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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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Why does Berry Curvature vanish everywhere in k space except at k=0 in monolayer Graphene, when k=0 is not a Dirac Point?

For Monolayer Graphene, the band structure contains 6 Dirac points around the origin in k-space. I understand that the Berry Curvature has to vanish everywhere except at the Dirac points where it ...
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What is the tight binding Hamiltonian for Graphene in terms of the Pauli Matrices?

I have been unable to find an expression for the tight binding Hamiltonian of Graphene in terms of the Pauli Matrices. Please share any reference available. Thank You
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Spinwaves, Mermin-Wagner theorem, Two-point correlation function and Heisenberg model

I was looking at the Mermin-Wagner theorem (as following the previous question) and the Heisenberg model seems to be presented, and they split the Hamiltonian $H$ in the matrix or vector n-components ...
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Mermin-Wagner and graphene

I have been told that the Mermin-Wagner theorem disallows the existence of the crystal of graphene. However, I don't have enough knowledge to understand the Mermin-Wagner theorem. If possible can ...
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How could skin be made as hard as diamond or graphene, whilst retaining it's current flexibility? [closed]

I want to understand what exactly the difference is between skin, on a molecular, atomic and quantum level, and materials like diamond and graphene. Then I wish to understand the changes that would ...
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Experiments measuring temperature dependence of graphene's specific heat in low-temperature regime?

I am currently studying the Debye model and I've found out that for two-dimensional materials the specific heat in low temperature limit should scale with temperature as ~T$^2$ as opposed to the "...
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How to map the symmetry property of the lattice unit cell to the symmetry properties of eigen modes

For example, in $\mathbf{r}$ space, a honeycomb lattice (like graphene) has C6v symmetry about the center of the unit cell. The ground state (singlet) eigen mode has C6v symmetry and the 1st order ...
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Peierls phase in graphene

In the introduction of the paper presented here, a derivation of the Peierls phase is presented, using a Wannier base of eigenfunctions and the Kohn-Sham Hamiltonian. After it symbolises the hopping ...
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Would graphene as a bulk material act the same as the single layer

Graphite is supposed to be layers of graphene so the first natural question when thinking about how to use graphene is, why doesn't graphite have such amazing properties, however.. I think graphite ...
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Derivation of the Berry Curvature and Bloch Magentic Moment in Graphene

I am attempting to derive equations 2 and 6 from Xiao et al. paper "Valley contrasting physics in graphene" (Link to paper). The Hamiltonian for graphene with a staggered sublattice potential (in ...
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What is energy band gap?

Explanations for graphene's high electrical conductivity often discuss energy band gap. What is energy band gap and how does it relate to the conductivity of a material?
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Lattice hopping at boundary in graphene lattice with magnetic field

Let's say I have a tight binding model for graphene, where I have a two-atom basis and three nearest neighbor vectors. I've applied a homogenous magnetic field $B$ in the z-axis, and can take the ...
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Can we call a hexagonal system with two different atoms as inversion symmetric?

Graphene is two-dimensional honeycomb crystal lattice with the two Carbon atoms in its unit cell. Clearly, it is inversion symmetric. But, suppose we have two different atoms in the hexagonal system ...
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Graphene with onsite coulombic term

Why is it that when you add the onsite coulombic term in graphene,the mass term is multiplied by Pauli matrix in z direction?Had it been multiplication by identity matrix,then youget the same diagonal ...
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density of state function for semi Dirac materials

Respected members I have a problem in finding density of state for semi Dirac system (linear dispersion relation in one direction and parabolic in other direction). $$E(k)=\pm\sqrt{{(\hslash^2k_x^...
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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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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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$4\times4$ 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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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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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 ...