# Questions tagged [tight-binding]

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### Converting Hamiltonian of a 2-atom basis tight binding model to k-space and finding its hopping factors (using Fourier transform)

Hi could someone please help in finding the hopping factors of this Hamiltonian and also explain how to do it. H = sin(Kx)/σx + sin(Ky)/σy + (m-2 (2- cos(Kx)- cos(Ky )) /σz 0<m<4 4<m<8
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### Help. In tight binding 2d square lattice with two atoms basis

How we get the equations inside the box, which represent hopping between p and d orbital. I mean why we consider only two neighbouring. Thanks in advance
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### High symmetry point formulas for energy bands in empirical tight binding

I have a question about some intriguing formulas that I found. I am following ...
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### Disorders in tight binding model and periodicity

Does introducing disorders in tight binding models disrupt the periodicity of the lattice? If it does, doesn't this contradict with the assumptions and purposes of the tight binding model as a ...
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### Band structure of the Hubbard model

I know about the single particle band structure of the Hubbard model in (1+1)-dimensions, however, what I am not sure about is how the band structure would look when we consider the many particle case?...
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### Deriving Continuum BdG equation from Tight-Binding model for Graphene-Superconductor interface

Background My question concerns Beenakker's paper on "Specular Andreev Reflection in Graphene": cond-mat/0604594 (arxiv)/Phys.Rev.Lett. 97, 067007 (The same topic is also discussed in Rev. ...
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### How can I easily generate $\rm GaAs$ band structure?

Is there a program where I can easily generate $\rm GaAs$ band structure that shows lowest conduction band valleys?
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### Instrinsic spin orbit coupling in tight-binding Hamiltonian

I'm looking to write down a second quantized Hamiltonian to include the intrinsic spin-orbit coupling term in addition to the hopping spin-orbit coupling Rashba effect. How would I construct the term ...
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### Tight-binding in a semi-infinite square lattice

I have a problem understanding how changing the boundaries from a periodic lattice to a finite lattice. For example, if we have a 2D square lattice of lattice constant $a$ whose $x$ axis has only $N_x$...
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### Lattice harmonics for the point group D$_{3d}$

I have been looking into the concept of lattice harmonics used to construct tight-binding models based on the symmetry of the system instead of going through the standard Fourier transformation ...
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### Analog of Anderson localization caused by random hopping

Consider the tight-binding Hamiltonian: $$H = \sum_i \epsilon_i a^\dagger_i a_i + \sum_i V_i (a^\dagger_i a_{i+1} + a^\dagger_{i+1} a_i)$$ Random on-site energy $\epsilon_i$ leads to the famous ...
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### How can electron hopping occur in the tight binding model if the energy levels are localized to atomic orbitals on each atom?

In other words, what is the reason for electron hopping? Is not to related to overlap of orbitals between adjacent atoms ( say, in nearest neighbour hopping Tight binding models)?
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### Are the definition of superfluid order parameter in real space and $k$-space same?

Considering fermions tight bind model,in real space the superfluid order parameter can be writed as $$\Delta=g\langle c_{i \uparrow}c_{i\downarrow}\rangle$$ In k space, the definetion of ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...