# What is Tight binding: Definition and 46 Discussions

In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. The method is closely related to the LCAO method (linear combination of atomic orbitals method) used in chemistry. Tight-binding models are applied to a wide variety of solids. The model gives good qualitative results in many cases and can be combined with other models that give better results where the tight-binding model fails. Though the tight-binding model is a one-electron model, the model also provides a basis for more advanced calculations like the calculation of surface states and application to various kinds of many-body problem and quasiparticle calculations.

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1. ### A Can I calculate partial density of states using tight binding?

I am studying a 2D material using tight binding. I calculated density of states using this method. Can I also calculate partial density of states using tight binding?
2. ### Problem on SSH Model Tight Binding Approach

I'd like to proceed in a linear fashion, taking each part on one by one. For the first part, we can write the Hamiltonian as ##H = \sum_{n}^{N} w(c_{An}^{\dagger}c_{Bn}+c_{Bn}^{\dagger}c_{An})+v(c_{Bn}^{\dagger}c_{A(n+1)}+c_{A(n+1)}^{\dagger}c_{Bn})##. We can convert the creation and...
3. ### A Empirical tight-binding sp3s* band structure of semiconductors

I'm simulating on code the tight-binding sp3s* bandstructure of certain semiconductors, such as GaAs, AlP, InP, ZnSe, etc. with spin-orbit coupling at a temperature of T = 0 K but I'm having trouble at finding the corresponding spin-orbit splitting parameters. For example, I've found in this...
4. ### The Cooper Problem in tight binding

We have a one dimensional lattice with a lattice constant equal to a (I'm omitting vector notation because we are in 1D). The reciprocal lattice vector is k_n=n\frac{2 \pi}{a}. So to get the nearest neighbour approximation I need to sum over k = -\frac{2 \pi}{a}, 0, \frac{2 \pi}{a}. If I...
5. ### A potential well with 3-fold reflection symmetry

When we are talking about Bloch's theorem and also the tight-binding approximation, we can use them to help finding eigenstates of a system. However, I am so confused how to apply it in this case (below is my homework) and don't even know how to start it... All I understand about the Bloch's...
6. ### A Green's function calculation of an infinite lattice with periodicity in 1D

I am currently trying to compute the Green's function matrix of an infinite lattice with a periodicity in 1 dimension in the tight binding model. I have matrix ##V## that describes the hopping of electrons within each unit cell, and a matrix ##W## that describes the hopping between unit cells...
7. ### Assignment on the tight binding model

Summary:: Due tight-binding model I derived the energy spectrum of the particle, showing that it comprises three energy bands E+(k), E−(k) and E0(k)=0. Now, I have to find the dispersion laws. Why do I have a flat energy band? What is its physical significance?. Also, what happens to the...
8. ### A Graphene wavefunction expressed in tight binding form

In the framework of tight binding approximation, does the wavefunction for atom A (or B) has two spinorial components(2 components) in "real space"? If so how does this spinorial component propagate in the graphene?
9. ### A Half filling? Free electron gas? 2D tight binding lattice?

It is well known that the 2D free electron gas fermi momentum can be expressed as follows, k_F=\left(2\pi n\right)^{1/2} where n is the electron surface density. Assuming this 2D electron system can be considered as 2-D tight-binding square lattice whose eigenergy can be written as...
10. ### I Understand Tight Binding Method: Coulomb Potential, 2D Case & More

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 ahead of where my understanding is. I understand it's an approach to calculating the band...
11. ### I Bloch Waves within Tight Binding Approximation

So I thought I understood something well, and then I went to explain it to someone and it turns out I'm missing something, and I'd appreciate any insight you might have. If I think about Bloch's theorem, it states that ψk(r)=eik⋅ruk(r) where uk has the periodicity of the lattice. If u is...
12. ### Electron distribution using tight binding band structure?

Hi everyone, I am just wondering how to calculate electron distribution using tight binding band structure for a system like graphene or any other solid. So the goal is to get |\psi(r)|^2 which \psi is the band state and it is the linear combination of Bloch sum...
13. ### I Dispersion relation in tight binding model

Hamiltonian of tight binding model in second quantization is given as H = -t \sum_{<i,j>} a_i^{\dagger} a_j After changing basis it is H = \sum_{\vec{k}} E_{\vec{k}} a_{\vec{k}}^{\dagger} a_{\vec{k}} where E_{\vec{k}} = -t \sum_{\vec{b}} e^{i \vec{k} \cdot \vec{b}} where \vec{b} is a nearest...
14. ### Tight binding model (covalent bonding)

Homework Statement (linear combination of atomic orbitals): Lets consider two atoms which are bond together with a covalent bond. Let's consider any sets of wavefunctions |n\rangle for n=1,2,...,N. Let's call orbital |1\rangle around nucleus 1 and orbital |2\rangle around nucleus 2 and so on...
15. A

### Tight binding for graphene pz orbital

Can anyone explain what is tight binding method . I don't understand much .for solids mostly for graphene with one atom per site
16. ### Second Quantization Tight Binding Model of Rashba Spin-Orbit

Resolved. (not sure how to delete the entire post)
17. ### Tight Binding Wave Functions

Dear all, Could somebody please, indicate me some tutorial, in order to generate a 3D grid to plot the wave function using the Hamiltonian eigenvalues and the slater type orbitals ? Thanks in advance, Wellery
18. ### A question about band structure silicene by tight binding

Dear forum people, I know that electronic properties silicene is the same graphene but i can not figure out how can I plot band strcture silicene. I want to plot that in the following path: K→Γ→M→K
19. ### Problem With solving the Eigenvalues of Tight Binding Method

Dear All, this is my first post on this forum and hopefully I can get what I want. . I am trying to build the band structure of graphene using the tight-binding method based on slater-koster correction. I use a special code to construct both Hamiltonian and overlapping matrix. I have seen when...
20. ### Tight binding dispersion for graphene

Hi I have Hamiltonian matrix and overlap matrix. How to calculate tight binding dispersion for graphene in matlab? I would be appreciated if could some one give me a hand on my problem.
21. ### Coupling to an electric field in a tight binding model

Hi i'm looking for some references (prefer books) or explanations as to how one couple electrons so an EM field in a second quantized formalism tight binding model. from what i know, one need to replace the hopping parameter with the same parameter multiplied by an exponent of the line integral...
22. ### Tight binding s-orbital for 2D binary compound

Hi guys! I'm new to the forum, i hope you can help me with this trouble! it really is important =D i have a 2D binary compound AB (made of one of the 100 family of planes of a rocksalt structure) and i am asked to "consider a single s-orbital on each atom (atomic energies Ea,Eb) and nearest...
23. ### Tight Binding Model: mathematics

From the textbook of Omar: Can someone explain me the summation of this? I simply don't get it? Thanks in advance.
24. ### How Does the Fermi Surface Form a Perfect Square in a 2D Tight Binding Model?

On the attached file the tight binding dispersion for a 2d square lattice is described. It is then assumed that the fermi surface is a square. My question is: How can it ever be a perfect square when the dispersion looks as it does. Also can someone explain: Why does the half filled case...
25. ### Tight Binding Hamiltonian and Potential (U)

Hi All, Greetings ! Here is what I wish to know. Specifying a tight binding hamiltonian requires values of potential (U). Consider a 3d solid. If I have potential profile in x direction (U1, U2, U3...so on) can I directly plug in these U values into the tight binding hamiltonian or do I...
26. ### Tight binding in graphene (complex energy?)

Hi, I'm a 4th-year physics undergrad and I have a question about calculating the band structure of graphene using tight binding. Following the calculation here...
27. ### Understanding tight binding model

Explain to me the Fig 10.6 given on page 184 in Ashcroft and Mermin. How is line along gamma k not doubly degenerate and line along gamma L doubly degenerate ?
28. ### Help with the Tight Binding model

Hi everyone, I'm trying to fit the Tight Binding molecule for a more complicated system, so I'm first trying to understand it for a simpler one, graphene. I've read several guides but they're all confusing me. Right now, I'm trying to understand the graphene example on this site. My biggest...
29. ### Using Density Functional Theory to make a Tight Binding model?

Hi all, A professor asked me to do something, but I'm not quite sure what he means -- He asked me to use Density Functional Theory (DFT) calculations of the band structure of a certain crystalline metal and adjust the matrix elements of a Tight Binding (TB) model to make a "minimal" TB model...
30. B

### Tight binding - evaluate integral

Homework Statement The energy of an electron within a band as a function of its wavevector is given by the tight-binding expression (in one dimension), E(k)=-\alpha-\gamma\Sigma_{m} exp (-ik\rho_{m}) (a)What are typical expressions for integrals \alpha and \gamma? (b) Evaluate the...
31. ### Tight binding method for a 1D crystal with a diatomic basis

Hi, I'd be most grateful for any help regarding the following problem: Consider a 1D crystal with 2 atoms in a primitive cell (let's call them atoms A and B). Each atom has only one valence orbital denoted as \left|\psi_A(n)\right> and \left|\psi_B(n)\right> respectively. Show that the...
32. ### Tight Binding Hamiltonian for Graphene

Hello, I am trying to write a program that will automate the creation of a tight binding Hamiltonian matrix for armchair cut graphene. However, I have almost no experience coding and would need some help to get started. This would be assuming that the energy between nearest neighbor carbon...
33. ### Tight Binding Description of Graphene (Hamiltonian and Overlap Matrix)

http://edu.ioffe.ru/register/?doc=galperin/l3pdf2.tex I don't understand how do you get from equation 21 to 22? How did the summations of exponentials becomes cosine functins?
34. ### Tight binding hamiltonian matrix

Can somebody explain to me why, when we work with fermions, the tight binding Hamiltonian matrix has a form 0 0 -t -t 0 0 +t +t -t +t 0 0 -t +t 0 0 the basis are |\uparrow,\downarrow>, |\downarrow,\uparrow>, |\uparrow\downarrow,0>, |0,\uparrow\downarrow>, Why there is +t and -t? (I...
35. ### Hopping Probabilities in Tight Binding Model

We recently covered the tight binding model. I have a question from an early lecture regarding sign conventions for the hopping parameter t(T). It was explained that t>0 due to MO theory. I agree and understand why; orbital overlap. It was then stated that tnn<0; that is, tnn=-t. I am not...
36. ### Tight Binding Model: Reference Book for Band Structure

Can anyone give a reference to book in which the model of tight binding is well explained. This model is used to find band structure of metals and semiconductors. I'm interested in a book which states all needed assumptions and gives logically consistent mathematical reasoning explaing why...
37. ### Tight Binding calculation of band structure

Dear all, I want to calculate the band structure of graphene for a unit cell with 8 atoms in the Tight Binding approximation. There is no problem about drawing the band structure for a unit cell with 2 atoms. But by increasing the unit cell size, first brillouin decrease and there is a gap in...
38. ### How Do You Construct a Tight Binding Hamiltonian for a 2X1X1 GaAs Supercell?

Hi I am trying to construct the tight binding Hamiltonian for 2X1X1 GaAs supercell in SP3S* model and to study band folding. I am a newcomer to this field so kindly reply me how and where to start I know that there would be 20 orbitals in the supercell unit cell, 10 in the first primitive cell...
39. ### Supercell Tight Binding: Understanding and Troubleshooting

Hello all, I have been having trouble getting my tight binding code to work. For those interested, I am using an spds* orbital basis set on silicon and coding in matlab. My largest problem is that I simply cannot find out what is wrong with my code so I am inclined to think that I have...
40. ### Tight binding in cubic crystals

\phiHi all, I would like to make band structure calculations with tight binding method and I start reading about this method from Ashcroft - Mermin, Chapter 10: The Tight Binding Method and try to solve the problems at the and of the chapter. In problem 2 a. As a consequence of cubic...
41. ### Tight binding model, help please

Homework Statement In the tight binding model, (E=Eo + alpha + (2gamma coska)), how are parameters alpha and gamma affected if the lattice spacing, a, is increased? I know the equations for gamma and alpha but can't type them in here because they involve integrals and I don't know how to...
42. ### Transmission function(probability) T(E) in tight binding

I am working on tight binding formulation of CNTs. The transmission function T(E), which is the trace of the product of the lead self energies and the retarded and advanced green's function. This value is a complex entity. T(E) needs to be calculated at different energy levels and then...
43. ### Solid State in tight binding approximation, Brillouin zone, Fermi

Hello, In few days, I have an examination, and I still have some dark zone in my head! If somebody could help me by giving me some advices/answers/way of reflexion/books to consult, it could be very great! Here is my questions: How to determine energy levels and wavefunction of the...
44. ### Tight binding (FCC structures)

I'm reading my lectures on TBM and I don't understand the following thing: \omega(\overrightarrow k)=\omega_0-4t\cdot[\cos(k_xa/2)\cos(k_ya/2)+...] It's related to FCC structures, in which the number of Nearest Neighbors (Z) of an atom is equal to 12. Basically the three dots at the end...
45. ### Tight binding model and bandwidth

According to tight binding moment, for BCC crystalographic structures (such as Fe), energy E depends on wave vector kx, ky, kz: E(x) = const - 8t cos(kx * a/2)*cos(ky * a/2)*cos(kz * a/2), where t>0 is the model parameter. What is the bandwidth W in terms of parameter t? Can you find kx, kz, and...
46. ### Investigating Logarithmic Singularity in 2D Tight Binding Approximation

Homework Statement Given some dispersion relation for the tight binding approximation in 2D: e(k_x,k_y) = -2t_1[cos(k_x*a)+cos(k_y*a)]-4t_2[cos(k_x*a)cos(k_y*a)] Show that the density of states has a logarithmic singularity for some choice of parameters t_i. Homework Equations g(e)de=g...