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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Tight-binding model of graphene - filling in a few steps

I'm trying to figure out the tight-binding model for graphene after not using any of my solid-state knowledge for a few years. I am getting lost in notation and I was hoping for some help filling in ...
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Inversion symmetry points of graphene

I have question about graphene. When you have the graphene lattice two types of atoms can be distinguished, let's call them type A and B.You can draw a unit cell that has the shape of a ...
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Drude Conductivity of Graphene

Use the Drude model to estimate the low temperature conductivity of a sheet of graphene, up to a dimensionless constant. (Assume the electron dispersion relation is $E(\mathbf{k})=\hbar ...
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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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Making a conductive paint out of graphite powder [closed]

I want to make a conductive paint out of graphite powder and gum to use as an electrode. What shall be the best gum to use, as i need a low resistance of around some kilo Ohms. I am getting very high ...
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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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Graphene - Can it produce a magnetic field?

So it's probably a quick no on this one, but since I haven't majored in physics or chemistry I have no idea if it's possible to make Graphene generate a magnetic field. Assuming power or current is ...
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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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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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Are Dirac points the norm for 2D band structure?

I've been doing simulations of band structure for 2D optical lattices, and something I've noticed is that, for sufficiently shallow lattices, there are typically points on the edge of the first ...
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What is the Fermi energy of (undoped) graphene?

All of the sources I have found for this online have been wildly unclear. Many use the phrase "Fermi energy" to refer to the "Fermi level" (which is emphatically not what I'm looking for; I want the ...
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Mechanical Exfoliation, Scotch Tape Method

I'd like to use the Scotch tape method, heavily used with graphene, to exfoliate some rare earth tellurite sample. I understand the process except for the last step. How do you transfer the sample ...
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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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Intervalley scattering in graphene in presence of impurities

A long range impurity like coulomb impurity does not induce an inter valley scattering between the two Dirac points. Is there any mathematical explanation for the same although this is explained by ...
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57 views

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} ...
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29 views

Derivation of polarizability

I am currently reading some papers on Dirac and Weyl physics on condensed matter. Very often, the following result for the polarizability is used: $$ \Pi(q,\omega) \propto \sum_{k,s,s'} ...
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29 views

Difficulty in dissolving scotch tape

The scotch tape peeling of graphene is the classical way to do it. But I am having difficulties in dissolving the scotch tape gum and it is giving noise in the Raman signal. How can I transfer the ...
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23 views

Understanding derivation of tight-binding model of graphene

I am trying to understand the derivation of the tight-binding model for graphene. In several papers I have come across on the subject, I see notation like that found in equation 4 here: ...
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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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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 ...
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How do I determine the stacking order of Bilayer Graphene from a Raman scan?

I have high-purity samples of exfoliated bilayer graphene on SiO2. I get raman scans with four clearly differentiated Lorentzians in the 2D peak. Similar to http://users.aalto.fi/~mtomi/jssfig2.png ...
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115 views

Density of states for graphene

I have seen a lot of plots for the density of states for graphene: but have been unable to find the calculation explicetely. I know the dispersion relation for graphene is $E_{\pm} (\textbf{k}) ...
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46 views

Eigenvalues of Hamiltonian with on-diagonal coordinate

A bit abstract, but if I take the standard graphene Hamiltonian (around the Dirac point) and introduce an on-diagonal term proportional to the coordinate $\hat{y}$, how would I find the eigenstates ...
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Wavefunction overlap in graphene

In calculation of the response functions of graphene we need to calculate the 4-point correlation function of the form : $$ \langle T \rho(q,\tau)\rho(-q,0)\rangle $$ The article I'm reading states ...
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Graphene is organic or inorganic material?

I have confusion about graphene, whether the material is organic or inorganic. I read that materials with carbon backbone and hydrogens attached (basically hydrocarbons), or materials of living ...
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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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51 views

Why are Brillouin zones for graphene and monolayers of transition metal dichalcogenides the same?

The geometrical model of graphene is the flat honeycomb lattice, so the Brillouin zone is also flat honeycomb lattice. However, monolayer of transition metal dichalcogenides is not flat as it consists ...
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Topological invariant in 1D

In 2D, with state $\psi(k_x, k_y)$, it is common to calculate measure of topology of material: 1 - Calculate Berry connection $a = -i <\psi | \partial_{\boldsymbol{k}} | \psi>$. 2 - Calculate ...
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2D materials with isotropic Dirac cones

The celebrated material graphene has electrons which can be described by the simple 2D Hamiltonian $H = v_F \left( \sigma_x p_x + \sigma_y p_y \right)$, where $v_F$ is a Fermi velocity. Silicene, ...
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How to plot graphene conductivity as a function of chemical potential and frequency

I want to plot Graphene Complex Conductivity as a function of two variables in Matlab.The variables are chemical potential and freqency, but I am not sure my code would be corect
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41 views

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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Matrix representation of a fermionic creation and annihilation operator in graphene nanoribbons?

From the other question Matrix representation for fermionic annihilation operator, what if we have to find the matrix representation for the operators $a_{\sigma}^{\dagger}(k,n)$ and $b_{\sigma}(k,n)$ ...
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257 views

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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How to measure the Fermi velocity in Dirac materials?

Suppose that one has a Dirac material (e.g., graphene), i.e., a system where there exists a number $N$ of identical Dirac cones (linear dispersion) at the Fermi energy $E_F=0$. How can one measure ...
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How to cut graphene?

How is graphene cut, given that it is similar in strength and hardness to diamond? I assume you cannot just take a pair of regular scissors to a sheet of it and cut out the shape you want?
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What exactly makes transmittance of graphene change from linear to exponential?

Up to 5 layers, the transmittance of graphene is linear (2.3% per layer): (source) Beyond 5 layers (I assume) the transmittance is exponential, following Beer–Lambert law. What gives rise to this ...
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cicumfernatial vector

Once a sheet of graphite is rolled up into a nanotube, the allowed values of k are constrained by the imposition of periodic boundary conditions along the circumferential direction. this periodic ...
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what is the theoretical reason behind the new paper, Highly tunable hybrid metamaterials employing split-ring resonators built using graphene?

A few days ago, a group of University of Exeter physicists published a paper titled: Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface ...
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Josephson junction exceeding the coherence length of the cooper pair

In this recent paper http://arxiv.org/abs/1504.03286, the authors present the data that they measured Fraunhofer-like diffraction pattern in a Josephson junction with graphene sandwiched between ...
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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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Symmetry arguments for valley physics in graphene with broken inversion

I am trying to understand this paper: http://link.aps.org/doi/10.1103/PhysRevLett.99.236809 (Here is an arXiv version: http://arxiv.org/abs/0709.1274) In the introduction, they mention certain ...
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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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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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Is there any conductive graphene with functional groups in markets or I have to modify graphene myself?

My thesis is a comparative study between 2 kind of nanocomposites based on graphene. We should use of graphene with and without functional groups and both should be electrical conductive. But I don't ...
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Why is graphene “gate tunable”?

I am reading Geim and Novoselov's classic paper on electrostatic doping of graphene: http://arxiv.org/abs/cond-mat/0410550 Three parts to the same broad question: 1) I am looking for some rigorous ...
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Classical - quantum analogy of Berry phase

I am reading this webpage about Berry phase: http://materia.fisica.unimi.it/manini/berryphase.html I am happily convinced about the first "elementary geometry" example they provide. Now I am trying ...
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Tuning the frequency in graphene

As is well known, the frequency of transverse optical phonons in single layer graphene ranges from $10^{11}$ to $10^{12}$ Hertz. How can one "tune" the frequency to a specific value?
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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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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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Why electron acts like massless when it's moving through graphene sheet? [duplicate]

It has been observed that when electron moves through graphene sheet,it shows a relativistic motion.why does that occurs?