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Register a new userCoherent control of current injection in zigzag graphene nanoribbons
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We present Fermis golden rule calculations of the optical carrier injection and the coherent control of current injection in graphene nanoribbons with zigzag geometry, using an envelope function approach. This system possesses strongly localized states (flat bands) with a large joint density of states at low photon energies; for ribbons with widths above a few tens of nanometers, this system also posses large number of (non-flat) states with maxima and minima close to the Fermi level. Consequently, even with small dopings the occupation of these localized states can be significantly altered. In this work, we calculate the relevant quantities for coherent control at different chemical potentials, showing the sensitivity of this system to the occupation of the edge states. We consider coherent control scenarios arising from the interference of one-photon absorption at $2hbaromega$ with two-photon absorption at $hbaromega$, and those arising from the interference of one-photon absorption at $hbaromega$ with stimulated electronic Raman scattering (virtual absorption at $2hbaromega$ followed by emission at $hbaromega$). Although at large photon energies these processes follow an energy-dependence similar to that of 2D graphene, the zigzag nanoribbons exhibit a richer structure at low photon energies, arising from divergences of the joint density of states and from resonant absorption processes, which can be strongly modified by doping. As a figure of merit for the injected carrier currents, we calculate the resulting swarm velocities. Finally, we provide estimates for the limits of validity of our model.
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We theoretically investigate the one-color injection currents and shift currents in zigzag graphene nanoribbons with applying a static electric field across the ribbon, which breaks the inversion symmetry to generate nonzero second order optical responses by dipole interaction. These two types of currents can be separately excited by specific light polarization, circularly polarized lights for injection currents and linearly polarized lights for shift currents. Based on a tight binding model formed by carbon 2p$_z$ orbitals, we numerically calculate the spectra of injection coefficients and shift conductivities, as well as their dependence on the static field strength and ribbon width. The spectra show many peaks associated with the optical transition between different subbands, and the positions and amplitudes of these peaks can be effectively controlled by the static electric field. By constructing a simple two band model, the static electric fields are found to modify the edge states in a nonperturbative way, and their associated optical transitions dominate the current generation at low photon energies. For typical parameters, such as a static field 10$^6$ V/m and light intensity 0.1 GW/cm$^2$, the magnitude of the injection and shift currents for a ribbon with width 5 nm can be as large as the order of 1 $mu$A. Our results provide a physical basis for realizing passive optoelectronic devices based on graphene nanoribbons.
Graphene-based nanostructures exhibit a vast range of exciting electronic properties that are absent in extended graphene. For example, quantum confinement in carbon nanotubes and armchair graphene nanoribbons (AGNRs) leads to the opening of substantial electronic band gaps that are directly linked to their structural boundary conditions. Even more intriguing are nanostructures with zigzag edges, which are expected to host spin-polarized electronic edge states and can thus serve as key elements for graphene-based spintronics. The most prominent example is zigzag graphene nanoribbons (ZGNRs) for which the edge states are predicted to couple ferromagnetically along the edge and antiferromagnetically between them. So far, a direct observation of the spin-polarized edge states for specifically designed and controlled zigzag edge topologies has not been achieved. This is mainly due to the limited precision of current top-down approaches, which results in poorly defined edge structures. Bottom-up fabrication approaches, on the other hand, were so far only successfully applied to the growth of AGNRs and related structures. Here, we describe the successful bottom-up synthesis of ZGNRs, which are fabricated by the surface-assisted colligation and cyclodehydrogenation of specifically designed precursor monomers including carbon groups that yield atomically precise zigzag edges. Using scanning tunnelling spectroscopy we prove the existence of edge-localized states with large energy splittings. We expect that the availability of ZGNRs will finally allow the characterization of their predicted spin-related properties such as spin confinement and filtering, and ultimately add the spin degree of freedom to graphene-based circuitry.
The influence of periodic edge vacancies and antidot arrays on the thermoelectric properties of zigzag graphene nanoribbons is investigated. Using the Greens function method, the tight-binding approximation for the electron Hamiltonian and the 4th nearest neighbor approximation for the phonon dynamical matrix, we calculate the Seebeck coefficient and the thermoelectric figure of merit. It is found that, at a certain periodic arrangement of vacancies on both edges of zigzag nanoribbon, a finite band gap opens and almost twofold degenerate energy levels appear. As a result, a marked increase in the Seebeck coefficient takes place. It is shown that an additional enhancement of the thermoelectric figure of merit can be achieved by a combination of periodic edge defects with an antidot array.
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 interface solitons rather than setting them in the conduction band.
We present an analytical tight-binding theory of the optical properties of graphene nanoribbons with zigzag edges. Applying the transfer matrix technique to the nearest-neighbor tight-binding Hamiltonian, we derive analytical expressions for electron wave functions and optical transition matrix elements for incident light polarized along the structure axis. It follows from the obtained results that optical selection rules result from the wave function parity factor $(-1)^J$, where $J$ is the band number. These selection rules are that $Delta J$ is odd for transitions between valence and conduction subbands and that $Delta J$ is even for transitions between only valence (conduction) subbands. Although these selection rules are different from those in armchair carbon nanotubes, there is a hidden correlation between absorption spectra of the two structures that should allow one to use them interchangeably in some applications. The correlation originates from the fact that van Hove singularities in the tubes are centered between those in the ribbons if the ribbon width is about a half of the tube circumference. The analysis of the matrix elements dependence on the electron wave vector for narrow ribbons shows a smooth non-singular behavior at the Dirac points and the points where the bulk states meet the edge states.
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