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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Derivation of effective mass equation in carbon nanotubes

I am trying to reproduce the calculations in the paper here by Ando and Nakanishi and am already stuck on equation 1. It is stated that in the vicinity of $\epsilon=0$ the amplitude of the ...
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What's the conductivity of graphene nanostructres (nanoribbon, nanomesh)?

As we know, the conductivity of graphene can be expressed with Kubo formula,including intra transition and inter transition. But does graphene nanoribbon or graphene nanomesh have the same ...
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Graphene sheet resistance compared

I am trying to understand how the sheet resistance would vary between a suspended sheet of graphene and a sheet of graphene on an insulating substrate (say SiO2). I am not looking for a law telling me ...
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Klein tunneling in graphene including intervalley scattering

In calculations relating to Klein tunneling (in particular in graphene) I have seen the treatment of a "smooth" potential (on the scale of the Fermi wavelength) or the more typical treatment of a ...
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Relation between interlayer tunneling amplitude and external potential in Bilayer graphene

What is the relation between interlayer tunneling amplitude ($\gamma_1$) and external potential applied ($U_{ext}$)? Is there any mathematical relation?
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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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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 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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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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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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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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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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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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42 views

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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1answer
30 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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33 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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83 views

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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99 views

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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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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25 views

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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1answer
182 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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204 views

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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65 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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129 views

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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73 views

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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42 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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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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28 views

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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173 views

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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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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120 views

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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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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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?
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Electrons in graphene will behave as in 2D space?

Will electrons in graphene behave as in pure 2D space, that is they interact with eachother by a Coulomb potential ~ $\ln r$ instead of $1/r$? I think many force lines will "leak" out of graphene ...
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134 views

What is continuum limit (low energy limit) in condense matter physics?

In condensed matter theory, I can sometimes encounter such a term as continuum limit, also known as low energy limit. I have a question about this term, let me illustrate my question through an ...
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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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why do edge states in Graphene exist between the Valence and Conduction band?

I read in a review that there are 2 Dirac points in graphene, where the conduction band and valence band touch each other. Near these points electrons obey a linear dispersion relation. Breaking of ...
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107 views

What color does graphene glow when heated?

If you heat graphene hot enough, what color would it glow? Is the color within the visible range?
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249 views

How to calculate the dispersion relation of graphene?

Graphene is a well investigated two-dimensional material in nano-physics. My teacher asked me to calculate its phonon dispersion with interactions between the first and second nearest neighbors, both ...