parametrized to fit relevant quantities obtained from the first-principles calculations based on the density-functional theory (DFT). With only a handful of parameters, we were able to reproduce the full band structure of graphene obtained by DFT with a negligible difference. Our method is simple to use and much more efficient than the DFT calculation. We then applied this SEP method to calculate the band structures of graphene nanoribbons. By adding a simple correction term to the local pseudopotentials on the edges of the nanoribbon (which mimics the effect caused by edge creation), we again obtained band structures of the armchair nanoribbon fairly close to the results obtained by DFT. Our approach allows the simulation of optical and transport properties of realistic nanodevices made of graphene nanoribbons with very little computation effort.

Valley-polarized and enhanced transmission in graphene with a smooth strain profile

We explore the influence of strain on the valley-polarized transmission of graphene by employing the wave-function matching and the non-equilibrium Green's function technique. When the transmission is along the armchair direction, we show that the valley polarization and transmission can be improved by increasing the width of the strained region and increasing (decreasing) the extensional strain in the armchair (zigzag) direction. It is noted that the shear strain does not affect transmission and valley polarization. Furthermore, when we consider the smooth strain barrier, the valley-polarized transmission can be enhanced by increasing the smoothness of the strain barrier. We hope that our finding can shed new light on constructing graphene-based valleytronic and quantum computing devices by solely employing strain.

Effects of metallic electrodes on the thermoelectric properties of zigzag graphene nanoribbons with periodic vacancies

We theoretically analyze the thermoelectric properties of graphene quantum dot arrays (GQDAs) with line- or surface-contacted metal electrodes. Such GQDAs are realized as zigzag graphene nanoribbons (ZGNRs) with periodic vacancies. Gaps and minibands are formed in these GQDAs, which can have metallic and semiconducting phases. The electronic states of the first conduction (valence) miniband with nonlinear dispersion may have long coherent lengths along the zigzag edge direction. With line-contacted metal electrodes, the GQDAs have the characteristics of serially coupled quantum dots (SCQDs) if the armchair edge atoms of the ZGNRs are coupled to the electrodes. By contrast, the GQDAs have the characteristics of parallel quantum dots if the zigzag edge atoms are coupled to the electrodes. The maximum thermoelectric power factors of SCQDs with line-contacted electrodes of Cu, Au, Pt, Pd, or Ti at room temperature were similar or greater than 0.186 nW K^-1; their figures of merit were greater than three. GQDAs with line-contacted metal electrodes have much better thermoelectric performance than surface contacted metal electrodes.

Contact Effects on Thermoelectric Properties of Textured Graphene Nanoribbons

The transport and thermoelectric properties of finite textured graphene nanoribbons (t-GNRs) connected to electrodes with various coupling strengths are theoretically studied in the framework of the tight-binding model and Green's function approach. Due to quantum constriction induced by the indented edges, such t-GNRs behave as serially coupled graphene quantum dots (SGQDs). These types of SGQDs can be formed by tailoring zigzag GNRs (ZGNRs) or armchair GNRs (AGNRs). Their bandwidths and gaps can be engineered by varying the size of the quantum dot and the neck width at indented edges. Effects of defects and junction contact on the electrical conductance, Seebeck coefficient, and electron thermal conductance of t-GNRs are calculated. When a defect occurs in the interior site of textured ZGNRs (t-ZGNRs), the maximum power factor within the central gap or near the band edges is found to be insensitive to the defect scattering. Furthermore, we found that SGQDs formed by t-ZGNRs have significantly better electrical power outputs than those of textured ANGRs due to the improved functional shape of the transmission coefficient in t-ZGNRs. With a proper design of contact, the maximum power factor (figure of merit) of t-ZGNRs could reach 90% (95%) of the theoretical limit.

Driving interference control by side carbon chains in molecular and two-dimensional nano-constrictions

Interference pattern modulation by side carbon chains is a general phenomenon, which is demonstrated in a benzene molecular device, a zigzag graphene nanoribbon device and a SiC nanoribbon device.

Mechanically controlled quantum interference in graphene break junctions

The ability to detect and distinguish quantum interference signatures is important for both fundamental research and for the realization of devices such as electron resonators¹, interferometers² and interference-based spin filters³. Consistent with the principles of subwavelength optics, the wave nature of electrons can give rise to various types of interference effects⁴, such as Fabry-Pérot resonances⁵, Fano resonances⁶ and the Aharonov-Bohm effect⁷. Quantum interference conductance oscillations⁸ have, indeed, been predicted for multiwall carbon nanotube shuttles and telescopes, and arise from atomic-scale displacements between the inner and outer tubes^9,10. Previous theoretical work on graphene bilayers indicates that these systems may display similar interference features as a function of the relative position of the two sheets^11,12. Experimental verification is, however, still lacking. Graphene nanoconstrictions represent an ideal model system to study quantum transport phenomena^13-15 due to the electronic coherence¹⁶ and the transverse confinement of the carriers¹⁷. Here, we demonstrate the fabrication of bowtie-shaped nanoconstrictions with mechanically controlled break junctions made from a single layer of graphene. Their electrical conductance displays pronounced oscillations at room temperature, with amplitudes that modulate over an order of magnitude as a function of subnanometre displacements. Surprisingly, the oscillations exhibit a period larger than the graphene lattice constant. Charge-transport calculations show that the periodicity originates from a combination of the quantum interference and lattice commensuration effects of two graphene layers that slide across each other. Our results provide direct experimental observation of a Fabry-Pérot-like interference of electron waves that are partially reflected and/or transmitted at the edges of the graphene bilayer overlap region.

Valley Filtering and Electronic Optics Using Polycrystalline Graphene

In this Letter, both the manipulation of valley-polarized currents and the optical-like behaviors of Dirac fermions are theoretically explored in polycrystalline graphene. When strain is applied, the misorientation between two graphene domains separated by a grain boundary can result in a mismatch of their electronic structures. Such a discrepancy manifests itself in a strong breaking of the inversion symmetry, leading to perfect valley polarization in a wide range of transmission directions. In addition, these graphene domains act as different media for electron waves, offering the possibility to modulate and obtain negative refraction indexes.

Quantum Interference in Graphene Nanoconstrictions

We report quantum interference effects in the electrical conductance of chemical vapor deposited graphene nanoconstrictions fabricated using feedback controlled electroburning. The observed multimode Fabry-Pérot interferences can be attributed to reflections at potential steps inside the channel. Sharp antiresonance features with a Fano line shape are observed. Theoretical modeling reveals that these Fano resonances are due to localized states inside the constriction, which couple to the delocalized states that also give rise to the Fabry-Pérot interference patterns. This study provides new insight into the interplay between two fundamental forms of quantum interference in graphene nanoconstrictions.

The Talbot Effect for two-dimensional massless Dirac fermions

A monochromatic beam of wavelength λ transmitted through a periodic one-dimensional diffraction grating with lattice constant d will be spatially refocused at distances from the grating that are integer multiples of . This self-refocusing phenomena, commonly referred to as the Talbot effect, has been experimentally demonstrated in a variety of systems ranging from optical to matter waves. Theoretical predictions suggest that the Talbot effect should exist in the case of relativistic Dirac fermions with nonzero mass. However, the Talbot effect for massless Dirac fermions (mDfs), such as those found in monolayer graphene or in topological insulator surfaces, has not been previously investigated. In this work, the theory of the Talbot effect for two-dimensional mDfs is presented. It is shown that the Talbot effect for mDfs exists and that the probability density of the transmitted mDfs waves through a periodic one-dimensional array of localized scatterers is also refocused at integer multiples of z_T. However, due to the spinor nature of the mDfs, there are additional phase-shifts and amplitude modulations in the probability density that are most pronounced for waves at non-normal incidence to the scattering array.

Electron Interference in Ballistic Graphene Nanoconstrictions

We realize nanometer size constrictions in ballistic graphene nanoribbons grown on sidewalls of SiC mesa structures. The high quality of our devices allows the observation of a number of electronic quantum interference phenomena. The transmissions of Fabry-Perot-like resonances are probed by in situ transport measurements at various temperatures. The energies of the resonances are determined by the size of the constrictions, which can be controlled precisely using STM lithography. The temperature and size dependence of the measured conductances are in quantitative agreement with tight-binding calculations. The fact that these interference effects are visible even at room temperature makes the reported devices attractive as building blocks for future carbon based electronics.

Contact conductance of a graphene nanoribbon with its graphene nano-electrodes

Electronically contacted between two graphene nano-electrodes, the contact conductance (G0) of a graphene nanoribbon (GNR) molecular wire is calculated using mono-electronic Elastic Scattering Quantum Chemistry (ESQC) theory. Different nano-electrode contact geometries are considered ranging from a top face to face van der Waals contact to an adiabatic funnel like planar chemical bonding. The Tamm state contributions to the GNR-graphene nano-electrode electronic interactions are discussed as a function of the molecular orbital hybridization. Contrary to the common belief, the adiabatic-like triangle shaped contact nano-graphene electrode does not provide a large G0 as compared to the abrupt contact geometry. The abrupt contact geometry is even worth than a top face to face van der Waals electronic contact with a metal.

Correlating atomic structure and transport in suspended graphene nanoribbons

Graphene nanoribbons (GNRs) are promising candidates for next generation integrated circuit (IC) components; this fact motivates exploration of the relationship between crystallographic structure and transport of graphene patterned at IC-relevant length scales (<10 nm). We report on the controlled fabrication of pristine, freestanding GNRs with widths as small as 0.7 nm, paired with simultaneous lattice-resolution imaging and electrical transport characterization, all conducted within an aberration-corrected transmission electron microscope. Few-layer GNRs very frequently formed bonded-bilayers and were remarkably robust, sustaining currents in excess of 1.5 μA per carbon bond across a 5 atom-wide ribbon. We found that the intrinsic conductance of a sub-10 nm bonded bilayer GNR scaled with width as GBL(w) ≈ 3/4(e(2)/h)w, where w is the width in nanometers, while a monolayer GNR was roughly five times less conductive. Nanosculpted, crystalline monolayer GNRs exhibited armchair-terminated edges after current annealing, presenting a pathway for the controlled fabrication of semiconducting GNRs with known edge geometry. Finally, we report on simulations of quantum transport in GNRs that are in qualitative agreement with the observations.

Charge transport through graphene junctions with wetting metal leads

Graphene is believed to be an excellent candidate material for next-generation electronic devices. However, one needs to take into account the nontrivial effect of metal contacts in order to precisely control the charge injection and extraction processes. We have performed transport calculations for graphene junctions with wetting metal leads (metal leads that bind covalently to graphene) using nonequilibrium Green's functions and density functional theory. Quantitative information is provided on the increased resistance with respect to ideal contacts and on the statistics of current fluctuations. We find that charge transport through the studied two-terminal graphene junction with Ti contacts is pseudo-diffusive up to surprisingly high energies.

Chirality-assisted electronic cloaking of confined States in bilayer graphene

We show that the strong coupling of pseudospin orientation and charge carrier motion in bilayer graphene has a drastic effect on transport properties of ballistic p-n-p junctions. Electronic states with zero momentum parallel to the barrier are confined under it for one pseudospin orientation, whereas states with the opposite pseudospin tunnel through the junction totally uninfluenced by the presence of confined states. We demonstrate that the junction acts as a cloak for confined states, making them nearly invisible to electrons in the outer regions over a range of incidence angles. This behavior is manifested in the two-terminal conductance as transmission resonances with non-Lorentzian, singular peak shapes. The response of these phenomena to a weak magnetic field or electric-field-induced interlayer gap can serve as an experimental fingerprint of electronic cloaking.

Valley-dependent Brewster angles and Goos-Hänchen effect in strained graphene

We demonstrate theoretically how local strains in graphene can be tailored to generate a valley-polarized current. By suitable engineering of local strain profiles, we find that electrons in opposite valleys (K or K') show different Brewster-like angles and Goos-Hänchen shifts, exhibiting a close analogy with light propagating behavior. In a strain-induced waveguide, electrons in K and K' valleys have different group velocities, which can be used to construct a valley filter in graphene without the need for any external fields.

Electron transport and Goos-Hänchen shift in graphene with electric and magnetic barriers: optical analogy and band structure

Transport of massless Dirac fermions in graphene monolayers is analysed in the presence of a combination of singular magnetic barriers and applied electrostatic potential. Extending a recently proposed (Ghosh and Sharma 2009 J. Phys.: Condens. Matter 21 292204) analogy between the transmission of light through a medium with modulated refractive index and electron transmission in graphene through singular magnetic barriers to the present case, we find the addition of a scalar potential profoundly changes the transmission. We calculate the quantum version of the Goos-Hänchen shift that the electron wave suffers upon being totally reflected by such barriers. The combined electric and magnetic barriers substantially modify the band structure near the Dirac point. This affects transport near the Dirac point significantly and has important consequences for graphene-based electronics.

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

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

Anisotropy induced localization of pseudo-relativistic spin states in graphene double quantum wire structures

We study the single-particle properties of Dirac Fermions confined to a double quantum wire system based on graphene. We map out the spatial regions where electrons in a given subband display the largest occupation probability induced by spatial anisotropic effects associated to the interaction strength between the graphene wires and the substrate. Here, the graphene-substrate interaction is considered as an ad hoc parameter which destroys the zero-gap observed in the relativistic Dirac cone characteristic of graphene electronic energy dispersions. Furthermore, the results indicate that the character of quasi-extended spin states, viewed by multisubband probability density function, is highly sensitive to spatial asymmetries and to the graphene-substrate interaction strength.

Guided modes near the Dirac point in negative-zero-positive index metamaterial waveguide

Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), we make theoretical investigations of the guided modes in the NZPIM waveguide near the DP by using the graphical method. Due to the linear Dirac dispersion, the fundamental mode is absent when the angular frequency is smaller than the DP, while the behaviors of NZPIM waveguide are similar to the conventional dielectric waveguide when the angular frequency is larger than the DP. The unique properties of the guided modes are analogous to the propagation of electron waves in graphene waveguide [Appl. Phys. Lett., 94, 212105 (2009)], corresponding to the classical motion and the Klein tunneling. These results suggest that many exotic phenomena in graphene can be simulated by the relatively simple optical NZPIM.