Questions tagged [tight-binding]
The tight-binding tag has no usage guidance.
100
questions
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Extension of the the single-fermion tight-binding model to multiple-fermions clusters
The tight-binding model describes the properties of tightly bound single fermions crystals. Has the model been extended to multiple tightly bound fermions per site? In other words, I'm interested in ...
1
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1answer
45 views
Spin operator in tight-binding model
While reading Altland and Simons (Condensed Matter Field Theroy, p. 60), I came across the following problem. In tight-binding models, the exchange interaction contributes to the Hamiltonian in a form ...
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0answers
30 views
Constructing a band structure analog for a system with open boundaries
In systems with periodic boundary conditions, we can use translation invariance to find simultaneous eigenstates of total energy and momentum. With open boundary conditions, this symmetry is destroyed,...
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1answer
38 views
Interpreting Slater-Koster files for DFTB
I have a question about interpreting .SKF files, I am using these parameters to model defective graphene,
when I use parameter set given here: dftbBaby/C-C (I think this is from Hotbit) or the ...
2
votes
2answers
478 views
Spin-orbit coupling Hamiltonian in tight-binding models
Consider spin-orbit coupling (of strength $\lambda_1$) on lattice, with the below Hamiltonian
$$H = i \lambda_1 \sum_{<ij>} ~\frac{E_{ij} \times R_{ij}}{|E_{ij} \times R_{ij}|} \cdot \sigma ~...
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0answers
21 views
In tight binding model, why can the Hamiltonian be expressed in terms of the creation and annihilation operators of atomic orbitals?
In the second quantization formalism of tight binding model, why can the Hamiltonian be expressed in terms of the creation and annihilation operators of atomic orbitals when they are not orthogonal? I ...
1
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1answer
85 views
Simplest tight binding
My lecturer is teaching the Bloch theorem, which I saw many years ago in Griffiths textbook on Quantum mechanics. I cannot recognise it in the form that my lecturer is using.
We are studying a tight-...
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0answers
48 views
Tight Binding Hamiltonian simulation help
Just want to make sure I am setting this up correct.
I am trying to find the eigen energies for a tight binding Hamiltonian, let's say with nearest neighbor hopping term $t$. We can solve for the ...
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0answers
33 views
Derivation of LCAO/Tight-binding method for energy bands
I'm having a bit of trouble properly understanding the LCAO/tight-binding method for calculating the band structure of metals. I'll try to go through the derivation/explanation given in our lecture ...
0
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1answer
131 views
Electron and holes in tight binding Hamiltonian on two sublattices
Background
Say that I have a tight binding Hamiltonian (with spinless fermions) of the form
$$H = - 2t \sum_{ij} (c_i^{\dagger} c_j + h.c) - 2\mu \sum_i c^{\dagger}_i c_i$$
where we only sum over ...
0
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0answers
63 views
Slater Koster Tight Binding Method
I am reading the paper (J. C. Slater and G. F. Koster, Simplified LCAO Method for the Periodic Potential Problem, Phys. Rev. 94, 1498, also here) about Slater Koster tight binding method. I can ...
2
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3answers
194 views
Tight binding model contradiction
I have been studying recently the tight binding model and there is a point I cannot understand. First, it starts from the idea that the electrons belong to the atom more than to the crystal, so they ...
0
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1answer
33 views
Is the Hubbard 2-body potential non diagonal in both direct and momentum space?
I was looking at the following table from these lecture notes:
http://www.lassp.cornell.edu/clh/Book-sample/1.1.pdf
And was wondering if the 2-body potential is always non-diagonal, or if there is a ...
1
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0answers
27 views
Low energy continuous model to lattice model(tight binding) in solid physics state
It is widely employed to link the low-energy continuous model to lattice tight-binding model using this strategy as shown in Section IIA Page.1063 of RMP 83, 1057 :
Just replace $k_i$ by using $\frac{...
0
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1answer
48 views
How does the Hubbard hamiltonian change when considering a Peierls distortion (bipartite lattice)?
The following is the Hubbard contribution to the hamiltonian in the Hubbard-Tight Binding model.
$$H_{hubbard}=U \sum_i n_{i \uparrow}n_{i\downarrow}$$
where $n_{i \sigma}=c_{i\sigma}^\dagger c_{i\...
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0answers
10 views
How many bands does one expect to get in the band diagram for a 4 atoms, 12 total orbitals and 15 valence electrons in the Tigh Binding Aproximation?
The question, as the title say, refers to understand how many bands do we expect to get in the band diagram for a solid with 4 atoms, 12 total orbitals and 15 valence electrons in the Tigh Binding ...
0
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1answer
56 views
Why is there a need to add the complex conjugate in the tight binding hamiltonian?
So we start with the following hamiltonian describing non-interacting free fermions:
$$ \hat{H}_{\text{free}}
= \sum_{i,j,\sigma}\tilde{t}_{ij} \hat{c}_{i\sigma}^\dagger\hat{c}_{j\sigma}.$$
Then ...
0
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0answers
55 views
Harper-Hofstadter model in symmetric gauge
If I have l a square lattice, with the total flux = $\pi$, I can work in the symmetric gauge, which will have my vector potential be $A = \frac{\pi}{2}(-y,x)$. In a tight-binding model with Peirels ...
1
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1answer
71 views
Why hopping amplitude with no negative sign?
I'm learning SSH model now.
I notice people use tight-binding model of this form,
$$H=t\sum_{<i,j>} c_i^†c_j+\mathrm{H.c}$$
where $t>0$ in Lecture 1 : 1-d SSH model, or A Short Course on
...
0
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1answer
81 views
Tight Binding Hamiltonian for graphene
The TB Hamiltonian for the tetragonal lattice is
$ \hat H_0 = -J\sum_{m,n} (\hat a_{m+1,n}^\dagger \hat a_{m,n}+\hat a_{m,n}^\dagger \hat a_{m,n+1}+h.c.) $
How can this be derived for the hexagonal ...
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0answers
81 views
Calculating topological invariants under different conventions of tight-binding models
There are two widely used conventions to construct the Bloch-like basis in a tight-binding model [1].
Convention I:
$$
\psi_\mathbf{k}=\frac{1}{\sqrt{N}}\sum_{\mathbf{R},j}c_j(\mathbf{k})e^{i\mathbf{...
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0answers
33 views
Wave Function of the Tight Binding Model
The Gutzwiller wavefunction, i talked in brief in this other question, is introduced to compute the expectation value of the Hubbard Hamiltonian.
It is composed by a uncorrelated Slater determinant (...
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0answers
53 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
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72 views
Slater-Koster parameter for SC
I want to use SK method to calculate the interatomic matrix element for $P_{y}$ and $P_{z}$ for the nearest, second and third neighbors in simple cubic crystal.
based on paper written by Slater-Koster ...
0
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0answers
65 views
Tight binding hopping
The definition of the tight-binding model is that the electrons are sited on certain points(the Wannier centers) and that they can hop in linear paths, when we refer to sites that belong to the ...
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0answers
72 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 ...
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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
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1answer
151 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}
\...
0
votes
1answer
111 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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56 views
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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1answer
96 views
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
169 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 = \...
2
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0answers
105 views
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
97 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
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1answer
85 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 ...
2
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1answer
274 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
46 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
102 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 $$\...
0
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1answer
84 views
Can someone give a simple mathematical explanation of the tight binding method?
I'm trying to understand the tight binding method but I'm struggling with a lot of the mathematical formalism. A lot of the mathematical formalism I read jumps into explaining it a few too many steps ...
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0answers
133 views
Derivation of Slater and Koster Table
Im currently struggling with the description of the Slater-Koster (SK) method. I should calculate the SK table. But I do not know how they calculated the formulas. There are some other references ...
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0answers
265 views
One-band 1D tight-binding model: how to find the two-particle eigenstates?
Consider the simple hopping model in second quantization,
$\hat{H} = -J \sum_{i,j=1}^\infty \left(\hat{c}_i \hat{c}^\dagger_j + h.c.\right)$
where $J$ is real and $\hat{c}_i$ are annihilation ...
0
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1answer
129 views
Dispersion relation in tight binding model with even indices only
Given a tight binding model with Hamiltonian
$H= \sum_{i(even)}t[c_{i+1}^\dagger c_i+h.c]$
containing even indices only, how can we find out the dispersion relation?
Attempt:
My guess is that the ...
4
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1answer
739 views
Number of bands in 1D tight-binding model
I was reading about the one-dimensional tight-binding Hamiltonian (TBH) with one quantum state per atom $$H=E_0\sum\limits_{n}|n\rangle\langle n|-t\sum\limits_{n}\Big(|n\rangle\langle n+1|+|n+1\rangle\...
0
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1answer
992 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 ...
5
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0answers
620 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
30 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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0answers
77 views
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
662 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
439 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
289 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}
...
