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.

Filter by
Sorted by
Tagged with
1 vote
0 answers
12 views

How can I create 4 atoms basis graphene in Vesta? [closed]

How can I create 4 atoms basis graphene in Vesta? This is the Poscar file for two atoms basis graphene. As an example. Similar to these I got to make a 4 atoms basis graphene primitive cell. graphene ...
  • 11
1 vote
0 answers
59 views

New representation of annihilation operator in tight binding model for graphene

In this article about the electronic properties of graphene, in section b the author considers the usual tight binding hamiltonian for graphene $$ H=-t\sum_{<i,j>,\sigma}(a_{\sigma,i}^{\dagger} ...
  • 671
0 votes
0 answers
37 views

Band Structure of Graphene from Exact Diagonalization of Finite Lattice

Say I write down a real space matrix Hamiltonian for a finite graphene lattice, perhaps a rectangle with N sites along each axis. Of course if I had an infinite lattice then I can use Bloch's theorem ...
  • 65
0 votes
0 answers
29 views

Is graphene a topological material?

I understand that graphene is a great material with many exotic properties. Hoever, does it have a non-trivial band topology? It's mentioned that graphene has a weak spin-orbit coupling, which is ...
  • 1
1 vote
0 answers
34 views

Landau levels in graphene - unbounded from below spectrum

Considering the case of monolayer graphene in a perpendicular magnetic field arises LL in it. The final spectrum is given by $$ \epsilon_n=\mathrm{sign}(n)\hbar\omega\sqrt{|n|} $$ where $n\in\mathbb{Z}...
0 votes
0 answers
12 views

Representation of honeycomb lattice inversion symmetry operator acting on 2x2 Bloch Hamiltonian

I am considering a spinless nearest neighbor tight binding model of graphene, leading to a 2x2 Bloch Hamiltonian $$H(\vec{k}) = \vec{h}(\vec{k}) \cdot \vec{\sigma} = \begin{bmatrix} 0 & t(e^{-i\...
1 vote
2 answers
64 views

Don't Understand Screened Potential Expression

Can someone explain to me please why this screened potential has the following expression? $$ V(r)=\frac{e^{2}}{\epsilon}\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}}{\sqrt{r^{2}+\xi^{2}n^{2}}} $$ It is ...
0 votes
0 answers
40 views

Quantum Hall state at $\nu=0$ in graphene

I don't understand the meaning of the observed quantum Hall (QH) state at filling fraction $\nu=0$ in graphene at a high magnetic field. A high magnetic field lifts the four-fold degeneracy of the ...
1 vote
0 answers
45 views

What's a Sewing Matrix?

I'm reading a paper on graphene that talks about these sewing matrices, but I don't understand their definition. Upon researching it on the internet, I've found the term in other papers, so I assume ...
0 votes
0 answers
36 views

QFT Graphene and Fine structure constant

I've found these two references about the QFT model of graphene http://arxiv.org/abs/1112.2054v1 http://arxiv.org/abs/1608.03261v1 They both use the Fermi velocity $v_F=c/300$. What confuses me is ...
  • 1,694
2 votes
1 answer
192 views

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 ...
  • 3,295
2 votes
1 answer
88 views

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 ...
  • 671
2 votes
2 answers
88 views

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'...
  • 671
1 vote
0 answers
87 views

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-...
0 votes
1 answer
315 views

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 ...
  • 1,337
0 votes
1 answer
42 views

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 ...
0 votes
0 answers
44 views

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 ...
0 votes
0 answers
83 views

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}{...
  • 671
0 votes
0 answers
42 views

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 ...
0 votes
0 answers
71 views

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 ...
2 votes
0 answers
66 views

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 ...
  • 877
2 votes
0 answers
74 views

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 ...
3 votes
0 answers
175 views

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 ...
3 votes
1 answer
140 views

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{...
1 vote
1 answer
106 views

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 ...
1 vote
0 answers
104 views

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 &...
0 votes
0 answers
56 views

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 ...
  • 1
0 votes
1 answer
103 views

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 ...
  • 1,691
1 vote
0 answers
25 views

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 ...
0 votes
0 answers
87 views

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 ...
  • 965
3 votes
2 answers
140 views

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 ...
0 votes
0 answers
17 views

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 ...
2 votes
1 answer
114 views

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)=\...
  • 371
1 vote
0 answers
20 views

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 ...
1 vote
0 answers
51 views

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 ...
2 votes
1 answer
97 views

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 ...
1 vote
0 answers
36 views

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\...
0 votes
1 answer
102 views

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 ...
's user avatar
1 vote
1 answer
61 views

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 ...
2 votes
0 answers
563 views

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 ...
  • 402
1 vote
0 answers
80 views

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. ...
3 votes
2 answers
582 views

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 ...
  • 57
1 vote
1 answer
292 views

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,...
  • 3,368
2 votes
0 answers
112 views

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 ...
  • 506
1 vote
1 answer
78 views

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 ...
-1 votes
1 answer
102 views

What does '%BZ' mean in materials science?

Also, for that matter, what does k_II mean?
  • 3,725
0 votes
1 answer
249 views

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 ...
  • 57
0 votes
1 answer
350 views

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: $...
1 vote
2 answers
203 views

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 &&...
0 votes
0 answers
224 views

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. ...
  • 402

1
2 3 4 5 6