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3 questions
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Why phonons outside the First Brillouin zone can be represented by phonons inside the First Brillouin zone?
I cannot understand clearly that why phonons outside the First Brillouin zone (in terms of wave numbers) can be represented by phonons within the First Brillouin zone.
For the 1-D monoatomic case, ...
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Fourier transform of atomic displacements
In lattice dynamics and the study of phonons, authors always start with a "Fourier transform" of atomic displacements $\mathbf{u}_j$ for each atom $j$ in a unit cell:
$$ \mathbf{u}_j=\frac{1}{\sqrt{N}...
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Proof that 1d lattice displacement by phonons is given $u_{n\pm 1}(t) = A_ke^{i\omega_k t} e^{i knd}e^{\pm i k d}$
I looked in «Kittel - Introduction to solid state physics», Wikipedia and Google for the derivation that: A phonon of wavenumber $k$ displaces the $s$-th atom in a monoatomic 1d crystal lattice by a ...
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