# Questions tagged [tight-binding]

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### What's the difference in chemical potentials between nearly free electron model and tight-binding model?

In nearly free electron model, we know that when temperature is zero, the chemical potential $\mu$ is same as the Fermi energy $E_F$, $\mu=E_F$. For a good metal, $E_F$ is roughly $10\mathrm{eV}$, so ...
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### Tight binding hamiltonian graphene [duplicate]

I'm stuck on solving a question regarding the tight-binding hamiltonian for graphene. I have been given a hamiltonian that looks like this (where the spin has been omitted since hopping is independent ...
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### Tight-Binding Hamiltonian Graphene

I'm stuck on solving a question regarding the tight-binding hamiltonian for graphene. I have been given a hamiltonian that looks like this (where the spin has been omitted since hopping is independent ...
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### How can I identify momentum eigenstates in a tight binding model with degenerate energy eigenstates?

Summary: I numerically diagonalize a tight binding Hamiltonian to get energy eigenvectors, some of which are degenerate. However, the numerically diagonalized degenerate eigenvectors are not ...
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### Impact of labeling in a bloch-crystal with orbital basis

If I'm diagonalizing a hamiltonian of electrons in a crystal that is written in the orbital basis, does it matter whether I calculate the matrix element between one atom and another atom (or the image ...
1 vote
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### Current Operators on Lattice

Peierls substitution method by taking the functional derivative of Hamiltonian can be used to determine the form of current-operator in continuum model (See Bruus-Flensberg) as well as lattice model. ...
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### Signal in hopping term in diatomic chain using the tight binding method

I am currently studying the tight binding method, and while solving solving a problem I came across something I don't understand. There are two atoms A and B, A has only type s orbitals and B has only ...
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### How the $-2t\cos(k)$ term appears in the dispersion of the $1D$ tight binding model?

I am trying to derive the tight binding dispersion relation with periodic boundary condition with $N$ lattice sites of the simplest Hamiltonian: \begin{equation} \label{ham} \tag{1} H = -t\sum\...
1 vote
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### Complex values for the dispersion relation obtained through an $s$-band only tight binding model for diamond cubic crystal

Any given atom in a diamond cubic lattice (Like Si or Ge) has four nearest neighbours at at a distance $\sqrt{3}a/4$, being $a$ the lattice constant. The translation vectors to these neighbours can be ...
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### How to calculate a momentum space of a semi-finite lattice?

If we have a 2D square lattice of lattice constant a whose $x$ axis has only $N_x$ cells each with one atom and no with spin degeneracy, and periodic boundary conditions on $y$ with $N_y$ cells along ...
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### Position space representation of tight-binding model with composite lattice

Consider a composite lattice such as silicon or graphene (with sublattice A and B). We may call the sublattice tight-binding Bloch sums $\left| k, \alpha \right>$ with $\alpha$ being the sublattice ...
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### Can we use hybridised orbitals in Tight-Binding Method for calculation energy dispersion?

I am working on a model of a Fe square planar complex with nitrogen and oxygen given below is a monomer of that polymer. While constructing the hamiltonian matrix of this monomer I'm confused as to if ...
1 vote
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### Time evolution of non-interacting field operators [closed]

I learned that for a non-interacting tight-binding system $H=\sum_{n}\varepsilon_na^\dagger_n a_n$, the time evolution of $a_n$ is simply $a_n(t)=e^{-i\varepsilon_nt}a_n$. I tried to prove this: \...
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### Can I calculate partial density of states (PDOS) using tight binding approximation? [closed]

I am using tight binding approximation for a 2D material by 2*2 Hamiltonian, and I have ploted the density of states correctly. Can I also calculate the partial density of states using tight binding? ...
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### Berry connection in SSH model

In the SSH model for the 1D case, we get the eigenvectors as $$|(\pm)k>= \begin{pmatrix} \pm e^{-i\phi} \\ 1 \end{pmatrix}$$ where $\phi = tan^{-1}(\frac{wsin(k)}{v+wcos(k)})$. We can calculate the ...
1 vote
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### Dispersion Relation and Eigenvectors of SSH Model in Tight Binding

Consider a one-dimensional chain of atoms as shown in the figure. Let the spacing between the atoms be $a$. Assume that the onsite energy is the same at each point and is equal to $0$ (without any ...
1 vote
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### Empirical tight-binding sp$^3$s* 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 ...
1 vote
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### Is there any method for folding a Hamiltonian matrix to lower dimension?

I want to solve a tight-binding Hamiltonian which is $6\times6$. I'm only interested in two of the six bands which lie near zero energy at $\vec{k}=(0,\frac{4\pi}{3\sqrt{3}a})$. Is there any way to ...
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### How should I plot a tight-binding dispersion when I use multiple gridpoints in real space?

Consider a simple tightbinding calculation with spacing $a$. I can write down a dispersion relation $$E(k) = 2t - te^{ika} - te^{-ika}$$ Say I am solving a simple tightbinding problem numerically, on ...
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### Variational method in the tight binding approach

I'm trying to read Professor David Tong's notes to understand the principles behind the tight-binding model - section 2.3.5 'Deriving the Tight-Binding Model'. He first considers the Hamiltonian of ...
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### Interface between two different Su-Schrieffer-Heeger (SSH) chains

When I was exploring the interface (edge) states between two different SSH chains, I noticed some strange solutions. I was considering the following system. Two different SSH chains are connected as a ...
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### Band structure of Graphene and Tight Binding

Consider the $sp^2$ hybridization of Carbon in Graphene depicted in the following picture: When considering the LCAO TB method, one would expect conduction properties to be determined by the ...
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### Tight binding model, get dispersion relation in crystal

I know the theory of tight binding model but don't know how to apply them in the real lattice
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### What does band inversion mean for occupation?

I am thinking about Topological Insulators at the moment and am not clear about how to understand the occupation of the inversed band. I understand that due to energetic and symmetry reasons the ...
1 vote
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### Chemical potential $\mu$ controls filling?

If total magnetization of a spin 1/2 system is zero, does it mean that system is at half filling? or chemical potential $\mu=0$? I was trying to show that chemical potential controls filling by taking ...
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### Green's functions of disordered tight binding models

A research problem has led me to calculate a Green's function of a tight binding model with both onsite disorder and hopping amplitudes which vary in space. Since so much is known about tight binding ...
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### Alternating Tight Binding Hamiltonian

The alternating Hamiltonian may be written as: $$H = t \sum_{n} (-1)^{n} \left[c^{\dagger}_{n+1}c_{n} + c^{\dagger}_{n}c_{n+1} \right] \; \; .$$ I wanted to know the energy dispersion for this system, ...
1 vote
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Tight binding summary When computing the electronic bands of a crystal in the tight-Binding approximation, the standard way to do it is to construct Bloch solution as $$\Psi_n(\textbf{r}, \textbf{k}) ... 1 vote 0 answers 86 views ### Number density equation in BCS Theory In this paper, The author has given two-equation$$\frac{1}{U}=\sum_k \frac{1}{E(k)}\tanh\left(\frac{\beta E(k)}{2}\right)$$and$$2\rho-1=-\sum_k \frac{\epsilon(k)}{E(k)}\tanh\left(\frac{\beta E(k)}{...
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In this paper, on page 3, the authors go from the tight binding model w the Peierls substitution  H = \sum_{i,j} \sum_{a,b} t_{a,b} \exp\left(i \int_{\textbf{R}_{j,b}}^{\textbf{R}_{i,a}} dr'_{\mu} ...