Questions tagged [tight-binding]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
0answers
17 views

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
1
vote
1answer
42 views

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
0
votes
0answers
15 views

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 ...
0
votes
1answer
22 views

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 ...
0
votes
0answers
28 views

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?...
0
votes
0answers
29 views

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. ...
3
votes
1answer
67 views

Exact Diagonalization of a tight-binding Hamiltonian with periodically alternating potential

My question is, can we diagonalize a general Hamiltonian , $$H=-t\sum_i^N (c_i^{\dagger}c_{i+1}+h.c.)+\sum_i \mu_i c_i^{\dagger}c_i$$ where, $$\mu_i=\begin{cases} \mu_0, &\text{if mod}(i,p)=0 \\ 0,...
2
votes
0answers
30 views

Is dynamical localisation an interference effect?

The question refers to the well-known phenomenon of dynamical localisation due to an oscillating electric field, as explained in Dunlap & Kenkre, PRB 34,6 (1986). Here, a particle initially ...
0
votes
0answers
13 views

Current $j(q)$ in tight bindng

How is the Fourier transform of the current derived in tight binding? In this paper, Prelovsek uses the hypercubic lattice (for which I will only use the 1D case for simplicity) with nearest-neighbor ...
0
votes
0answers
25 views

Studying the Hopping parameter for tight binding model

I'm currently trying to study the tight binding Hamiltonian and Apart from the book, "Ashcroft, David Mermin: Solid State physics", I'm unable to find a proper source to study the tight ...
0
votes
0answers
45 views

Fourier transform of the current operator in tight binding

In several places, e.g. Mahan's Many-Particle Physics, I have seen the derivation of the current operator in the tight binding model, and it generally has the form $$ \hat{\jmath}=\frac{1}{i} \sum_{R ...
0
votes
0answers
26 views

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?
1
vote
0answers
52 views

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 ...
2
votes
2answers
44 views

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 $N_x$...
0
votes
0answers
19 views

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 ...
6
votes
0answers
59 views

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 ...
0
votes
1answer
39 views

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)?
0
votes
1answer
51 views

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 ...
1
vote
0answers
21 views

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
vote
1answer
69 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 ...
1
vote
0answers
96 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,...
-1
votes
1answer
83 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
645 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 ~...
0
votes
0answers
27 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
vote
1answer
139 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-...
0
votes
0answers
73 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 ...
0
votes
0answers
86 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
votes
1answer
176 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 ...
2
votes
3answers
279 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
votes
1answer
35 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
vote
0answers
35 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
votes
1answer
62 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\...
0
votes
1answer
72 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
votes
0answers
61 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
vote
1answer
150 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
votes
1answer
111 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 ...
2
votes
1answer
138 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{...
1
vote
0answers
80 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
1
vote
0answers
67 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
votes
1answer
190 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
118 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?
0
votes
0answers
57 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 ...
0
votes
1answer
124 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 ...
1
vote
0answers
229 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
votes
0answers
109 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}= ...
3
votes
2answers
142 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
votes
1answer
95 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
votes
1answer
377 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.
1
vote
0answers
51 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. $\hat{H}$ = $\sum_j$ $\...
5
votes
1answer
151 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 $$\...