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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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Why the Moire Brillouin zone (BZ) of twist bilayer graphene is hexangular?

Usually, we have the definition of the basis vectors of Moire BZ, which is \begin{align} \boldsymbol{b}_1^m=\boldsymbol{b}_1-\boldsymbol{b}_1^\theta,\quad\boldsymbol{b}_2^m=\boldsymbol{b}_2-\...
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Expression for energy dissipation in electron hydrodynamics

I was looking at the paper Hydrodynamic Description of Transport in Strongly Correlated Electron Systems by Andreev, Spivak and Kivelson. The paper covers how resistivity in an electron fluid depends ...
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Emergence of Dirac Cones: Triangular Lattice vs. Honeycomb Lattice

I'm reading the paper 'Honeycomb Lattice Potentials and Dirac Points' by Fefferman&Weinstein. To my understanding they claim that the existence of Dirac Cones at K/K' points is entirely determined ...
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Semiconductor-graphene-semiconductor junction

In the literature, I've found Graphene-semiconductor junctions are treated as Schottky junctions. So by reverse-biasing a graphene n-semiconductor junction, we inject carriers into the graphene ...
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How does the Fermi level of graphene change if it is placed in a biased pn junction or in a plate capacitor?

I ran into a problem on which I can't really find any solutions in literature. I am looking at a Graphene sheet that is sandwiched in a biased pn junction (current flows orthogonal to the Graphene ...
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Graphene dispersion at Dirac points

After deriving the dispersion relation of graphene: $$ E(k) = \pm t \sqrt{3+2\cos{(k_y \sqrt{3} a)} + 4\cos{\bigg(\frac{3a}{2} k_x \bigg)} \cos{ \bigg(\frac{\sqrt{3}}{2}a k_y \bigg)} } $$ how do I see ...
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Free electron in weak periodic potential (Graphene)

I am trying to model the potential of 2-D graphene monolayer as a sum of delta functions. I don't know where to begin. Also, after defining it, I also wish to obtain the energy gap and fermi surfaces. ...
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Why does graphene tend to break during mechanical exfoliation?

Is there any specific physical reason that can explain why graphene produced by tape exfoliation tends to break into fragments instead of remaining as a original size perfect piece? Some of the ...
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Relationship between drift velocity and processor speed

Does having higher drift velocity for electrons lead to faster processors? If yes, how? The speed of processors is higher or lower depending on the speed of the on off states, i.e. the speed of the ...
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Why are zero-modes preserved on turning on coupling in twisted bilayer graphene model?

In the paper https://arxiv.org/abs/1808.05250 on page 3, they talk about how when the parameter $\alpha$ in the Hamiltonian in Eq. (5) equals $0$, we get zero modes at the Dirac points K and K’. This ...
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How does the $z$-component spin operator change while you rotate the Dirac cone

Normally, we have the $z$-component Pauli matrix $\begin{pmatrix} 1 & 0 \\ 0 & -1\end{pmatrix}$. For the graphene with a magnetic field, the Hamiltonian is \begin{align} \hat{H} = v_{F} \left(\...
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Interpreting the van der Waals Energy Discrepancy between $\rm MoS_2$ and Graphene Layers in Computational Simulations

I am conducting computational simulation tests and have observed that when simulating systems like molybdenum disulfide ($\rm MoS_2$), the interaction between layers (S-S interaction) is quite strong, ...
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What is the Chern number of twisted bilayer graphene without hBN substrate?

I am approaching at the study of topological materials and I need help to understand the role of Berry curvature in the twisted bilayer graphene. The raise up of the Moire lattice and consequently the ...
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How does graphene Fermi velocity $v_F$ link to the envelope propagation?

my questions stemmed from reading the article in Physica E. Vol. 86, 10-16. (https://doi.org/10.1016/j.physe.2016.10.014) Why does the graphene Fermi velocity $v_F$ appear in Eq.(11) in this article,? ...
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Effective Hamiltonian for twisted bilayer graphene

I'm trying to follow along with this paper, which reviews the Bistrizer--MacDonald model of twisted bilayer graphene. I'm particular, I'm struggling to derive their Eq. (100). Starting from the ...
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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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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 ...
Muhammad Hasan's user avatar
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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 ...
IDs Just's user avatar
2 votes
1 answer
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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'...
prashanth's user avatar
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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, ...
mtooling's user avatar
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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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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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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 ...
Jyminn Yu's user avatar
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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 ...
Zhang Ge's user avatar
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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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