# Questions tagged [tight-binding]

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### Tight binding on a square lattice with three orbitals symmetries

I came across a tricky problem while studying tight binding within the second quantization frame: Consider a square lattice with one atom per unit cell, where each atom has three active hydrogen atom ...
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### Dispersion Relation for one dimensional monoatomic lattice in Kronig-Penny model and in Tight-Binding Approximation model

In the tight binding approximation model, we have the dispersion relation for a one-dimensional atomic lattice given as: $$E(k) = E_0 - \alpha - 2\beta \cos(ka)$$ Here, $\alpha$ and $\beta$ are ...
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### Confusion about linear combination of atomic orbitals (LCAO)

In an YouTube video, that I used some information from it to work out my homework, Link: https://youtu.be/5vOvjeTRcqM?si=NzIcx_9QTNQ9Nhff the linear combination of atomic orbitals (LCAO) was discussed ...
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### Why is the effective mass of top band just $-1$ times that of the bottom band? [duplicate]

In band theory, the formula for effective mass is $$m^* = \frac{\hbar^2}{\frac{d^2E}{dk^2}}$$ and $m_{top}^* = -1 \times m_{bottom}^*$ the effective mass of top band is just -1 times the bottom band. ...
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### Second quantization: Hamiltonian in field operators vs Tight binding form

Hamiltonian written in terms of field operators: The kinetic energy (KE) part of Hamiltonian is $$H=-\frac{\hbar^2}{2m}\int d\mathbf{r} \Psi^\dagger(\mathbf{r}) \nabla^2\Psi(\mathbf{r}) \tag{1}$$ ...
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