All Questions
71 questions
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Why are phonons and photons orthogonal in $k$-space?
Within solid-state physics and semi-conductor theory, the band-gaps of various semiconductors are often shown using $k$-space diagrams. Within the diagram, momentum is on the $x$-axis while on the $y$-...
- 157
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1
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137
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What does a negative frequency (omega) of vibration of atoms in a 1-D Crystal Lattice mean?
Assuming that the forces on an atom in a 1-D Crystal Lattice (unit cell is periodic) is due to its adjacent atoms, and behave like spring forces($F=kx$), I tried to calculate the frequency of atoms ...
- 41
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2k
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Umklapp Scattering of electrons by phonons
Kittel has a figure in his Solid State text in the free electron chapter depicting the scattering of electrons from phonons.
He explains that, if an electron (with, say, $k=4\pi/5a$) scatters out of ...
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49
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Linear force vs. displacement relationship for crystalline solid
I did a series of density functional theory (DFT) calculations on crystalline silicon.
These consisted of 50 total displacements of one atom from equilibrium in the x-direction until the displacement ...
- 1,772
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1
answer
7k
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Reduced $\mathbf{k}$-vector in the first Brillouin zone
The first Brillouin zone boundaries are at the wave vectors $\mathbf{k}= \pm \pi / a$, so that a normal dispersion curve looks something like this:
It is common to identify the $\mathbf{k}$ vectors ...
- 131
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2
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1k
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Why are sound waves associated with modes obeying linear dispersion relation?
Update to clarify The dispersion relation for an one-dimensional chain of atoms each of mass $m$ and attached to each other by identical springs of force constant $K$ (which for a continuous medium ...
- 27.2k
2
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431
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Electron - phonon interaction and perturbation theory
It might be not so clear what the question actually is, so I'll start with that: why do we often use perturbation theory for non-degenerate spectrum in solid state physics, while the spectrum of $H_0$ ...
- 246
3
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210
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Understanding heat conduction by phonons using phonon wavefunction?
The electrons in a perfect metal are described by Bloch waves having a particular form given by \begin{equation}\psi(\textbf{r})=e^{i\textbf{k}\cdot\textbf{r}}u_{n\textbf{k}}(\textbf{r}).\end{equation}...
- 27.2k
4
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539
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How the number of atoms in the basis affects the density of states?
When dealing with phonons and specific heat of solids, it seems the really important quantity to obtain is the density of states $N(\omega)$. When we have it, we can find the internal energy as
$$U(T)...
- 37.4k
6
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3
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What actually is the wavevector in the context of phonons and lattice vibration?
When we deal with Electromagnetic waves the wavevector has the meaning that it encodes the information about the direction of propagation, together with the wavelength.
In Quantum Mechanics, the ...
- 37.4k
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434
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How one can count how many phonon modes is there in the crystal?
I'm reading the review on phonon and Raman scattering in 2D transition metal dichalcogenides (2D TMDCs). At the beginning of Section 2.1 it is said that, since there are two X-M-X units in the crystal'...
- 1,040
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2
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524
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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 ...
- 1,426
1
vote
1
answer
90
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How do phonons affect the work function?
How do phonons affect the work function? Could phonons that are directed towards a single atom, such as in a body-centered cubic crystal, increase the amount of thermal excitation and thus decrease ...
- 55
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1
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3k
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Help needed to understand the dispersion curve of a 1D lattice with diatomic basis
I am trying to understand the dispersion curve (as shown below) of a 1D lattice with diatomic basis.
Here are my questions:
Can both optical and acoustic branch of phonon simultaneously exist in ...
- 69
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3
answers
24k
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Can someone explain LO-TO Splitting?
LO-TO splitting occurs in an ionic (i.e. polar) solid such as GaAs or NaCl. What happens is that the degeneracy of the transverse optical (TO) and longitudinal optical (LO) phonons at $k=0$ is broken ...
- 2,897
1
vote
1
answer
349
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Phonon-phonon-interaction as higher order terms in the potential
Is there a simple way to understand why phonon-phonon-interaction is described by higher order terms in the potential?
I mean: Having a quadratic potential is essential for the definition of the ...
- 2,157
1
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331
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What is the physical meaning of group velocity for elastic waves through crystals?
In a chapter about phonons they define group speeds for elastic waves in crystals as the derivative of the dispersion relation:
$$v_g = \frac{d{\omega}}{d{k}} $$
I wonder though how they come to ...
- 1,021
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1
answer
261
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What are degenerate transversal oscillation modes?
This is just a question about terminology that is used in the beginning of a chapter about phonons.
In a simple cubic crystal, we can consider elastic oscillations in f.i. the [100] direction. In ...
- 1,021
2
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1
answer
10k
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Phonon Momentum
I am reading Charles Kittel's solid state physics and wondering what's the mechanism that neutron waves and photons can interact with phonons and the process obey the generalized momentum-energy ...
- 421
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2k
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Why do phonons cause excellent heat conduction in diamonds?
Phonons are the quantum of lattice vibrations in crystals and are not to be confused with photons, the gauge bosons of the electromagnetic force. Apparently, they contribute to heat conduction, but I ...
- 609
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19k
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Is crystal momentum really momentum?
Almost every solid state physics textbook says crystal momentum is not really physical momentum. For example, phonons always carry crystal momentum but they do not cause a translation of the sample at ...
- 1,515