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Questions tagged [graphene]

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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Stability criterion for leapfrog in relativistic physics

I am doing a 2D MD simulations of charge carriers in graphene using the Leapfrog algorithm. I am trying to prove that, in some specific cases (when distance between particles is small), the method is ...
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Matching band momenta of zigzag and infinite graphene

Let's say the zigzag line is along the $x$-direction. The 2D 1st Brillouin zone (BZ) of an infinite graphene is a hexagon with inequivalent Dirac points located alternately at the 6 corners as shown. ...
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Why do we consider spin degeneracy in graphene quantum hall effect and not in the conventional one?

When dealing with quantum hall effect in graphene we say that each landau level (with $n\neq 0$) has 4 times the degeneracy of a simple landau level derived for an electron in a magnetic field because ...
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Interpretation of tilted energy dispersion cones in a Dirac Semimetal

The energy dispersion of a Dirac semimetal with an effective Dirac Hamiltonian of the form $$H=v_x \sigma_xk_x+v_y\sigma_yk_y+v_t\sigma_0k_y$$ is tilted in the y direction and the tilting increases ...
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Is numerical lattice wavefunction smooth? — graphene tight binding case

I tried to follow exactly Sec. II.K [page 112-113, Hamiltonian after Eq. (113)] of the standard Review of Modern Physics paper on graphene, which is a tight-binding model of a graphene stripe under ...
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Massless Dirac fermions vs helical Dirac fermions

Some papers when, dealing with graphene, write about charge carriers called helical Dirac fermions that have a conical energy–dispersion relation and a conserved quantity $\sigma\cdot k$ (pseudospin–...
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Why does the 2D hexagonal lattice have a different tight binding band structure than Graphene?

Here you can find band structures for various tight binding models. I was wondering, why the 2-D hexagonal lattice has a different band structure than Graphene, even though they have the same lattice.
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Different Creation/Annihilation operators for neighbouring sites in Tight-binding model of Graphene

The treatments that I have seen of Graphene's Band structure assume an overlaying of two inequivalent lattices. However, can the reason for choosing different annihilation and creation operators (such ...
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$4\times4$ Dirac Hamiltonian in Graphene

When linearizing the Hamiltonian of Graphene in reciprocal space around $\vec{q} = \vec{k}-\vec{K}_\pm = \vec{0}$, where $\vec{K}_\pm$ are two independent Dirac points, one can get two Hamiltonians, ...
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How to determine the degree of how high a symmetry of high-symmetry points in the first Brillouin zone?

For exmple, we have a hexagonal lattice with hexagonal Brillouin zone, shown in the picture The points $\Gamma$, K, M and $\Lambda$ are high symmetry points. Now, $\Gamma$ point is the highest-...
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Help me understand a little bit about this abstract

I was reading a story on phys.org: Holographic image of a black hole proposed in a graphene flake (Lisa Zyga, 25 July 2018, phys.org) From there I followed a link to the paper Quantum ...
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Why are the electrons in graphene massless?

I was reading Tommy Ohlsson's book on Relativistic Quantum Mechanics where he goes to a little digression on electrons and holes in Graphene. He claims that electrons and holes in Graphene can be ...
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Relativistic scattering off Dirac delta potential

Consider the case of a relativistic electron on a graphene lattice described by the Hamiltonian $$ \mathcal{H} = v\begin{pmatrix} 0 & p_x+ip_y \\ p_x-ip_y & 0 \end{pmatrix}, $$ where $v$ is ...
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Heating a monolayer atop a substrate with a laser

This problem is briefly mentioned in various research papers I'm reading, but it's never addressed in detail. The monolayer is attached atop a substrate as shown below The centre of the monolayer ...
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raman tensor of graphène and its polarisability

I want ask about the raman tensor of graphene all that I know, the raman spectrum of graphene has 2 main peak G and 2D. but what about its tensor raman. I know that the metals materials don't have ...
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Conserved quantity in Graphene

The computation of the band structure of Graphene basically leads to the diagonalization of the following Hamiltonian: $$ H = -t \left( \begin{array}{cc} 0 & \epsilon(\vec{k}) \\ \epsilon^*(\vec{...
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What does negative filling mean for Landau levels?

I'm trying to read this paper, but I've never heard of Landau levels like $\nu=-1.$ What does it mean?
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Helicity in Graphene

In Graphene, there are two independent points, the Dirac points, where the conduction and the valence band touch. Let's call these points $K_+$ and $K_-$. In a low-energy description, the Hamiltonians ...
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Can the graphene's conductivity be explained using only orbitals?

I am trying to find a 'easier' or more 'intuitive' way to calculate the conductivity of graphene. I want do this by using atomic or molecular orbitals. Anyone have a clue about how this can be done? ...
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Berry phase in graphene

For a low-energy description of graphene the Hamiltonian is given by $$ H = v_F \left(\begin{array}{cc} 0 & p_x-ip_y\\p_x+ip_y & 0 \end{array} \right)$$ where $v_F$ is the Fermi-velocity and $...
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Calculate Chern number from band structure

When we use a tight-binding approach in order to calculate the band structure of electrons on a 2D honeycomb lattice such as Graphene we find that there are two energy bands touching in six points, ...
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D-peak of Raman Spectra of Graphite explanation

The D peak in the Raman Spectrum of Graphite is attributed to the breathing mode of $A_{1g)$ symmetry involving phonons near zone boundary. The explanation is the following: The change of bond ...
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Energy and momentum conservation argument for electron-phonon transitions in Bilayer Graphene

I'm reading a paper which says that the interband transitions ($\pi_1^* \rightarrow \pi_2^*$) involving phonons at $q= 0 $ and $ q = K$ in Bilayer Graphene are prohibited by energy and momentum ...
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Edges states dispersion relation of gapped graphene

I'm currently looking at this paper: Domain wall in gapped graphene. I do know how to get the dispersion relation of the gapped graphene without the domain wall. But according to this article, it ...
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Are graphene and coal are the same?

I recently read about the atomic structure of graphene, which is carbon arrange in hexagon shape but only 1 atomic thick(2d). And then I remember that coal is also made of carbon arrange in hexagon ...
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Berry curvature and time reversal symmetry

When the time reversal operator, $\hat{\Theta}$ acts on a phase, $e^{i\phi}$ it gives $e^{-i\phi}$. Since the Berry phase factor is $e^{i\gamma}$, where $\gamma$ is the Berry phase, if the Berry ...
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Graphene conductivity from Kubo formula

I'm trying to understand the Kubo Formula for the electrical conductivity in the context of the Quantum Hall Effect. How can you derive graphene conductivity from the Kubo formula? $$\sigma_{xy}=...
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Characterization of graphene using optical microscopy

Number of layers of mechanically exfoliated graphite on silicon wafer can be estimated by observing through optical microscope. This is possible due to fact that huge colour contrast between different ...
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Chemical potential of graphene : is $1~\rm eV $ too high?

I am working on graphene plasmonics and I read the following paper that discusses graphene nanoantennas. https://www.osapublishing.org/oe/abstract.cfm?uri=oe-21-3-3737 They use a chemical potential ...
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Obtaining low energy effective model of Bernal stacking bilayer graphene

I am now reading some articles about the electronic properties on Bernal stacking bilayer graphene. (https://arxiv.org/abs/1205.6953). In the section II-C-1, the general procedure of obtaining the ...
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Electrical conductivity simulation of thin films (COMSOL, …?)

I'm currently studying composite materials made from thin films with extremely anisotropic properties such as graphene. I am running finite element simulations to support my results but simulating ...
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Positive and negative winding number related by time-reversal symmetry

I am now reading some articles about Dirac fermions in condensed matter physics and the most famous example is graphene. I am now trying to understand page 5 in this article : https://arxiv.org/abs/...
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How is the $\pi$ bond of carbon in graphene possible?

This paper states that the carbon atoms in a sheet of graphene form 3 $\sigma$ bonds with the neighbouring carbons and a $\pi$ bond that comes out of the plane (in the $z$ direction). Unfortunately ...
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Relation of Berry phase and winding number

I am reading the following article dealing with the properties of Dirac fermion in condensed matter physics : https://arxiv.org/abs/1410.4098 In the page 5 of this article, the formula for the ...
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Primitive cell of graphene

I have spent hours on finding the primitive cells of honeycomb lattice of graphene. Based on the definition of graphene from most of solid state physics books, as I quoted from Wikipedia, and in which ...
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Using ladder operators to solve for Landau levels of graphene

I had recently been studying the Dirac equation, and as an example of how the equation is used, I was given a problem about the Landau levels of graphene (but I personally have no knowledge about ...
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How to make sense of the multiple bands obtained for multiple-atoms-per-unitcell crystals, such as graphene?

Graphene has a honeycomb lattice which can be described as a triangular lattice but with two atoms per unit cell. Therefore, when solving for the band structure of the graphene, we expand the ...
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How to determine the degeneracy of an energy level for a periodic quantum system from its band structure over the Brillouin zone?

The following figure shows the 1st Brillouin zone of graphene (shaded area). At the $K$ and $K'$ points (called Dirac points), the upper (conduction) band touches the lower (valence) band, and ...
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Heuristic argument for boson of Möbius graphene strip at low temperatures?

I recently was thinking of the implications of how electrons behave in the Möbius graphene strip at low temperatures. At high temperatures we know that there will be a parity symmetry of the system ...
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Massless Electrons and Effect on Graphene Mass

I've read that electrons in graphene can travel masslessly, due to the effect of the graphene crystal around them. I'd also read that the application of an electric field can change this behavior and ...
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Landau-Peierls Substitution in Haldane Model

In his 1988 paper "Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the parity anomaly" [1], Haldane performs a Landau-Peierls Substitution $\hbar\delta\mathbf{k}\...
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Is there a material that can stretch to 12 times it's size on the x & y axis (not concerned about the z), and can still return to it's original shape? [closed]

I've been looking for a solid square (non-pourus) that can expand to 12x it's size and back again. This needs to grow and shrink on only the x and y axis, the z doesn't matter whether it grows or not. ...
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Linear electronic dispersion of graphene

The energy dispersion relation of graphene with the tight-binding approximation and interactions up to nearest neighbors is $$E(k_1,k_2)=\pm |t|\sqrt{3+2\cos(ak_1) + 4\cos\left(\frac{a}{2}k_1\right)\...
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What is the definition of the pseudo spin of bilayer graphene

The Hamiltonian for graphene at $\vec{k}$ away from the $K$ point is $$ H=\vec{\sigma} \cdot \vec{k} =\begin{pmatrix} 0 & k_x - i k_y \\ k_x + i k_y & 0 \\ \end{pmatrix} = k \begin{pmatrix} 0 ...
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Why and how Dirac cones are “tilted”?

Given a Weyl Hamiltonian, at rest, $ H = \vec \sigma \cdot \vec{p} $, A Lorentz boost in the x-direction returns $ H = \vec\sigma\cdot\vec {p} - \gamma\sigma_0 p_x $ The second term gives rise to a ...
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Orthogonalization of a hexagonal unit cell

I am using the Multislice technique to produce simulated TEM images. For Graphene, the unit cell is no longer rectangular but hexagonal. I have data for the projected potential in each rhombic slice ...
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The strange behave of wave function of the hexagonal lattice. Not single-valued, strange at K and K' Points

I want to know a wave function should be periodic or not in the Brillouin Zone. I calculated the eigenvalues and wave function of the hexagonal lattice by the tight-binding approach. The wave ...
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Scanning tunneling spectroscopy of graphene: Energy gap and momentum mismatch

In some early experiments on scanning tunneling spectroscopy (STS) of graphene the gap of $\pm60\,\mbox{meV}$ around zero bias voltage was found (see the figure from Y. Zhang et al., Nature Phys. 4, ...
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Graphene Tight binding 2D Hamiltonian

I got stuck on Homework problem, where I need to construct Hamiltonian of 2D Graphene layer and obtain Dispersion graph from it. I already went trough a lot of materials but all I find is $2\times 2$ ...
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How to show that Chern number gives the amount of edge states?

When talking about topological insulator and talking about bulk-edge correspondence, it seems to be widely accepted conclusion that the band Chern number (winding number) is equal to, when the ...