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The geometry of two-dimensional crystalline membranes dictates their mechanical, electronic and chemical properties. The local geometry of a surface is determined from the two invariants of the metric and the curvature tensors. Here we…
In this document we explore graphene, a two-dimensional material with remarkable properties. We center our discussion around its electronic characteristics and their applications. We begin by giving a simple electronic model which will then…
We introduce effective field theories for the electronic properties of graphene in terms of relativistic fermions propagating in 2+1 dimensions, and outline how strong inter-electron interactions may be modelled by numerical simulation of a…
The effect of screening of the coulomb interaction between two layers of two-dimensional electrons, such as in graphene, by a highly doped semiconducting substrate is investigated. We employ the random-phase approximation to calculate the…
One of the most interesting aspects of graphene is the tied relation between structural and electronic properties. The observation of ripples in the graphene samples both free standing and on a substrate has given rise to a very active…
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…
Electron transport in graphene is along the sheet but junction devices are often made by stacking different sheets together in a "side-contact" geometry which causes the current to flow perpendicular to the sheets within the device. Such…
We analyze the role of boundary geometry in viscous electronic hydrodynamics. We address the twin questions of how boundary geometry impacts flow profiles, and how one can engineer boundary conditions -- in particular the effective slip…
Spatial separation of electrons and holes in graphene gives rise to existence of plasmon waves confined to the boundary region. Theory of such guided plasmon modes within hydrodynamics of electron-hole liquid is developed. For plasmon…
In graphene, where the electron-electron scattering is dominant, electrons collectively act as a fluid. This hydrodynamic behaviour of charge carriers leads to exciting nonlinear phenomena such as solitary waves and shocks, among others. In…
Graphene has attracted significant interest both for exploring fundamental science and for a wide range of technological applications. Chemical vapor deposition (CVD) is currently the only working approach to grow graphene at wafer scale,…
We consider graphs made of one-dimensional wires connected at vertices, and on which may live a scalar potential. We are interested in a scattering situation where such a network is connected to infinite leads. We study the correlations of…
The electronic structure, bonding and magnetism in graphene containing vacancies are studied using density-functional methods. The single-vacancy graphene ground state is spin polarized and structurally flat. The unpolarized state is non…
Edge states in biased bilayer graphene in a magnetic field are studied within the four-band continuum model. The analysis is done for the semi-infinite graphene plane and for the graphene ribbon of a finite width, in the cases of zigzag and…
The computational research that will be presented compares the coherent states of multiple layer graphene versus the coherent states of lithium ions diffused within this multilayer graphene. Unlike the prevailing research on graphene…
With the unique possibilities for controlling light in nanoscale devices, graphene plasmonics has opened new perspectives to the nanophotonics community with potential applications in metamaterials, modulators, photodetectors, and sensors.…
The electrical potential on the surface of $\sim 300$ nm thick SiO$_2$ grown on single crystalline Si substrates has been characterized at ambient conditions using electric field microscopy. Our results show an inhomogeneous potential…
The carriers in graphene tuned close to the Dirac point envisage signatures of the strongly interacting fluid and are subject to hydrodynamic description. The important question is whether strong disorder induces the metal-insulator…
We introduce a different perspective describing electron-phonon interactions in graphene based on curved space hydrodynamics. Interactions of phonons with charge carriers increase the electrical resistivity of the material. Our approach…
A variational technique is used to derive analytical expressions for the sensitivity of several geometric indicators of flow separation to steady actuation. Considering the boundary layer flow above a wall-mounted bump, the six following…