Graphene is a quasi-2D material formed by carbon atoms in a hexagonal lattice. Graphene-based materials are of great interest for Nanoscience and Nanotechnology, mainly for Nanoelectronics.

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How is graphene a 2D substance?

How is graphene a 2D substance? It has length, width and some thickness to it, else it would be invisible. Why is it considered a 2D substance?
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Graphene and Klein bottle?

I am trying to understand graphene as a topological insulator. The spin orbital interaction in graphene is very small (~10mK?). But if we consider that, then graphene should be a topological ...
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How do Dirac fermions arise in graphene, and, what significance (if any) does this have for high-energy physics?

Graphene has a honeycomb lattice (in the absence of defects and impurities). By considering the low-energy limit of the half-filled Hubbard model used to model the strongly interacting electron gas we ...
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Could you help me understand this paper (PRL 106:136806)?

I'm struggling to understand the paper PRL 106:136806 (2011). It is highly cited, but I cannot reproduce their results. Let me quickly summarize the authors' argument and raise my questions. It is ...
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Graphene as optical and UV mirrors

One usually hears about graphene as a good thermal conductor, and good light absorber due to its tunable bandgap properties. But i haven't heard about its aplicability as an optical mirror. In fact, ...
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Why do electrons in graphene behave as Dirac fermions near the Dirac points?

I've been learning about graphene, and I recently calculated the band structure for it using a nearest-neighbor tight-binding model for the $\pi$ electrons: $$\varepsilon(\vec k)=\pm t\sqrt{3+2 \cos \...
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Why is Graphene Transparent?

Graphene is always in the news now a days and its key features are that it is; very strong, conductive and transparent. It is so transparent that each layer of graphene will only absorb 2% of Light ...
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Graphene +1 extra carbon bond

I'm not a physicist just a curious mind, so please go easy! I was just watching a BBC Horizon Documentary that featured a piece on the recently discovered material Graphene. One of the facts ...
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Material implementations of the holographic principle

I'm afraid this question is a little too open-ended, but bear with me while I find a better formulation. carbon allotropes (like fullerenes and graphene) are regular patterned. Conduction bands of ...
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What type of solar energy technology has the most future potential?

In terms of dollars per watt, using theoretical efficiency limits, what technology holds the most promise to become the primary solar energy capture technology? My hunch is carbon-based modules, ...
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How to derive electron number equation of Bogoliubov Hamiltonian using thermodynamic relations.

My question arise from this article: Edge superconducting correlation in the attractive-U Kane-Mele-Hubbard model. I will describe my question in detail so that you might not need to look into that ...
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Why does the n=0 Landau level in graphene have half the degeneracy of the other levels?

I've looked through several papers that talk about the anomalous integer quantum Hall effect of graphene (such as http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.95.146801), and they all state ...
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Graphene Moebius Strip

I'm refering to the Paper: PHYSICAL REVIEW B 80, 195310 (2009) "Möbius graphene strip as a topological insulator" Z. L. Guo, Z. R. Gong, H. Dong, and C. P. Sun. The paper is also available as a ...
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Tight Binding Model in Graphene

I'm following a calculation done by a guy who's done it a bit different than what I've done before (used nearest neighbour vectors and a DFT instead of what I will show below), I'm not quite sure how ...
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227 views

Lattice geometry and dispersion relation

Is there a general theorem which gives some information about which influence have the lattice geometry (for example sub-lattice structure, square lattice, honeycomb lattice, lattice symmetries, ...) ...
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609 views

effective theory of graphene

This is a question about deriving effective mass theory for graphene. For the two sub-lattice atoms, the wave equation can be written as the massless Dirac equation: $ \displaystyle -i\hbar v_F \...
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What is the boundary condition of graphene flake with zigzag edges?

It is a question about free carrier behavior in graphene flakes. (or may be called charge confinement) Say if we have a perfect hexagonal free standing graphene flake terminated with zigzag edges. ...
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Superconductivity in graphene with spin orbital coupling, is it proper to let the order parameter on two sub-lattice equal?

I am reading this article: Edge superconducting correlation in the attractive-U Kane-Mele-Hubbard model. Considering just the first part of the article, where a negative-U Hubbard model with the ...
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Significance of Dirac cones in condensed matter physics

In condensed matter physics, Dirac cones can be found in graphene, topological insulators, cuprates, and iron-pnictides. This means that electrons behave as massless particles near the Dirac points. ...
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Why electrons are relativistic in Graphene and non relativistic in vacuum?

If a free region in space has a potential difference of one volt, an electron in this region will acquire kinetic energy of 1 eV. Its speed will be much smaller than the speed of light hence it will ...
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Graphene space elevator possible?

I just read this story on MIT working on industrial scale, km^2 sheet production of graphene. A quick check of Wikipedia on graphene and Wikipedia on space elevator tells me Measurements have ...
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How to write BdG Hamiltonian in graphene?

In Beenakker's paper:Specular Andreev Reflection in Graphene, the BdG Hamiltonian is written as: $$ H_{BdG}=\begin{pmatrix}H-E_F&\Delta\\ \Delta^*& E_F-H\end{pmatrix} $$ from equation (1). ...
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Commercial large scale production of graphene

I am a third year undergraduate Physics student, and for my solid state physics course I am asked to give a short (10 minute) qualitative presentation on the current standings of graphene production, ...
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How can one confirm creation of magnetic graphene?

Recently my high school physics teacher contacted me looking for an expert to ask about this situation. I am paraphrasing his correspondence below: I just had a a student accidentally create ...
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How to generalize BdG equation in order to match a graphene with a metal superconductor?

I want to generalize BdG equation in order to compute the conductance of a junction of graphene with a metal superconductor. The previous works done until now on this hetrojunction is devotted to use ...
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Density of states and elliptic integral

It is known, for example Equation (14) in the graphene review of Castro Neto (arXiv), that the full expression for the density of states (DOS) of graphene is in terms of an elliptic integral. Close ...
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Kane and Mele's argument on the existence of edge states in quantum spin Hall effect of graphene

Borrowing from Laughlin's argument on quantum Hall effect, Kane and Mele argued why there must be edge states in graphene with spin-orbit coupling in one paragraph, which is above the one with ...
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Why is Graphene So Strong?

There has been a lot of news about Graphene since its discovery in 2004. And as we are all told it is a revolutionary material which is very strong, conductive and transparent. But what is it about ...
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What limits the maximum attainable Fermi Energy for a material experimentally?

Either through doping or gating. What are some good terms to search for if I'm looking for some experimentally obtained values for particular materials? I'm particularly interested in what the limit ...
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Current operator in continuum model of graphene

For the graphene hamiltonian with NNN hopping, the wavefunctions are of the form: $(\psi_A ,\psi_B)^T$. The current from A(i) to B(j) site in the lattice model is given by: \begin{equation} J_{ij}=\...
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Relation between Berry phase and degeneracies, the example of Hall effect in graphene

In principle, the Berry-curvature can be related to the degeneracy of some underlying energy levels, using the adiabatic picture and expanding the Berry's expression in the language of instantaneous ...
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What does a bucked honeycomb lattice mean?

I was going through some literature where they have mention about bucked honeycomb lattice, but I was unable to understand about the bucked honeycomb term.
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Why does graphene exist?

I started to read some articles on graphene and almost all say that graphene was discovered late because physicists thought it would be unstable. Despite this, I didn't found a clear explanation of ...
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Exact diagonalization of graphene's tight binding Hamiltonian

While directly diagonalize graphene's tight binding Hamiltonian, which is numerical. We have to use a finite-sized graphene. So how to deal with boundary conditions? The usual solutions are zigzag or ...
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Are there measurable quantities which directly depends on the Fermi velocity?

The dispersion relation of electrons in, for example, graphene exhibits Dirac cones. The dispersion relation of a Dirac point at $\mathbf{k}=\mathbf{K}$ is linear in the momentum magnitude: $$E=\pm ...
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How to show time reversal symmetry does not break in the tight binding Hamiltonian for the honeycomb lattice?

The Hamiltonian of the honeycomb lattice is $$ H=\sum_{k\sigma}t(k) a_{k\sigma}^\dagger b_{k\sigma}+h.c $$ Where $t(-k)=t^*(k)$. If we do a time reversal transformation(according the answer to this ...
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What is making these subatomic honeycomb shapes and gaps in this graphene image?

I just read yet another graphene discovery and saw this STM image: Nice photo, it begs two questions: What is that secondary honeycomb structure, the one about 20x smaller than the atoms ...
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Easy to do experiments that clearly show outstanding properties of graphene

By chance we received for free some monolayer graphene sheets (20 cm x 20 cm) and mixed coper-graphene wires at our University. I would like to prepare some very easy to do experiments for the ...
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Thomas-Fermi approximation and the dielectric function (+ small bit on graphene)

1) With the dielectric function, which is a function of wavenumber and frequency,how is it possible to take the limit of either to zero without changing the other one? I thought that frequency and ...
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What's an efficient way to produce graphite on TEM-Grids?

I am trying to produce graphene with few layers(<10) on a TEM-Grid. Until now I've been trying this with the scotch-tape-method with slight modifications. Unfortunately it requires a lot of time ...
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What does a sheet of graphene look like?

What does a sheet of graphene look like? At one atom thick, is it visible to the naked eye? Can it be handled (by hand) with being torn? Can it be felt at all? [Assuming a large enough sheet ...
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What is the mechanism for graphene to conduct so well?

If metals have always been the best conductors, what is it about graphene that makes it such a good conductor in the plane? Specifically, in the metals silver is better than copper. I always assumed ...
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Graphene with a disclination and the spin-orbit coupling

I am trying to follow the methods used in this paper (http://arxiv.org/pdf/1208.3023.pdf) to construct the Hamiltonian of a graphene cone, but taking into account the spin-orbit coupling. The paper ...
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Does graphene actually remain strong for macroworld engineering?

I heard that people envision strong structural materials made out of graphene, but I heard it may weaken when being stack in layers. Is graphene viable for macroworld structural engineering or is it ...
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Berry phase in 1D materials

The Berry phase $\phi_B$ is the phase that an eigenstate acquires after its momentum vector goes around a circle at constant energy around the Dirac point. It is defined as $\phi_B = -i \int \langle\...
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Measurements for thermal diffusivity of graphene?

We have known for a long time that graphene has in-plane thermal conductivity ranging between 2000 and 4000 $W m^{-1} K^{-1}$. But in order to model heat transport on a sheet of graphene, we need more ...
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It would take an elephant, balanced on a pencil, to break through a sheet of graphene the thickness of Cling Film

I'm currently doing some work on a presentation about graphene, and have come across numerous articles which claim something along the lines of It would take an elephant, balanced on a pencil, to ...
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What is the approximate electrical conductivity $\sigma$ of graphene in S/m or S/cm?

I am trying to find an approximate value of the electrical conductivity $\sigma$ of graphene in units of S/m or S/cm. This table on Wikipedia gives $\sigma$ values for a variety of materials (...
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Why a mono-atomic crystal layer (2D) can't be stable?

According to Peierls and Landau, 2D crystals were thermodynamically unstable. They can't exist! Of course, this theory was disapproved in 2004 (example: graphene). What is the general definition of ...
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Effective Mass and Fermi Velocity of Electrons in Graphene:

In graphene, we have (in the low energy limit) the linear energy-momentum dispersion relation: $E=\hbar v_{\rm{F}}|k|$. This expression arises from a tight-binding model, in fact $E =\frac{3\hbar ta}{...