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
0answers
19 views

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?
1
vote
1answer
122 views

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 ...
0
votes
0answers
40 views

Berry phase in graphene

I was recently reading about the non-Abelian Berry phase and understood that it originates when you have an adaiabatic evolution across a degenerate manifold of states. Am I correct in thinking that a ...
1
vote
2answers
53 views

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 ...
0
votes
1answer
106 views

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), ...
0
votes
0answers
19 views

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 ...
0
votes
0answers
7 views

Is there spatial separation between quantum hall edge channels if there are more than one?

In 2-d electron systems, for example, when a piece of graphene is tuned to N=2 quantum hall state, the hall conductance should be $6e^2/h$. So there must be more than one edge channels? My question is,...
1
vote
0answers
40 views

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 ...
0
votes
0answers
21 views

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 ...
0
votes
0answers
30 views

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 ...
0
votes
0answers
18 views

What are the limits of spin speed on a graphene ribbon?

In my previous question, link below, I asked what are the limitations on spinning an object with the goal of achieving relativistic speeds at the edge of the spinning object. In the comments, someone ...
0
votes
0answers
28 views

Method for making graphene plausible?

Gallium does not wet quartz or graphite. I’m pretty sure graphite doesn’t stick to quartz (or not well) especially if smooth. So what if on a round flat plate of polished fused quartz you set a small ...
0
votes
1answer
59 views

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-...
1
vote
0answers
34 views

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 ...
0
votes
1answer
81 views

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 ...
1
vote
0answers
27 views

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 ...
2
votes
0answers
124 views

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^...
0
votes
0answers
29 views

What “manifold in band parameters ” means?

I was reading an article https://arxiv.org/abs/0907.0500 in which they write about manifold in band parameter ,like in first line in my picture , and then they call it band parameter . can some ...
2
votes
0answers
47 views

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?
1
vote
0answers
154 views

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\\ \...
0
votes
0answers
23 views

Chiral tunnelling in graphene

I am trying to reproduce the results of this paper: Chiral tunnelling in single and bilayer graphene. I have done all the math but I couldn't figure out how the $s(=sgn(E))$ and $s'(=sgn(E-V_0))$ ...
1
vote
0answers
52 views

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
0
votes
0answers
58 views

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 ...
8
votes
1answer
349 views

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 ...
0
votes
1answer
51 views

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 ...
0
votes
0answers
20 views

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 "...
1
vote
0answers
16 views

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 ...
0
votes
0answers
71 views

Peierls phase in graphene

In the introduction of the paper presented here, a derivation of the Peierls phase is presented, using a Wannier base of eigenfunctions and the Kohn-Sham Hamiltonian. After it symbolises the hopping ...
0
votes
1answer
86 views

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 ...
2
votes
1answer
209 views

Derivation of the Berry Curvature and Bloch Magentic Moment in Graphene

I am attempting to derive equations 2 and 6 from Xiao et al. paper "Valley contrasting physics in graphene" (Link to paper). The Hamiltonian for graphene with a staggered sublattice potential (in ...
2
votes
1answer
386 views

What is energy band gap?

Explanations for graphene's high electrical conductivity often discuss energy band gap. What is energy band gap and how does it relate to the conductivity of a material?
1
vote
0answers
59 views

Lattice hopping at boundary in graphene lattice with magnetic field

Let's say I have a tight binding model for graphene, where I have a two-atom basis and three nearest neighbor vectors. I've applied a homogenous magnetic field $B$ in the z-axis, and can take the ...
0
votes
2answers
37 views

Can we call a hexagonal system with two different atoms as inversion symmetric?

Graphene is two-dimensional honeycomb crystal lattice with the two Carbon atoms in its unit cell. Clearly, it is inversion symmetric. But, suppose we have two different atoms in the hexagonal system ...
1
vote
0answers
27 views

Graphene with onsite coulombic term

Why is it that when you add the onsite coulombic term in graphene,the mass term is multiplied by Pauli matrix in z direction?Had it been multiplication by identity matrix,then youget the same diagonal ...
2
votes
0answers
38 views

Stability criterion for leapfrog in relativistic physics

I am doing a 2D MD simulations of charge carriers in graphene using the Leapfrog algorithm. I am trying to prove that, in some specific cases (when distance between particles is small), the method is ...
0
votes
2answers
176 views

Why do we consider spin degeneracy in graphene quantum hall effect and not in the conventional one?

When dealing with quantum hall effect in graphene we say that each landau level (with $n\neq 0$) has 4 times the degeneracy of a simple landau level derived for an electron in a magnetic field because ...
1
vote
0answers
31 views

Interpretation of tilted energy dispersion cones in a Dirac Semimetal

The energy dispersion of a Dirac semimetal with an effective Dirac Hamiltonian of the form $$H=v_x \sigma_xk_x+v_y\sigma_yk_y+v_t\sigma_0k_y$$ is tilted in the y direction and the tilting increases ...
1
vote
1answer
95 views

Is numerical lattice wavefunction smooth? — graphene tight binding case

I tried to follow exactly Sec. II.K [page 112-113, Hamiltonian after Eq. (113)] of the standard Review of Modern Physics paper on graphene, which is a tight-binding model of a graphene stripe under ...
2
votes
1answer
271 views

Why does the 2D hexagonal lattice have a different tight binding band structure than Graphene?

Here you can find band structures for various tight binding models. I was wondering, why the 2-D hexagonal lattice has a different band structure than Graphene, even though they have the same lattice.
0
votes
1answer
101 views

$4\times4$ Dirac Hamiltonian in Graphene

When linearizing the Hamiltonian of Graphene in reciprocal space around $\vec{q} = \vec{k}-\vec{K}_\pm = \vec{0}$, where $\vec{K}_\pm$ are two independent Dirac points, one can get two Hamiltonians, ...
3
votes
0answers
233 views

How to determine the degree of how high a symmetry of high-symmetry points in the first Brillouin zone?

For exmple, we have a hexagonal lattice with hexagonal Brillouin zone, shown in the picture The points $\Gamma$, K, M and $\Lambda$ are high symmetry points. Now, $\Gamma$ point is the highest-...
1
vote
1answer
71 views

Help me understand a little bit about this abstract

I was reading a story on phys.org: Holographic image of a black hole proposed in a graphene flake (Lisa Zyga, 25 July 2018, phys.org) From there I followed a link to the paper Quantum ...
2
votes
1answer
370 views

Why are the electrons in graphene massless?

I was reading Tommy Ohlsson's book on Relativistic Quantum Mechanics where he goes to a little digression on electrons and holes in Graphene. He claims that electrons and holes in Graphene can be ...
5
votes
0answers
116 views

Relativistic scattering off Dirac delta potential

Consider the case of a relativistic electron on a graphene lattice described by the Hamiltonian $$ \mathcal{H} = v\begin{pmatrix} 0 & p_x+ip_y \\ p_x-ip_y & 0 \end{pmatrix}, $$ where $v$ is ...
1
vote
1answer
38 views

Heating a monolayer atop a substrate with a laser

This problem is briefly mentioned in various research papers I'm reading, but it's never addressed in detail. The monolayer is attached atop a substrate as shown below The centre of the monolayer ...
0
votes
0answers
64 views

Conserved quantity in Graphene

The computation of the band structure of Graphene basically leads to the diagonalization of the following Hamiltonian: $$ H = -t \left( \begin{array}{cc} 0 & \epsilon(\vec{k}) \\ \epsilon^*(\vec{...
1
vote
1answer
97 views

What does negative filling mean for Landau levels?

I'm trying to read this paper, but I've never heard of Landau levels like $\nu=-1.$ What does it mean?
1
vote
1answer
136 views

Helicity in Graphene

In Graphene, there are two independent points, the Dirac points, where the conduction and the valence band touch. Let's call these points $K_+$ and $K_-$. In a low-energy description, the Hamiltonians ...
1
vote
1answer
39 views

Can the graphene's conductivity be explained using only orbitals?

I am trying to find a 'easier' or more 'intuitive' way to calculate the conductivity of graphene. I want do this by using atomic or molecular orbitals. Anyone have a clue about how this can be done? ...
2
votes
0answers
269 views

Calculate Chern number from band structure

When we use a tight-binding approach in order to calculate the band structure of electrons on a 2D honeycomb lattice such as Graphene we find that there are two energy bands touching in six points, ...

1
2 3 4 5