In this review, recent developments in the fabrication and understanding of the electronic properties of graphene nanostructures are discussed. After a brief overview of the structure of graphene and the two-dimensional transport properties, the focus is put on graphene constrictions, quantum dots and double quantum dots. For constrictions with a width below 100 nm, the current through the constriction is strongly suppressed for a certain back gate voltage range, related to the so-called transport gap. This transport gap is due to the formation of localized puddles in the constriction, and its size depends strongly on the constriction width. Such constrictions can be used to confine charge carriers in quantum dots, leading to Coulomb blockade effects.

Adopting a purely two-dimensional relativistic equation for graphene's carriers contradicts the Heisenberg uncertainty principle since it requires setting the off-the-surface coordinate of a three-dimensional wavefunction to zero. Here we present a theoretical framework for describing graphene's massless relativistic carriers in accordance with this most fundamental of all quantum principles. A gradual confining procedure is used to restrict the dynamics onto a surface and normal to the surface parts, and in the process the embedding of this surface into the three-dimensional world is accounted for. As a result an invariant geometric potential arises in the surface part which scales linearly with the mean curvature and shifts the Fermi energy of the material proportional to bending. Strain induced modification of the electronic properties or 'straintronics' is clearly an important field of study in graphene. This opens an avenue to producing electronic devices: micro- and nano-el...

Ferroelectric switching in BiFeO ₃ multiferroic thin films was studied by piezoresponse force microscopy, as a function of the tip voltage and sweep direction, for samples with two different intrinsic domain structures. In all films, the switched polarization direction follows the in-plane and out-of-plane components of the highly inhomogeneous electric field applied by the microscope tip. In films with 'bubble-like' intrinsic domains, we observed in-plane switching assisted by out-of-plane switching for lower voltage values, and independent in-plane and out-of-plane switching for higher voltages, in both cases allowing full control of the ferroelectric polarization depending on the tip voltage polarity and sweep direction. In films with 'stripe-like' intrinsic domains, independent in-plane and out-of-plane switching was observed, but unswitched stripe domains prevented full control of the ferroelectric polarization over large areas. We correlate the observed switching ...

We review the recent experimental findings concerning the magnetic and magnetoelectric excitations in multiferroic manganites with special focus on orthorhombic RMnO ₃ (R = rare earth). The dynamics of these materials has attracted special attention recently due to the existence of novel magnetoelectric excitations which were termed electromagnons. In addition to the strong electric activity of the electromagnons, a series of other excitations of magnetic and magnetoelectric nature is observed in the same frequency range as the electromagnons. We summarize the systematics of the existing modes and the current understanding of the underlying mechanisms.

A 2.5 monolayer (ML) thick graphene film grown by chemical vapor deposition of thermally dissociated C ₂H ₄ on MgO(111), displays a significant band gap. The apparent six-fold low energy electron diffraction (LEED) pattern actually consists of two three-fold patterns with different 'A' and 'B' site diffraction intensities. Similar effects are observed for the LEED patterns of a 1 ML carbon film derived from annealing adventitious carbon on MgO(111), and for a 1.5 ML thick graphene film grown by sputter deposition on the 1 ML film. The LEED data indicate different electron densities at the A and B sites of the graphene lattice, suggesting that the observed band gap results from lifting the graphene HOMO/LUMO degeneracy at the Dirac point. The data also indicate that disparities in A site/B site LEED intensities decrease with increasing carbon overlayer thickness, suggesting that the graphene band gap size decreases with increasing number of graphene layers on M...

It is essential to know the arrangement of the atoms in a material in order to compute and understand its properties. Searching for stable structures of materials using first-principles electronic structure methods, such as density-functional-theory (DFT), is a rapidly growing field. Here we describe our simple, elegant and powerful approach to searching for structures with DFT, which we call ab initio random structure searching (AIRSS). Applications to discovering the structures of solids, point defects, surfaces, and clusters are reviewed. New results for iron clusters on graphene, silicon clusters, polymeric nitrogen, hydrogen-rich lithium hydrides, and boron are presented.