Questions tagged [tight-binding]
The tight-binding tag has no usage guidance.
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Using particle-hole symmetry of the Hubbard model to study the model at different densities
In Condensed Matter Field Theory by Altland and Simons, they state that the Hubbard Hamiltonian
$$
H = \sum_{\text{nearest neighbors } ij \text{ and spin } \sigma} a^\dagger_{i\sigma} a_{j\sigma} + U \...
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How do you see that the Wannier functions are localized on ion sites?
In Condensed Matter Field Theory by Altland and Simons, when discussing the tight-binding approximation for a lattice system with a periodic potential, they define the Wannier states as follows:
$$
|\...
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Equivalence of Wannier Functions and Atomic Orbital Wave Functions in the Tight Binding Approximation
In tight binding approximation, what I've learned is that we can write the wave function of an electron which satisfies Bloch theorem in lattice as
$$
\psi(\mathbf{r})=\sum_{\mathbf{R}_s} e^{i\mathbf{...
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Variables dependency after unitary transformation
Currently working on tight-binding model with external field that induced an extra phase factor, e.g. Peierls phase $e^{i\frac{q}{\hbar}{\int_{\vec{r}_j}^{\vec{r}_i}}\vec{A}\cdot d\vec{r}}$ which will ...
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Question about electrons in tight binding model?
I was wondering, in the 1D tight-binding derivation, is the expansion of the ket:
$$|\Psi\rangle=\sum_n\phi_n|n\rangle,$$
a superposition of all the electrons or only one thus $|n\rangle$ only ...
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Why are zero-modes preserved on turning on coupling in twisted bilayer graphene model?
In the paper https://arxiv.org/abs/1808.05250 on page 3, they talk about how when the parameter $\alpha$ in the Hamiltonian in Eq. (5) equals $0$, we get zero modes at the Dirac points K and K’. This ...
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Why is the first Brillouin zone size of a body center cubic is 4π/a?
According to many online sources that the first Brillouin zone of a body center cubic (bcc) has the shape illustrated below. Along the $k_x$ (or $k_y$, $k_z$, $(100)$...) direction, basically the $\...
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Tight binding of monoatomic chain
For the the 1D atomic chain tight binding calculation, if we choose 1 atom per unit cell, the band dispersion is simply: $\epsilon-2t\cos{(ka)}$.
However, if we redefine our unit cell as 2 atoms, 3 ...
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Understanding electric conduction in tight binding model
Let's consider a system of free electrons moving in a one dimensional lattice with dispersion $\varepsilon(k) = -2t\cos{ka}$, ($a$ is the lattice spacing and $t$ the hopping amplitude). Let's now ...
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Matrix representation of Slater-Koster parameters
I'm coding a program to calculate electronic bandstructures using the Slater-Koster formalism (I am aware that such programs exist already- this is a pedagogical exercise). I notice that the $p-p$ ...
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How to find the energy bands of a kagome lattice?
I've been trying to solve the tight binding for a kagome lattice. The thing is that I find a cubic equation and have no idea on how to solve it. There's this article though (https://arxiv.org/abs/2310....
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Must Tight binding model use real space Basis?
To construct a tight binding model, the basis must be real space?
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Renormalization of two-sublattice tight-binding Hamiltonian
I have a generic tight-binding Hamiltonian of the form
$$H=\sum_n A c_n^\dagger d_n+Bd_n^\dagger c_n +C c_{n+1}^\dagger d_n + D d_n^\dagger c_{n+1}$$
where $A,B,C,D$ are parameters (hopping amplitudes)...
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What is the difference bewteen atomic orbitals and wannier functions?
They both use the "s, px , py, pz, dxy...." formalism
Both of them are in real space.
Wannier is orthogonal but atomic orbitals are not...
But what's the fundamental difference between them?
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How does symmetry act on general case fermionic operator?
I am trying to understand symmetries and how they work in condensed matter physics to understand some concepts from topology.
In general second-qunatized Hamiltionian can be written in the following ...
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