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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Invesion symmetry is not point group symmetry?
I am currently reviewing a paper available at this link:
https://www.nature.com/articles/srep17571
In the introduction, the explanation caught my attention: "Due to the stability of the Dirac ...
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Tight binding hamiltonian graphene [duplicate]
I'm stuck on solving a question regarding the tight-binding hamiltonian for graphene.
I have been given a hamiltonian that looks like this (where the spin has been omitted since hopping is independent ...
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Tight-Binding Hamiltonian Graphene
I'm stuck on solving a question regarding the tight-binding hamiltonian for graphene.
I have been given a hamiltonian that looks like this (where the spin has been omitted since hopping is independent ...
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Symmetries near the K/K' points in graphene
I am trying to understand one paper and I have a problem with symmetries.
The authors introduce the 2x2 Bloch Hamiltonian as
$$
\mathcal{H}(\textbf{k}) = \textbf{h}(\textbf{k}) \cdot \sigma,
$$
where $...
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Position-dependent Fermi velocity
In models of strained graphene one seems to obtain a position-dependent Fermi velocity. By this I mean that if the original Dirac operator is
$$ H = v_0(\sigma_1 p_1 + \sigma_2 p_2),$$
with constant ...
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What's the difference between a rhombus lattice and a hexagonal lattice in photonics?
I am learning photonic crystal slabs. I try to figure out what the difference between a rhombus lattice and a hexagonal lattice in photonics is?
All I know is that they have diffefent Brillouin zones,...
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Graphene and Hubbard model
I am trying to understand the graphene Hamiltonian. As I see, the Hubbard model can be presented as follows
$$
\mathcal{H} = \sum_{i,j,\sigma} - t_{ij} \hat{c}^\dagger_{j,\sigma}\hat{c}_{i,\sigma} + h....
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The origins of the SOC in silicene
I read that silicene has a stronger SOC than graphene. As far as I know the SOC ~ $Z^4$. Thus, since silicon lies further in the periodic table, it explains why it has a stronger SOC than graphene. ...
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Hamiltonian for graphene
I am trying to get into graphene and I have a question about the Hamiltonian. As I read, the TB Hamiltonian for graphene is
$$
\mathcal{H} = -t \left[ a_{i,\sigma}^\dagger b_{i,\sigma} + b_{i, \sigma}^...
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Lennard-Jones potential can be valid at 0.2 Angstrom Distance between two particles?
I have modeled a graphene-vacuum-graphene system. Here two graphene sheets connected by L-J potential through vacuum gap (Phonon transfer through vacuum). I have simulated it considering 0.2 to 10 ...
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How can I identify momentum eigenstates in a tight binding model with degenerate energy eigenstates?
Summary:
I numerically diagonalize a tight binding Hamiltonian to get energy eigenvectors, some of which are degenerate. However, the numerically diagonalized degenerate eigenvectors are not ...
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How can valley coherence be defined if the crystal is initially in a mixed state?
In the field of valleytronics, they refer to valley coherence as: "the phase relationship between a particle in a superposition of two different valleys" [S. Vitale et al., Small 1801483 (...
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How is this paper published in Physical Review E not claiming to break the second law of thermodynamics?
This paper has the following abstract:
We theoretically consider a graphene ripple as a Brownian particle coupled to an energy storage circuit. When circuit and particle are at the same temperature, ...
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Berry curvature Weyl and Dirac points
I understand that Berry curvature sinks and sources correspond to Weyl points. However, I'm curious about the identity of points exhibiting a Berry curvature spiral, highlighted by red circles in the ...
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First brillouin in twisted bilayer graphene
When it comes to the reciprocal space of twist bilayer graphene, there is a very typical picture:
In this picutre it shows the hoppings bewteen the nearest Dirac point between two layers. And there ...
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What happens to the zeroth Landau level of monolayer graphene with broken $A$-$B$ sublattice symmetry?
The (non-interacting) Hamiltonian of an electron in monolayer graphene near the $K$ point in the Brillouin Zone can be approximated as $H = \begin{bmatrix}
0 & v(p_x-i p_y)\\
v(p_x+i p_y) & 0
...
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Why do physicists primarily study TMDCs when researching 2D materials, and not focus as much on many other 2D materials? [closed]
Why do physicists primarily study transition metal dichalcogenide (TMDC) monolayers when researching 2D materials, and not focus as much on many other 2D materials?
Other 2D materials also have ...
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2-body Umklapp scattering in graphene
It is claimed that the Umklapp scattering is forbidden in two-body collision in graphene due to the crystal symmetry in this paper . I am having a hard time to see why this is the case... why wouldn't ...
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How to construct the Wigner-Seitz cell if you don't know it is a two-atom basis?
Assuming we don't know that e.g., Graphene has a two-atom basis. How does the Wigner-Seitz Construction lead me to a two-atomic base?
So, assuming we do not distinguish jet between the green and red ...
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Nearest neighbour distance in Graphene [closed]
The lattice spacing in Graphene (Honeycomb Lattice) is 2.46Å. So, this should be the nearest neighbour distance in graphene. But I found it to be 1.42Å in this website. What am I doing wrong here?
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Graphene characteristics
I am trying to understand the physics of graphene and was unable to understand its I-V characteristics. Could anyone please explain it in simple terms. I have gone through the papers online but couldn'...
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Why perturbational approach fails to describe the bands?
I'm trying to find the band structure of Graphene using tight-binding for a unit cell with 6 carbon atoms(this is a toy model for my own research). The hamiltonian is as below:
$$H=
\left[\begin{...
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Raman Spectroscopy of Graphene
Why do graphite and graphene have different peaks in Raman Spectroscopy? Does a double layered graphite give us a graphite peak or a graphite peak?
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How to construct the Wigner-Seitz cell for a two-atom basis, like, e.g., a hexagonal lattice from Graphene?
I tried to construct the Wigner-Seitz cell with its perpendicular lines as explained in Wikipedia for a hexagonal (honeycomb) lattice.
(hexagonal lattice [1] with: Wigner-Seitz cell in green, ...
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How to express the $C_3$ Rotation symmetry in Graphene using sublattice basis?
In many articles, the $C_3$ Rotation matrix is expressed as $U=e^{i\frac{2\pi}{3}\sigma_z}$,where $\sigma$ is the pauli matrix in sublattice space, the symmetry of the tight binding hamiltonian is ...
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Optical matrix element in graphene: is electron $k$ perpendicular to $E$?
I faced some problems with understanding the process of light absorption in 2D (e.g. graphene). Suppose we have Dirac graphene hamiltonian, skipping all numerical factors:
$$ H = \hbar v\begin{pmatrix}...
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How to calculate electron and hole densities from a band structure?
Suppose we have the full band structure from tight-binding model for a hexagonal (or square) lattice. If there are only two bands, often in literature one band is called hole-band and the other is the ...
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Does resistance follow anti-Matthiesen's rule for ballistic - hydrodynamic electron transport?
Matthiessen's rule states that resistance due to various scattering mechanisms add up. For example, the resistance due to electron-impurity and electron-phonon interactions in metals is given by $\rho=...
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Is the statement that "It has dispersion relation with frequency(or energy)" equal to "It is a function of frequency(or energy)"?
I'm reading an article "RAMAN SPECTROSCOPY OF GRAPHENE AND RELATED MATERIALS" (https://www.physics.purdue.edu/quantum/files/Raman_Spectroscopy_of_Graphene_NOVA_Childres.pdf)
which describes ...
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What specifically defines a Dirac Point in a solid state system?
Is it that the low energy (long wavelength) Hamiltonian takes the form of the Dirac Hamiltonian as in Graphene? Or is it enough that there is a crossing in the electronic band structure?
For example, ...
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Graphene symmetry breaking
I was reading about the different symmetries that one could have in graphene.
Generally speaking, both the inversion symmetry of the honeycomb lattice and sublattice symmetry 'protect' the Dirac cones,...
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What are exactly the superconducting domes?
Do domes here mean the shape of some superconducting state?
Or does it have a different meaning here?
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What is the meaning of metallic gate in graphene?
While reading the paper: "Graphene bilayers with a twist"
I came across this sentence: "To carry out transport
or STS measurements, additional fabrication steps are necessary,
including ...
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About the graphene's Dirac points
I am studying Hasan & Kane's colloquim about topological insulators, and a question has emerged when I reahced the 4th page of this thesis. 1
Passages below the equation (3) show that near the ...
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Size of metal domain needed to reflect light ; are small graphene sheets shiny?
I remembered that shininess of a material is because of reflection, ie surface current responding to light. Mathematically, one can solve Maxwell equations under a relevant boundary condition, with ...
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What's the temperature dependence of electrical conductivity for semi-metals?
I am trying to teach undergraduate solid state physics when I realized that this problem is rarely discussed.
I know that metals' conductivity decrease with temperature due to increasing scattering at ...
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Symmetry Class of Graphene with Spin-orbit Coupling
I know that tight-binding graphene with $\text{p}_\text{z}$-, $\text{d}_\text{xz}$- and $\text{d}_\text{yz}$-orbitals and spin-orbit coupling is a $\mathbb{Z}_2$-topological insulator. But I want to ...
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What is the dynamic conductivity? How it differs from the conductivity we know? What are the types of conductivity?
In the paper I am reading, it was written that "The dynamic conductivity of graphene could elucidate features that would demonstrate unique properties of this system and allow for the ...
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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
...
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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
$$ H=-t\sum_{<i,j>,\sigma}(a_{\sigma,i}^{\dagger} ...
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Band Structure of Graphene from Exact Diagonalization of Finite Lattice
Say I write down a real space matrix Hamiltonian for a finite graphene lattice, perhaps a rectangle with N sites along each axis. Of course if I had an infinite lattice then I can use Bloch's theorem ...
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Landau levels in graphene - unbounded from below spectrum
Considering the case of monolayer graphene in a perpendicular magnetic field arises LL in it. The final spectrum is given by
$$
\epsilon_n=\mathrm{sign}(n)\hbar\omega\sqrt{|n|}
$$
where $n\in\mathbb{Z}...
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Don't Understand Screened Potential Expression
Can someone explain to me please why this screened potential has the following expression?
$$ V(r)=\frac{e^{2}}{\epsilon}\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}}{\sqrt{r^{2}+\xi^{2}n^{2}}} $$
It is ...
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What's a Sewing Matrix?
I'm reading a paper on graphene that talks about these sewing matrices, but I don't understand their definition.
Upon researching it on the internet, I've found the term in other papers, so I assume ...
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Spin orbit coupling in transitional metal dichalcogenides (TMDC)
I am doing studies on 2D materials, especially graphene and transitional metal dichalcogenides (TMDC). But I always have a question on the spin-orbit coupling (SOC) in TMDC: why does the spin-orbit ...
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Incredible electron drift velocity in atomic thin layer of graphene?
Free electrons in atomic thin layers of graphene behave more like photons (Bosons) than fermions reaching incredible drift velocities and mobility which reach speeds as reported by this article in the ...
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What is the meaning of this wave function?
In these notes here the tight binding model for graphene is worked out.
The tight Binding Hamiltonian is the usual:
$$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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