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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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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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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Is graphene on a sticky tape strong enough to compete with my hand stretching it?

As we know we can make graphene using sticky tape so after we make graphene on a sticky tape will that thin sheet of graphene on a sticky tape be strong enough to compete with my hand trying to ...
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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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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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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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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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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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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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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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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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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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Is a “supercritical charge” in graphene similar to Hawking Radiation?

These papers describe a phenomenon referred to as "atomic collapse" and "supercritical charge" in graphene: Wang et al., Pereira et al. "Atomic collapse" appears when you have a large enough Coulomb ...
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A question about Dirac operator

The Dirac operator at 2 dimension can be written as $$ D=\sum_{k=1,2}\sigma^{k}D_{k}=\left( \begin{array}{cc} 0 & \partial_{x}-i\partial_{y}-i(A_x-iA_y)\\ ...
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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 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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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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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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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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Importance of thickness of SiO2-substrate for observing graphene's monolayer

I've discovered that one should use 300-nm-thick SiO2 substrate in order to effectively observe graphene's monolayer through optical microscope. If thickness differs even by 5%, i.e. 315 nm, then ...
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Why graphene's substrate is important

I just have some feelings that somehow it is important what specific subtrate is used to grow graphene monolayer on. Some substrates are better, another ones are not so good. But I cannot completely ...
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Why do we use the massive dirac fermion model for MoS2?

I can derive the massive Dirac fermion Hamiltonian using a tight binding model of graphene with a staggered sublattice potential, but many (including Xiao et al, PRL 2012) use this model for MoS2 as ...
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How come graphene is considered to have two valleys?

The typical graphene band-structure is a double-cone (in opposite directions to each other) with Dirac point in the middle. I assume the bottom cone is like the valence band, while the top cone is ...
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Deriving Graphene energy dispersion in tight binding model

I'm trying to get into graphene, in detail, I try to derive the elec. energy dispersion. Sadly, I am not that familiar with condensed matter QM by now, so I got some basic questions and I hope to find ...
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Why doesn't Graphene have a band gap?

Is there any simple justification about graphene having no band gap? How bout its linear E-K? Why bilayer graphene has a quadratic E-K and electric field can open a band gap there? I do not ...
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Why is low resistance beneficial to ion exchange membranes?

http://scitation.aip.org/content/aip/journal/jcp/139/11/10.1063/1.4821161 The article states that the graphene filter has a much lower electrical resistance than existing ion exchange membranes, ...
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Graphene Chern number for Dirac nodes

Why do we add winding number at two Dirac nodes to determine topological phase?
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Symmetry argument about degeneracy of graphene energy band at Dirac point

This question is very related to the thread here. In the answer given by @BebopButUnsteady , the statement is that as long as the inversion and time-reversal symmetry are respected, the Dirac points ...
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291 views

Interpreting a Hamiltonian in terms of 'hopping' operators

I am having some trouble interpreting a Hamiltonian in terms of "hopping" operators. The Huckel model for nearest neighbour interaction in graphene is given by $$H=-t\sum_\vec{R}|\vec ...
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Thermal exfoliation of graphite oxide

I have been reading up on the production methods of graphene, and one that I found interesting in particular was the thermal exfoliation of graphite oxide. From what I gather the basic idea is that ...
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how does graphene affect the refractive index of an optical waveguide?

Could someone help me find data on the electro conductivity of graphene and its effect on the refractive index of an optical waveguide
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262 views

Construct the Hamiltonian of electrons on a graphene sheet ( in xy plane)

Graphene is a two-dimensional material formed by carbon atoms in a honeycomb lattice. Because of the symmetry of the honeycomb lattice, the electrons in graphene obey a linear dispersion relation ...
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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 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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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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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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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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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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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 ...
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Is a “cathode ray drive” feasible?

When I saw the headline, Fuel Free Spacecrafts Using Graphene, I thought it was another reactionless drive, but it turned out to be a bit more plausible :) Original paper here. Long story short, ...
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Klein paradox in graphene

When considering the Klein paradox in graphene Katsnelson, Novoselov and Geim introduce a potential barrier (see http://www.nature.com/nphys/journal/v2/n9/full/nphys384.html). But I cannot understand ...
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Textbook on 2D Crystals

I've become interested in $2$D crystals, and in particular graphene. I'm looking for a textbook which covers graphene -- possibly as part of a course on solid state theory -- for undergraduates. For ...
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questions about graphene applications

i have read that if we had a sheet of graphene the thickness of cling wrap it would take a elephant on a pencil to pierce it (so two fucktons of psi?) but if graphene is so strong why is it when we ...
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What are the conditions of wave function continuity when solving for Dirac Spinors as done in “Klein paradox” paper by Novoselov?

In the paper "Chiral tunneling and Klein paradox" paper by Katsnelson, Novoselov, and Geim, they use the wave function for Dirac spinors. What are the conditions for continuity of the wave function ...
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Integrals in tight-binding method

In the tight-binding method, as e.g. described in Ashcroft and Mermin one need to solve a few integrals in order to proceed. For example for the overlap between an orbital situated at two different ...