Stephen R. Power

Emergence of local magnetic moments in doped graphene-related materials

Motivated by recent studies reporting the formation of localized magnetic moments in doped graphene, we investigate the energetic cost for spin polarizing isolated impurities embedded in this material. When a well-known criterion for the formation of local magnetic moments in metals is applied to graphene we are able to predict the existence of magnetic moments in cases that are in clear contrast to previously reported density-functional theory (DFT) results. When generalized to periodically repeated impurities, a geometry so commonly used in most DFT calculations, this criterion shows that the energy balance involved in such calculations contains unavoidable contributions from the long-ranged pairwise magnetic interactions between all impurities. This proves the fundamental inadequacy of the DFT assumption of independent unit cells in the case of magnetically doped low-dimensional graphene-based materials. We show that this can be circumvented if more than one impurity per unit cell is considered, in which case the DFT results agree perfectly well with the criterion-based predictions for the onset of localized magnetic moments in graphene. Furthermore, the existence of such a criterion determining whether or not a magnetic moment is likely to arise within graphene will be instrumental for predicting the ideal materials for future carbon-based spintronic applications.

Indirect Exchange and Ruderman-Kittel-Kasuya-Yosida (RKKY) Interactions in Magnetically-Doped Graphene

Magnetically-doped graphene systems are potential candidates for application in future spintronic devices. A key step is to understand the pairwise interactions between magnetic impurities embedded in graphene that are mediated by the graphene conduction electrons. A large number of studies have been undertaken to investigate the indirect exchange, or RKKY (Ruderman-Kittel-Kasuya-Yosida), interactions in graphene. Many of these studies report a decay rate faster than expected for a two-dimensional material and the absence of the usual distance dependent oscillations. In this review we summarize the techniques used to calculate the interaction and present the key results obtained to date. The effects of more detailed parameterisations of the magnetic impurities and graphene host are considered, as are results obtained from ab initio calculations. Since the fast decay of the interaction presents an obstacle to spintronic applications, we focus in particular on the possibility of augmenting the interaction range by a number of methods including doping, spin precession and the application of strain.

Dynamic RKKY interaction in graphene

The growing interest in carbon-based spintronics has stimulated a number of recent theoretical studies on the RKKY interaction in graphene, based on which the energetically favourable alignment between magnetic moments embedded in this material can be calculated. The general consensus is that the strength of the RKKY interaction in undoped graphene decays as 1/D 3 or faster, where D is the separation between magnetic moments. Such an unusually fast decay for a 2-dimensional system suggests that the RKKY interaction may be too short ranged to be experimentally observed in graphene. Here we show in a mathematically transparent form that a far more long ranged interaction arises when the magnetic moments are taken out of their equilibrium positions and set in motion. We not only show that this dynamic version of the RKKY interaction in graphene decays far more slowly but also propose how it can be observed with currently available experimental methods. PACS numbers:

Magnetization profile for impurities in graphene nanoribbons

The magnetic properties of graphene-related materials and in particular the spin-polarised edge states predicted for pristine graphene nanoribbons (GNRs) with certain edge geometries have received much attention recently due to a range of possible technological applications. However, the magnetic properties of pristine GNRs are not predicted to be particularly robust in the presence of edge disorder. In this work, we examine the magnetic properties of GNRs doped with transition-metal atoms using a combination of mean-field Hubbard and Density Functional Theory techniques. The effect of impurity location on the magnetic moment of such dopants in GNRs is investigated for the two principal GNR edge geometries - armchair and zigzag. Moment profiles are calculated across the width of the ribbon for both substitutional and adsorbed impurities and regular features are observed for zigzag-edged GNRs in particular. Unlike the case of edge-state induced magnetisation, the moments of magnetic impurities embedded in GNRs are found to be particularly stable in the presence of edge disorder. Our results suggest that the magnetic properties of transition-metal doped GNRs are far more robust than those with moments arising intrinsically due to edge geometry.

Electronic structure of graphene beyond the linear dispersion regime

Among the many interesting features displayed by graphene, one of the most attractive is the simplicity with which its electronic structure can be described. The study of its physical properties is significantly simplified by the linear dispersion relation of electrons in a narrow range around the Fermi level. Unfortunately, the mathematical simplicity of graphene electrons is only limited to this narrow energy region and is useless when dealing with problems that involve energies outside the linear dispersion part of the spectrum. In this letter we remedy this limitation by deriving a set of closed-form analytical expressions for the real-space single-electron Green function of graphene which are valid across an enormous fraction of the energy spectrum. By extending to a wider energy range the simplicity with which graphene electrons are described, it is now possible to derive more mathematically transparent and insightful expressions for a number of physical properties that involve higher energy scales. The power of this new formalism is illustrated in the case of the magnetic (RKKY) interaction in graphene.

Graphene on graphene antidot lattices: Electronic and transport properties

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 dispersing bands (with a high concomitant mobility), which nevertheless can be made gapped with the perpendicular field. We analyze the electronic structure and transport properties of various types of GOALs, and draw general conclusions about their properties to aid their design in experiments.

Electronic transport in disordered graphene antidot lattice devices

Nanostructuring of graphene is in part motivated by the requirement to open a gap in the electronic band structure. In particular, a periodically perforated graphene sheet in the form of an antidot lattice may have such a gap. Such systems have been investigated with a view towards application in transistor or waveguiding devices. The desired properties have been predicted for atomically precise systems, but fabrication methods will introduce significant levels of disorder in the shape, position and edge configurations of individual antidots. We calculate the electronic transport properties of a wide range of finite graphene antidot devices to determine the effect of such disorders on their performance. Modest geometric disorder is seen to have a detrimental effect on devices containing small, tightly packed antidots, which have optimal performance in pristine lattices. Larger antidots display a range of effects which strongly depend on their edge geometry. Antidot systems with armchair edges are seen to have a far more robust transport gap than those composed from zigzag or mixed edge antidots. The role of disorder in waveguide geometries is slightly different and can enhance performance by extending the energy range over which waveguiding behavior is observed.

Theoretical analysis of a dual-probe scanning tunneling microscope setup on graphene.

Experimental advances allow for the inclusion of multiple probes to measure the transport properties of a sample surface. We develop a theory of dual-probe scanning tunneling microscopy using a Greens function formalism, and apply it to graphene. Sampling the local conduction properties at finite length scales yields real space conductance maps which show anisotropy for pristine graphene systems and quantum interference effects in the presence of isolated impurities. Spectral signatures in the Fourier transforms of real space conductance maps include characteristics that can be related to different scattering processes. We compute the conductance maps of graphene systems with different edge geometries or height fluctuations to determine the effects of nonideal graphene samples on dual-probe measurements.

RKKY interaction between adsorbed magnetic impurities in graphene: Symmetry and strain effects

The growing interest in carbon-based spintronics has stimulated a number of recent theoretical studies on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in graphene, with the aim of determining the most energetically favorable alignments between embedded magnetic moments. The RKKY interaction in undoped graphene decays faster than expected for conventional two-dimensional materials, and recent studies suggest that the adsorption configurations favored by many transition-metal impurities may lead to even shorter-ranged decays and possible sign-changing oscillations. Here, we show that these features emerge in a mathematically transparentmannerwhenthesymmetryoftheconfigurationsisincludedinthecalculation.Furthermore,weshow that by breaking the symmetry of the graphene lattice, via uniaxial strain, the decay rate, and hence the range, of the RKKY interaction can be significantly altered. Our results suggest that magnetic interactions between adsorbed impurities in graphene can be manipulated by careful strain engineering of such systems.

Friedel oscillations in graphene: Sublattice asymmetry in doping

Symmetry breaking perturbations in an electronically conducting medium are known to produce Friedel oscillations (FOs) in various physical quantities of an otherwise pristine material. Here we show in a mathematically transparent fashion that FOs in graphene have a strong sublattice asymmetry. As a result, the presence of impurities and/or defects may impact the distinct graphene sublattices very differently. Furthermore, such an asymmetry an be used to explain the recent observations that Nitrogen atoms and dimers are not randomly distributed in graphene but prefer to occupy one of its two distinct sublattices. We argue that this feature is not exclusive of Nitrogen and that it can be seen with other substitutional dopants.