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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Incredible electron drift velocity in atomic thin layer of graphene?

Free electrons in atomic thin layers of graphene behave more like photons (Bosons) than fermions reaching incredible drift velocities and mobility which reach speeds as reported by this article in the ...
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What is the meaning of this wave function?

In these notes here the tight binding model for graphene is worked out. The tight Binding Hamiltonian is the usual: $$H=-t\sum_{\langle i,j\rangle}(a_{i}^{\dagger}b_{j}+h.c.)$$ where two different ...
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Valley degree of freedom in graphene

I know that in the energy band structure of graphene there are six points where the valence and conductance band touch (At $E=0$), called Dirac points. Only 2 of these points are inequivalent, K and K'...
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Numerical calculation of berry curvature of Haldane model

I'm currently trying to simulate the Haldane model of graphene and am looking into the calculation of Berry curvature of the finite lattice. I'm using a tight-binding model of graphene with nearest-...
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Graphene lattice - honeycomb or hexagonal

Wikipedia says, in its page on hexagonal and honeycomb lattices: The honeycomb lattice is a special case of the hexagonal lattice with a two-atom basis. The centers of the hexagons of a honeycomb ...
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What makes carbon atomic structures stand out from other elements in terms of their properties?

Since lots of materials with some remarkable properties are some form of carbon structures: Incredible strength of graphene is often explained by it having a hexagonal atomic lattice. Hardness of a ...
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Room-temperature Quantum Hall Effect (QHE) in graphene

Quantum Hall plateaus can be observed in graphene with magnetic fields smaller than $20\,\mathrm{T}$ even at $300\,\mathrm{K}$. In the experiment, at room temperature, $h\omega_c$ exceeded the thermal ...
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Graphene energy bands at Dirac points

I know that the energy bands in Graphene (possible energies that an electron can take in the material) are given by : $E_{\pm}(k)=\pm t\sqrt{3+f(k)}$ where $f(k)=2\cos(\sqrt{3}k_{y}a)+4\cos(\frac{3}{...
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How does a Dirac cone split to two Weyl cones when magnetic field is applied?

The separation of a Dirac cone to two Weyl cones in Dirac semimetals in the presence of an applied field is said to be due to the spin Zeeman energy. I am unable to understand how this would lead to a ...
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Tilted Dirac cones and Lorentz invariance

New materials called Type II Dirac semi-metals have been discovered. They have a tilted Dirac cone instead of the straight linear dispersion. These particles are said to break Lorentz invariance. How ...
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How weak are the Van der Waals bonds? What is their contribution to the total mass of an object?

We know that every binding energy can be expressed as a negative mass contribution to the total mass of the system. It is well known, for example, that composite nuclei have a “mass defect” when ...
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How can i calculate the Berry Curvature for the Dirac points in Haldane graphene?

I want to calculate the berry curvature at the Dirac points in graphene with complex next nearest hopping (haldane model) in order to show that it is non-zero at the dirac points and use it to compute ...
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Numerically calculating the berry curvature for graphene

i'm trying to reproduce this density plot for the Berry curvature in the Brillouin zone of graphene from this website. In order to do this I am attempting to use this equation for the berry curvature ...
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Why aren't the eigenvectors of a tight-binding Hamiltonian periodic?

I try to calculate the Berry connection for a simple graphene model and stumbled across the following question. Suppose I have a tight binding Hamiltonian (further details here or here): $$H = \begin{...
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Why is Graphene Such a Good Conductor?

I'm doing a paper on graphene, and in the intro I need to elaborate why it has drawn so much attention. Well, I'm stuck on the good conductivity! Why is graphene such a good conductor? Does it relate ...
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Klein paradox in the massless case

I have a question about the Klein paradox in the massless case, for a potential step of height $V_0$ (this is exactly the situation described by Wikipedia). I don't have a problem to understand the &...
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Why does 2D crystalline lattice of Graphene overlap with its reciprocal lattice?

Can someone please explain why the 2D electron-diffraction pattern of graphene coincidentally overlaps with its reciprocal lattice? I want to understand/know the reason behind this coincidence in the ...
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What does Dirac cones at the $K$ and $K'$ point mean?

Graphene is a topological insulator with Dirac cones located at the points $K$ and $K'$ in the Brillouin zone. The bands at these points correspond to conducting edge modes. However, if we consider a ...
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Chirality effect in graphene [duplicate]

My BS research topic is 2-D nanomaterials. Currently, I am researching different 2-D nanosheets including graphene, silicene, and other elements of group IV-A. I study the chirality effect in them. I ...
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Wave-function (in real space) of electron in Graphene nano-ribbons

I was trying to solve the tight binding model of Graphene nano-strip in the zig-zag configuration. It looks something like this: It has a very beautiful band structure. In order to calculate the band ...
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Why can $\hbar q_x$ and $\hbar q_y$ be replaced by $\hat{p}_x=-i\hbar\frac{\partial}{\partial x}$ and $\hat{p}_y=-i\hbar\frac{\partial}{\partial y}$?

It is written in the book The Physics of Graphene (Page 10 and 17) that when the intervalley scattering is neglected, we can make the following substitution in the Hamiltonian of the graphene when ...
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How does field effect work on graphene?

I am trying to understand how the field effect from a gate works on graphene. Does the gate voltage affect the bands or the Fermi level? When studying how gate voltage affects a semiconductor, I ...
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Position of the Wannier center in tight-binding model

With the Fourier transform of the annihilation and creation operators, $$c_{m,n} = \frac{1}{\sqrt{N}} \sum_{k_x} \sum_{k_y} c_{kx,ky} e^{-i\mathbf{k}\cdot \mathbf{r}_{m,n}} \quad\text{and}\quad c^{\...
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Unit Cell of Twisted Bilayer Graphene

Would anyone please tell me how to build up the unit cell of twisted bilayer graphene? I know how to rotate the coordinate of atom with a certain angle through the multiplication of a rotation matrix, ...
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Expanding the Graphene Hamiltonian near Dirac points upto second order term

I was trying to solve the Graphene Hamiltonian near the Dirac points upto the second order term for the nearest neighborhood points. So expanding the function near the Dirac Point, we get$$g(K+q)=\...
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How does Quantum hall effect affect spin transport in single layer graphene?

I'm trying to figure out how QHE can change spin transport and spin relaxation in single-layer graphene. Also, What is the significance of spin relaxation in single-layer graphene.
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Brillouin Torus of graphene

I understand that the Brillouin Zone in a 2D momentum space is a torus if the corresponding edges that repeat are joined. What I cannot wrap around my head is how to do the same for the hexagonal BZ ...
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Berry Phase in Graphene

I am trying to understand the a) Concept of Berry Phase b) its effects/ observation in graphene. I am an experimental physicist and I want to understand these concepts without getting awed by ...
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How does back gating work on graphene?

I am reading a paper in which they have increased or decreased the carrier concentration in graphene by back gating. The charges are not flowing from the gate to graphene due to oxide. Due to ...
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Wavefunction magnitudes being degenerate everywhere on parameter space even though energy degeneracies occur at isolated points?

Cross-posted here: https://mattermodeling.stackexchange.com/questions/4974/wavefunction-magnitudes-being-degenerate-everywhere-on-parameter-space-even-thou $$ H(k,M)=-t \sum_{\delta} [\cos(k\cdot\...
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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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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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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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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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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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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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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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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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