Questions tagged [tight-binding]

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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 ...
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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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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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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 ...
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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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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 ...
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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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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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{...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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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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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 ...
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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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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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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 ...
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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} \...
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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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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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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 = \...
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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}= ...
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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 ...
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1answer
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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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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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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. $\hat{H}$ = $\sum_j$ $\...
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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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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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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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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 ...
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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 ...
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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\...
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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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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 ...
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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, ...
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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 ...
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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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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} ...