Questions tagged [tight-binding]
The tight-binding tag has no usage guidance.
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Strain field and periodic boundary conditions
Let's say I have a lattice, and I impose periodic boundary conditions. I want to construct a tight-binding model on a strained lattice, and I can determine the change in the hopping parameter based on ...
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0answers
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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 ...
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1answer
69 views
Momentum Space Representation of the Tight Binding Hamiltonian
I am trying to represent the tight-binding Hamiltonian
\begin{equation}
\hat{H}_{TB} = \sum_{\sigma} \sum_{\alpha,\beta} \sum_{\mathbf{R}_1,\mathbf{R}_2}
t^{\alpha,\beta}_{\mathbf{R}_1,\mathbf{R}_2}
\...
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1answer
37 views
Is the tight binding model an effective free fermion model?
The tight-binding Hamiltionian has the form
$$H=-t\sum_i\left(c_i^\dagger c_{i+1} + c_{i}c_{i+1}^\dagger\right)$$
But does this mean that it can be represented in the form of free fermion modes?
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Identity when Diagonalising Single-Particle Hamiltonian
Sorry the title is not precise; wasn't sure how to make it so (this is perhaps a straightforward question).
The following is an identity I see quite often when reading lecture notes about ...
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Is the SSH model a tight binding model?
Sorry if this is an obvious question. I have trouble understanding where the Hamiltonian of the Su-Schrieffer-Heeger model comes from? May I confirm if it is from the Tight Binding Model? The creation ...
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0answers
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Gutzwiller renormalization factors
I am computing the expectation value of the kinetic term of a tight-binding model, respect to the Gutzwiller wavefunction, in the limit of infinite lattice-coordination, i.e using these constraints (...
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31 views
2D BHZ tight binding model for Quantum spin Hall insulator
I am currently reading this article : https://arxiv.org/abs/cond-mat/0611341 and want to derive the k-space tight binding model of 2D BHZ.
The tight binding model is written as
\begin{equation}
H = \...
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Physical Meaning of the Gutzwiller Constraints
I have a doubt on the constraints for the expecation values obtained by Bünemann et all.
First i want to introduce my notation
To analytically solve a tight-binding model,
\begin{equation}
\hat{H}= ...
1
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1answer
58 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 ...
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0answers
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Loschmidt Amplitudes In Tight Binding Models
I am trying to understand the calculation in this paper which experimentally looks at dynamical phase transitions in a driven (shaken) haldene-like model.
The definition of the Loschmidt Amplitude is ...
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1answer
35 views
Tight-binding extended attractive Hubbard model for unconventional superconductivity
BCS theory suggest that the effective attraction between two electrons, due to electron-phonon coupling, is in momentum ($k-$)space. However, in literature, (real space) tight-binding Hubbard model ...
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1answer
65 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.
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0answers
36 views
1 Dimensional quantum chain
I had a question about the transformation of the hamiltonian of a 1 dimensional quantum chain, from real space to reciprocal space. Using the given discrete fourier transforms.
$\hat{H}$ = $\sum_j$ $\...
4
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1answer
57 views
What is nesting/ what is a nesting vector in energy contour plots?
I am making different plots for a 2-d non-interacting tight binding Hamiltonian
$$ H = - t \sum_{<ij>, \sigma} c_{i \sigma}^{\dagger} c_{j \sigma} + h.c$$
I get the dispersion relation $$\...
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1answer
58 views
Can someone give a simple mathematical explanation of the tight binding method?
I'm trying to understand the tight binding method but I'm struggling with a lot of the mathematical formalism. A lot of the mathematical formalism I read jumps into explaining it a few too many steps ...
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0answers
60 views
Derivation of Slater and Koster Table
Im currently struggling with the description of the Slater-Koster (SK) method. I should calculate the SK table. But I do not know how they calculated the formulas. There are some other references ...
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0answers
217 views
One-band 1D tight-binding model: how to find the two-particle eigenstates?
Consider the simple hopping model in second quantization,
$\hat{H} = -J \sum_{i,j=1}^\infty \left(\hat{c}_i \hat{c}^\dagger_j + h.c.\right)$
where $J$ is real and $\hat{c}_i$ are annihilation ...
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0answers
62 views
Writing the Tight Binding Hamiltonian as a Sum Over Unit Cells
Typically, the Tight Binding Hamiltonian of a lattice is written as a sum over nearest neighbours. Is there a straight forward way in which one can rewrite this as a sum over unit cells instead?
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1answer
71 views
Dispersion relation in tight binding model with even indices only
Given a tight binding model with Hamiltonian
$H= \sum_{i(even)}t[c_{i+1}^\dagger c_i+h.c]$
containing even indices only, how can we find out the dispersion relation?
Attempt:
My guess is that the ...
4
votes
1answer
533 views
Number of bands in 1D tight-binding model
I was reading about the one-dimensional tight-binding Hamiltonian (TBH) with one quantum state per atom $$H=E_0\sum\limits_{n}|n\rangle\langle n|-t\sum\limits_{n}\Big(|n\rangle\langle n+1|+|n+1\rangle\...
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1answer
591 views
Bloch Hamiltonian of a Hexagonal Lattice
As explained here (link in the first comment. couldn't post more than 2 links here!), the Bloch Hamiltonian of a lattice is obtained as
$$h_k = \sum_je^{i\mathbf{k.R_j}}h_j$$
where $h_j$ is the ...
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0answers
358 views
Can we write energy band of square lattice with vertical magnetic field?
I am interested in a square lattice with the vertical magnetic field. Without a magnetic field, we can know the energy dispersion of the square lattice easily. But, how about in case of with magnetic ...
0
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1answer
25 views
Does a core already need to be magnetized in order to establish flux in the core?
I was going through working of a real transformer and saw that there are two different branches of currents in the primary, one to magnetize the core I(m) and another whose flux links with the ...
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How to show transfer integral is a real number?
I want to know how to show transfer integral is a real number.
I am learning tight binding approach.
Now let's consider the two-dimensional system whose unit cell has two atoms (for example, ...
1
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1answer
501 views
Tight binding Hamiltonian for a slab
I want to study the surface states in a material using the tight binding model (the goal is to find surface states inside the bulk band gap). The material in question has rock salt crystal structure ...
0
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1answer
252 views
Graphene Tight binding 2D Hamiltonian
I got stuck on Homework problem, where I need to construct Hamiltonian of 2D Graphene layer and obtain Dispersion graph from it.
I already went trough a lot of materials but all I find is $2\times 2$ ...
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1answer
192 views
How can I compute the eigenstates of a tight-binding Hamiltonian describing a system?
I have the following set-up in a 3-site tight-binding system:
\begin{align}
i\hbar\frac{dc_1}{dt}&=-Ac_2,\\
i\hbar\frac{dc_2}{dt}&=-Ac_1-Ac_3,\\
i\hbar\frac{dc_3}{dt}&=-Ac_2,
\end{align}
...
1
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1answer
288 views
Green's function approach in Tight-Binding
I am studying single-particle Green's functions using Economou's textbook, and am interested in using them to calculate surface states in tight-binding models. What I don't really understand is what ...
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1answer
200 views
Symmetry of spectrum of tight binding model with quasiperiodic potential
In the Aubry-André model, a tight binding model with nearest neighor hopping and a cosine-like potential $\lambda_n = \lambda \cos(2\pi \beta n)$ (where $n$ is the lattice site, $\lambda$ is the ...
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1answer
364 views
explicit representation of creation/annihilation operators & its fourier transform (matrix form) (tight-binding hamiltonian, graphene)
While I'm a mathematician/computer-scientist myself, I've some problems trying to understand some paper about the electronic states of graphene nanoribbons modelled by the tight-binding Hamiltonian (...
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372 views
Position and type of carrier in 1st Brillouin zone
Provided the following dispersion relation for a band in a 2D crystal using the tight binding model:
E(k)=$E_0-2t_1cos(k_xa_1)-2t_2cos(k_ya_2)$
How can I identify the carrier types and their ...
2
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1answer
471 views
Getting tight binding density of states more accurately
I calculated numerically the density of states (DoS) for the 3-D tightbinding dispersion $\epsilon(k_x,k_y,k_z)=-2t\,(\cos k_x + \cos k_y + \cos k_z)$ and obtained the following plot [$t=1$ has been ...
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1answer
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Terms $\hat{c}^{\dagger}_{i\uparrow} \hat{c}^\phantom{\dagger}_{i+1\downarrow}+\text{h.c.}$ in tight-binding hamiltonians
The basic tight-binding hamiltonian consists of terms of the form
$$\hat{c}^{\dagger}_{i\uparrow} \hat{c}^\phantom{\dagger}_{i+1\uparrow}+\text{h.c.}$$
(where $\text{h.c.}$ denotes the adjoint of the ...
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0answers
372 views
Tight-binding model of diatomic solid
I am working on a problem based on Problem 1.6 in Gerald D. Mahan - Many Particle Physics, 3rd edition.
The problem:
Consider a tight-binding solid which has alternating atoms of type A and B. The ...
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1answer
416 views
What holds metal atoms together? And what accounts for the strength of metallic bonds?
From the wikipedia page for metallic bonding, I've noticed that there seem to be a few things at play:
(1) the delocalization of electrons, and
(2) the fact that there are a far larger number of ...
4
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2answers
191 views
How can localization of electrons in a solid be defined in a basis-independent way?
In the tight binding model, it's said that in a certain limit, we can regard electrons in the solid as localized to individual atoms. This statement shows up in most introductory condensed matter ...
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1answer
341 views
Which book do you recommend for extensive review of tight binding model in second quantization formalism?
I need a book that explains the tight binding model in second quantization formalism. for example by telling the meaning of the eigenfunctions of kernel of Hamiltonian in $k$ space. also explains $2$ ...
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1answer
322 views
Have edge modes of the SSH model (or Kitaev Chain) been observed?
I am putting together a presentation on topological phase transitions in 1D tight binding models for a course in Solid State Physics, and while I have found many sources for theoretical descriptions I ...
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1answer
189 views
Diagonalizable matrix tight-binding model
Given the following model for a particle on a lattice:
$$ \hat{H} = -t \sum_j[\left|\ j-2\right\rangle \left\langle j \right|+ \left|j+2\right\rangle \left\langle j \right|]$$
We introduce vectors $\...
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0answers
51 views
Finding the lowest energies of electrons in a box with a delta separator with a tight-binding model
I am asked to find the two lowest energies of a 1D situation with two electrons in two adjacent $0$-potential wells of width $L$ with infinitely high barriers and a 'coupling potential' of $V(z)=\...
0
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1answer
804 views
Slater-Koster parameter
When we use Slater-Koster parameter for tight binding model, we represent hopping integral using direction cosine (l,m,n) and bond intergral $V$.
For example, the energy between s and px orbital is ...
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1answer
730 views
Tight binding model
The origin of the phrase "nearly free" in the nearly free electron model comes from the fact that we introduce a small periodic potential in a metal lattice as a perturbation to free electrons, so ...
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0answers
203 views
Project a Bloch Hamiltonian to subspace
I have a Bloch Hamiltonian H(k) which describe a triangular lattice with six atoms inside one unite cell. This lattice is nothing but group six atoms instead of two in a honeycomb lattice. So as you ...
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2answers
356 views
Hamiltonian with periodic potential in second quantization
I'm working with the following Hamiltonian
$$\hat{H}=\int\mathrm{d}\mathbf{x}\sum_{\sigma\in\left\lbrace\uparrow,\downarrow\right\rbrace}\hat{\psi}_\sigma^\dagger(\mathbf{x})\left[-\frac{\hbar^2\...
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0answers
101 views
Total energy in tight binding methods
How to calculate total energy in tight binding methods?
The total energy is calculated as the sum of the eigenvalues of the occupied state?
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1answer
326 views
How to convert a Hamiltonian for the tight-binding model in silicene into $k$-space?
I am trying to convert the Hamiltonian from the paper "A topological insulator and helical zero mode in
silicene under an inhomogeneous electric field" (also on arXiv) into $k$-space.
$$
\begin{array}{...
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0answers
415 views
Tight binding Hamiltonian in the k-space
I want to find the band structure of this 2 dimensional lattice which isn't completely flat:
Using a tight binding model.And take unit cells as they are shown in the figure. And assuming that each ...
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0answers
49 views
Derivation of effective mass equation in carbon nanotubes
I am trying to reproduce the calculations in the paper here by Ando and Nakanishi and am already stuck on equation 1. It is stated that in the vicinity of $\epsilon=0$ the amplitude of the ...
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1answer
347 views
Paradox in topological phase of SSH model
Consider the SSH model, i.e. the dimerized tight-binding model with Hamiltonian
$$H = \sum_i (t+\delta t) c^\dagger_{Ai} c_{Bi} + (t-\delta t) c_{A(i+1)}^\dagger c_{Bi} + \text{h.c.}.$$
This describes ...
