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. ...
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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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Continuum limit of graphene

I am studying the continuum limit as described in section II B of this paper. The tight binding Hamiltonian for graphene is given by $$ H = -t \sum_{\langle i,j \rangle, \sigma}\left(a^\dagger_{\sigma,...
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Angular dependence of Moiré-pattern arising in twisted graphene bilayer

My question is, if there is any known expression for the angular dependence of Moiré-pattern formation in twisted hexagonal bilayers. The most well-known example for the occurance of the Moiré-effect ...
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Graphene Band Structure

I am currently trying to understand this graph: https://www.researchgate.net/figure/Top-Graphene-nanoribbons-with-zigzag-left-and-armchair-right-edges-with-disordered_fig1_258105786 Plotted is the ...
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Is it possible for the Kagome lattice to have edges of different lengths?

Is it possible for the edges of the Kagome lattice to be of different lengths? In other words, in the attached picture, is it possible to have $x\neq y$? If so, how will be the shape of that network? ...
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Confusion Regarding the Derivation of Graphene Dispersion Using Annihilation and Creation Operators

I am going through a text which derives the energy bands in graphene (https://cpb-us-w2.wpmucdn.com/u.osu.edu/dist/3/67057/files/2018/09/graphene_tight-binding_model-1ny95f1.pdf) and am stuck on a ...
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What does '%BZ' mean in materials science?

Also, for that matter, what does k_II mean?
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Extended Blonder Tinkham Klapwijk in graphene

Background In this paper the author studies the BdG equation for a metal-superconductor-metal system. The left metal is electron doped and is in the region $x<0$, the supercondcutor is in the ...
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Expanding a tight-binding hamiltonian around a Dirac point (1.D. Graphene) [closed]

My off diagonal terms for this Hamiltonian are the following: $H = e^{\mp ik_xa}(1+ 2e^{\pm i3k_xa/2}\cos(\sqrt{3}k_ya/2)) $ Next, I want to see the low energy bands, and for this I've been told to ...
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Chiral Symmetry Breaking in Graphene

I am trying to understand chiral symmetry breaking in the context of graphene with Coulomb interaction ; I understand how to move from a tight-binding Hamiltonian to a field theoretic setting (2+1 QED ...
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What is the full matrix form of the 2D Rashba Hamiltonian for Graphene and TMDCs?

I have been trying to derive the dispersion relation for the low energy Hamiltonian described in Ref. 1. The relevant equations are (1a) through (1d). I will re-write the equations here to save time: $...
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Dimensionality in Bistritzer MacDonald Hamiltonian

I was trying to understand the origin of flat bands for twisted bilayer graphene and had a basic misunderstanding. The starting Hamiltonian is $$H = \begin{bmatrix} -iv_0 \sigma_{\theta/2}\nabla &&...
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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 ...
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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
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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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Pseudospin in Graphene

According to my understanding, since the honeycomb lattice is not a Bravais lattice, we consider it a superposition of two lattices (say A and B). The spinor wavefunction $\begin{bmatrix}\psi_1\\ \...
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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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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 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" (...

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