# 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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### The tensor product in the Hamiltonian of graphene

I have the Hamiltonian of pristine graphene \begin{equation} H=v_{F}.\boldsymbol{\gamma}.\boldsymbol{p} \end{equation} with $\boldsymbol{p}=(p_{x},p_{y})$ is the momentum operator, $v_{F}$ is the ...
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### Recovering 3D properties from 2D materials

One of the biggest topics nowadays in Condensed Matter Physics is 2D materials. If we take graphite an peel it off we get graphene, the canonical example of 2D material which has very different ...
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### Dirac equation for the Kagome lattice

Background To model graphene we often use a nearest-neighbour tight-binding Hamiltonian $$H = - t \sum_{<ij>} c^{\dagger}_i c_j$$ embedded on a hexagonal lattice. By performing a Fourier ...
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### How some defect types can cause particle-hole symmetry breaking in graphene?

According to literature, some defect types (e.g. Stone-Wales) produce hopping between the same sublattice (e.g. A to A), which has been pointed out as the reason for particle-hole symmetry breaking. ...
2answers
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### Plotting a bandstructure along high-symmetry paths in the Brillouin Zone

I am trying to finalize my band structure plot for twisted bilayer graphene. I have been having some problems with the plot itself. To troubleshoot my code, I first just looked at the diagonal part of ...
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### How do I go from the eigenvalues (band structure) and eigenvectors of a 2D superconductor to its optical conductivity?

In the supplementary information of this Ni et al. paper "Plasmons in graphene moiré superlattices", we have a "Kubo formula" that's used to obtain the optical conductivity of a ...
0answers
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### Deriving Continuum BdG equation from Tight-Binding model for Graphene-Superconductor interface

Background My question concerns Beenakker's paper on "Specular Andreev Reflection in Graphene": cond-mat/0604594 (arxiv)/Phys.Rev.Lett. 97, 067007 (The same topic is also discussed in Rev. ...
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### What makes a symmetrical difference between a 2D semiconductor and graphene?

Compared to graphene, why does only 2d semiconductors have time reversal symmetry breaking properties? Please explain easily
0answers
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### About the symmetry protected issue at Dirac point in graphene

I have studied several resources about the band structure of graphene. They always mention that the Dirac point in graphene is protected by time reversal symmetry and inversion symmetry. I can ...
0answers
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### Calculating the Hamiltonain kernel of a Haldane model in zigzag graphene

Currently I'm learning how to calculate the edge effect of a material. I try to calculate edge state of a Haldane model in a zigzag graphene. Since Im writing in a second quantisation basis, each ...
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### Rashba Spin Orbit Coupling In graphene

I'm trying to understand the Rashba spin orbit coupling induced in graphene by proximity effect with Au(or any other metal)adatoms. It is not really clear for me. I know that the Rashba spin orbit ...
0answers
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### Missing factor in high-temperature phonon-limited resistivity of graphene (E. H. Hwang et al.)

I am trying to understand this paper by E. H Hwang and S. Das Sarma, where Boltzmann transport theory and relaxation time approximation are used to calculated the phonon-limited resistivity of ...
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### 2 different density of states for Graphene and Bismuth Selenide

I will solve the problem below by $1)$ working in reciprocal (wavenumber space) and in $2)$ energy space ($\epsilon$). But first some contextual background: Graphene is a single sheet of carbon ...
1answer
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### Why does graphene break on mechanical exfoliation?

We know that graphene is the strongest metal on earth. It has very high tensile strength. The inter-planar bonds are van der waals force but the covalent bond across the plane between C-C atoms is ...
0answers
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### distribution of atomic displacements in two-dimensional materials

In 3-dimensional materials, the thermal vibration of atoms can be described by mean-squared displacement values $\langle u_i u_j \rangle$ (where $u_i$ are displacements from equilibrium positions for ...
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### Graphene in torsional penulum

I know damping occurs in a SHM torsional pendulum because the layers of the rope,string, etc. experience shearing forces between them. My first is question : 1. If something like a copper wire or rod ...
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### what is superfluid weight？

In papers about twisted bilayer graphene, there is the conception of "superfluid weight" which is related to superconducting transition temperature. What do the words mean?
1answer
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### How do flat bands imply superconductivity?

I'm just doing a small ugrad assignment where I have to present a talk on twisted bilayer graphene. I'm having trouble understanding the meaning of a flat band. As far as I understand, a flat band ...
2answers
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### Why does the concept of effective mass fail for linear dispersion relations?

I had a discussion about graphene and stumbled about a conceptual problem of myself about the effective mass of electrons close to the Dirac point in graphene or for any linear dispersion relation in ...
1answer
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### What is the time reversal operator in graphene (do not consider spin)?

For graphene in one valley, the low energy Hamiltonian writes as: $$H_K(q)=\sigma_xq_x+\sigma_y q_y$$ The Hamiltonian on the other valley I remember has two ways of writing(not 100 percent sure), ...
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### synthesis of free standing silicene

Unlike graphene which can be isolated from graphite via exfoliation, the same thing can't be done with silicene. Most of the papers I see usually involve synthesis of silicene on a metal substrate ...
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### Nielsen-Ninomiya Theorem on a 2+1 lattice

(a) In the paper on the proof of the Nielsen-Ninomiya theorem, it is shown for 1+1 and 3+1 lattices. Does the proof hold on lattices with even number of spatial dimensions (e.g 2 spatial + 1 time)? If ...
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### Can we study the effects of Quantum reflection on heavy atoms?

From what I've looked at, it feels like QR has only been studied on light atoms like He, Ne, Na, H, etc. But can we study this effect on heavy atoms like Rb-87. If not, is it because of the ...
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### Is graphene a better thermal conductor than diamond?

I was listening to the BBC Inside Science Podcast episode about artificial diamonds and they mentioned that diamonds are the most thermally conductive material. One of the people on the episode was ...
1answer
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### Elastic energy of graphene: new idea for (non-chemical) battery

Is it possible to build a battery using the elastic property of graphene? Here is the stress-strain curve of graphene. Image source: https://www.researchgate.net/figure/Stress-strain-curves-of-...
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### Realtivistic interaction in graphene

Near the Dirac points, Graphene can be described by the Lagrangian equivalent to free massless Weyl spinors: $$L_0 = \overline{\Psi}\gamma^\mu\partial_\mu\Psi \quad.$$ From the theoretical point of ...
1answer
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### Tight Binding Hamiltonian for graphene

The TB Hamiltonian for the tetragonal lattice is $\hat H_0 = -J\sum_{m,n} (\hat a_{m+1,n}^\dagger \hat a_{m,n}+\hat a_{m,n}^\dagger \hat a_{m,n+1}+h.c.)$ How can this be derived for the hexagonal ...
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### Density of states LL in graphene [closed]

I am using the Kernel Polynomial Method to determine the spectral density of a 2DEG system that has been sujected to a perpendicular magnetic field B. I wish to determine (a) What the amplitudes of ...
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### Time reversal symmetry in Bilayer Graphene

In general the time reversal symmetry operation for spin half angular momentum requires $$H(-p)=\sigma_{y}H^{*}(p)\sigma_{y}.$$ The Hamiltonian of a bilayer Graphene is H(p)=\frac{1}{2m}(p^{2}_{x}-p^...
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### How can the velocity of electrons in graphene be measured?

I'm trying to understand how one can measure the velocity of electrons in graphene, from an experimental point of view. Does anyone have some clue?
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1answer
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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 ...
1answer
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### Derivation of the Berry Curvature and Bloch Magentic Moment in Graphene

(I found a workable solution, skip to the "Solution" part to see it) I am attempting to derive equations 2 and 6 from Xiao et al. paper "Valley contrasting physics in graphene" (...