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Abstract. The electronic properties of graphene may be changed from semimetallic to semiconducting by introducing perforations (antidots) in a periodic pattern. The properties of such graphene antidot lattices (GALs) have previously been studied using atomistic models, which are very time consuming for large structures. We present a continuum model that uses the Dirac equation (DE) to describe the electronic and optical properties of GALs. The advantages of the Dirac model are that the calculation time does not depend on the size of the structures and that the results are scalable. In addition, an approximation of the band gap using the DE is presented. The Dirac model is compared with nearest-neighbour tight-binding (TB) in order to assess its accuracy. Extended zigzag regions give rise to localized edge states, whereas armchair edges do not. We find that the Dirac model is in quantitative agreement with TB for GALs without edge states, but deviates for antidots with large zigzag regions.

Inspired by recent experimental realizations of monolayer Fe membranes in graphene perforations, we perform ab initio calculations of Fe monolayers and membranes embedded in graphene in order to assess their structural stability and magnetization. We demonstrate that monolayer Fe has a larger spin magnetization per atom than bulk Fe and that Fe membranes embedded in graphene exhibit spin magnetization comparable to monolayer Fe. We find that free-standing monolayer Fe is structurally more stable in a triangular lattice compared to both square and honeycomb lattices. This is contradictory to the experimental observation that the embedded Fe membranes form a square lattice. However, we find that embedded Fe membranes in graphene perforations can be more stable in the square lattice configuration compared to the triangular. In addition, we find that the square lattice has a lower edge formation energy, which means that the square Fe lattice may be favored during formation of the membrane.

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Selective and dynamically co-ordinated functional electrical stimulation (FES) of paralysed/paretic limbs in upper motor neuron lesioned people depends on optimal contact at the neural interface. Implanted nerve cuff electrodes may form a stable electrical neural interface, but may also inflict nerve damage. In this study the immediate and long-term effects of cuff implantation on the number and sizes of myelinated and unmyelinated axons have been evaluated with unbiased stereological techniques. Cuff electrodes were implanted in rabbit tibial nerves just below the knee joint, and the stereological analyses were carried out 2 weeks and 16 months after implantation. Myelinated axons were analysed at standardised levels proximal to, underneath, and distal to the cuff; unmyelinated axons underneath the cuff. A 27% loss of myelinated axons was found underneath and distal to the nerve cuff 2 weeks post surgery. All axonal sizes were equally lost except for the very smallest. At 16 months post surgery the number of myelinated axons was restored to control values at both levels. Except for the presence of regenerative sprouts at 2 weeks post surgery, no changes in the number or sizes of unmyelinated axons were revealed at either 2 weeks or 16 months post surgery. Our study demonstrates that implanted cuff electrodes may cause an initial loss of myelinated axons but with subsequent regeneration.