Questions tagged [phonons]
Collective excitations in periodic, elastic arrangements of atoms or molecules in condensed matter, like solids and some liquids. They are quasiparticle quantum modes of vibration of elastic structures of interacting particles.
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Ratio between Stokes and anti-Stokes scattering amplitudes in Raman scattering
I'm trying to understand the amplitudes and the ratio between those of Stokes and anti-Stokes scattering in Raman scattering. I understand that from a Boltzmann distribution point of view, the ratio ...
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Quantum effects on phonon transport?
Phonons are the quanta of vibrations in a crystal lattice. As the name suggest, phonons are already a quantum phenomena but when studying heat transfer the phonons are mostly very classical (wave ...
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How to make sense of phonon dispersion curves and dynamic stability?
I've been working on this material that I've been doing DFT calculations on and I've managed to obtain the phonon dispersion curves for it. Calculation for it took quite a while, but here it is:
Now ...
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How to understand crystal momentum, its relation to translational symmetry, Noether theorem, and to symmetry breaking/Landau-Ginzburg theory?
This question continues from my another question How to understand critical points of the Brillouin zone, (in)direct bands of transition-metal dichalcogenides?, and is related to Is crystal momentum ...
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How to calculate the mass for phonon vacuum fluctuations?
I am studying this paper, the precise content of which isn't relevant for the question.
In there, the authors consider quantized bulk vibrations in a diamond. As usual when quantizing such systems, ...
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What is the reduced mass of a diamond unit cell?
I am reading this paper to study so-called collapse models. However, the paper isn't really relevant to understand the problem here.
In the paper, the authors are considering a bulk vibration (optical ...
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Why there is maximum $n$ ($n_{Debye}$) for mode counting in phonon?
Hi!
I'm curious about the description in my textbook of maximum $n \rm (n_{debye})$ in mode counting for phonon. I can realize the $n$ has maximum, because $\lambda_n(min) = 2a(\rm{lattice-constant})$....
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Phonon, photon have chemical potential equal to zero
Hi I know the chemical potential of the phonon and photon is equal to zero. And I know the reason is the number of these particle isn't conserved.
But I don't know why the number of the phonon isn't ...
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What is the mass of collective oscillations?
When you step through the procedure of deriving a phonon dispersion relationship for a given crystal structure (i.e. small oscillations from equilibrium, harmonic approximation, collective coordinate ...
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What is the relation between phonon anharmonicity and thermal conductivity?
The textbook says that: if the vibration of the lattice were harmonic, then the states of phonons would be orthogonal to each other. As a result, there would be no interaction between phonons, hence ...
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Density states of phonons with different speed at different directions:
I was trying to get the density of states $g(v)$ for phonons which have $2$ polarizations transversally, and $1$ polarization longitudinally.
My approach:
$$dN = \frac{1}{8} 4 \pi n^2 dn, \lambda = c/...
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What prevents a "beam combiner" from being able to cancel out energy?
I understand that normally when two waves combine destructively this happens only in certain places; the energy doesn't disappear but is redistributed to other places where the interference is ...
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Polaron transformation in quantum optics
I'm trying to understand the so-called polaron transformation as frequently encountered in quantum optics. Take the following paper as example: "Quantum dot cavity-QED in the presence of strong ...
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Drawing reciprocal space phonon vectors
I'm a bit unsure about how the crystallographic directions work with phonon momentums and reciprocal space.
If I have a phonon that's travelling in some direction $[abc]$ in a cubic structure, I ...
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Why do we not use the Schrödinger equation/standard QM to describe phonons (or other quasi particles)?
We were just taught about phonons in solid state physics class. Last year we did QM and now we are starting QFT as well.
Phonons are excitations of a condensed matter field. I thought that we would be ...
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How to derive specific heat of a crystalline material from phonon density of states?
I have done a simulation of a crystalline material using DFT and have extracted its normal modes and its phonon density of states.
Does anyone have an algorithm/code or a detailed resource that can ...
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Electron transport in fluids VS solids ("structure factor" VS "phonons")
Assume to have a neutral plasma consisting of some ions $X^+$ in a neutralizing gas of electrons $e^-$. Imagine that the $X^+$ can be in a gaseous (G), liquid (L) or solid (S) phase. We want to ...
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Why are phonons bosons if they cannot occupy the same eigenstate?
I am reading the The Oxford Solid State Basics and on pages 82-83 it appears the following:
If a classical harmonic system (i.e., any quadratic Hamiltonian) has a normal oscillation mode at frequency ...
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What is physical meaning of terms like "Two-particle continuum" and "two-particle density of state"?
I am reading this article arXiv:2011.06543 about interacting magnons and they plot two-magnon density of states given by equation
$$
D_k(\epsilon) \propto \sum_{\gamma,\gamma'}\sum_q \delta (\epsilon -...
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Does free phonon propagator always vanish at zero momentum?
When discussing electron-phonon interaction, the simplest leading electron self-energy usually has only the simplest phonon bubble diagram and excludes the 'tadpole' diagram below with a phonon ...
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Is sound a classical mechanic phenomenon or is it a quantum effect?
I am just curious because sound is longitudinal waves, meaning the energy is passed from one particle to another nearby particle and produces a wave that continues on until it reaches our ear as a ...
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Phonon-electron interaction in superconductors
I'm trying to understand the phonon-electron interaction in superconductors. I'm a high school student doing a project on superconductors and I can't find understandable information about it. Almost ...
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How does the $T^3$ dependence for the thermal conductivity from phonons get derived (and linear $T$ for fermions)? Does anyone have resources?
I've been trying to find the derivation of the $T^3$ contribution for phonons and a linear $T$ dependence for fermions as I have seen it being mentioned multiple times in some publications. So far I'...
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Current State of Research on high $T_c$ Superconductors
After looking at these two RevModPhys articles, I have found myself perplexed by the current state of high $T_c$ superconductivity research. Seeing as I cannot find any SE articles more recent than 5 ...
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What are phonons actually?
I was reading about heat conduction in solids wherein it was stated that in crystalline solids heat conduction takes place via lattice vibrations. In relation to this, the word phonon was used.
In ...
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LO vs. TO phonons in a quasi-2D polar crystal at $Gamma$ point
In a polar quasi-2D crystal like hexagonal boron nitride, there seems to be a finite energy/frequency difference between the in-plane LO and TO phonon modes at the center of the Brillion zone (the $\...
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Can "bare" TO phonons in polar materials exist by themselves, or are they always phonon-polaritons?
We know that transverse optical (TO) phonons in polar crystals couple to light strongly and can form hybrid light-matter quasi-particles called phonon-polaritons (solid lines in the figure below).
My ...
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Partition Function from Dispersion Relation in Molecular Dynamics
I’ve seen there are ways to compute the dispersion relation of a crystal from molecular dynamics. An example of how to do this is discussed in this question: Computing phonon dispersion from molecular ...
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Phonons vs Normal mode
What is the difference between Phonons and Normal mode? My professor told me that they are the same and that one can get the other from some derivation (I'm a bit unsure if he really said the '...
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Electron phonon coupling field integral
I am stuck on the problem "electron-phonon coupling" part a in Altland and Simons page 187. There is a related question on PSE, but that concerns part b.
Borrowing from the notation in the ...
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Phonon modes and Raman scattering /IR absorption
Why are some phonon modes Raman-active and other are IR-active?
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Why is it possible for us to "hear" acoustic phonons, but not optical phonons?
The name itself suggests that we can hear acoustic branch of phonon modes (and not the optical branch), but other than that I do not see any reason whatsoever why we are able to hear them.
In order to ...
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What is a phonon and electron line width in phonon-electron interaction?
In case of phonon-electron interaction, I came across a term called "phonon linewidth", and I do not understand from where does it arises and what significance does it have. and why is it ...
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Reference request: Derivation of the $T^5$ dependence of resistivity from electron-phonon scattering?
The scattering of conduction electrons with phonons gives rise to a resistivity that varies with the temperature as $T^5$. Is there a simple textbook derivation of this? Where can I find this?
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What's the difference between inelastic X-rays scattering and Raman scattering?
In solids, inelastic scattering of X-rays can produce or absorb a phonon, which is equivalent to saying that solid ends up in excited vibrational level ( or if it was in a vibrational level to begin ...
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Can visible light be used for measuring phonon dispersion relation?
As phonon dispersion realtions can be studied using inelastic scattering of neutrons with phonons and X-ray. So, can visible light be used to do so?
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Why do optical phonons have such a high frequency at $k=0$?
Can you give me some intuitive explanation of this? How is there any frequency when wavelength becomes almost infinite?
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Heat Conduction in Deformed Solids
I am working on a model for isotropic elastic solids and have to make a decision about whether heat conduction should be isotropic in the reference or deformed configuration.
I have spoken to two ...
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Shortest wavelength of sound wave in solids
In the book Thermal Physics by Schroeder, it is mentioned that "sound wave in solids cannot have wavelengths shorter than twice the atomic spacing". I am wondering if this is related to ...
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Rotational invariance constraints on potential
I have a question about Nayak's lecture note , page 20, above equation (2.1)
'Rotational invariance implies that it can only be a function of the symmetric combination,
$$u_{ij}=\frac{1}{2}(\...
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Can phonons induce non-$s$-wave superconductivity?
In BCS theory the interaction is considered isotropic and the result is an $s$-wave superconductor. Is it possible anyway for unconventional superconductors to have SC driven by phonons (I intend this ...
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Standing wave and optical mode in a crystal
I want to understand how when the wavelength $ \lambda$ is equal to 2a, with a being the lattice constant, two neighboring building particles of the crystal move in opposite direction. The general ...
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Interaction of nonpolar optical phonons with light
How optical phonons in nonpolar insulators, such as diamond, interact with light and cause absorption lines in the infrared region? An example is the picture from this book chapter, where phonon ...
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Isothermal Gruneisen parameter for Germanium?
If phonon density of states peak shifts are purely quasiharmonic, we have $\omega$(V(T)).
If phonon density of states peak shifts shifts are purely anharmonic, we have $\omega$(T).
Does anyone know if ...
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Reality of dynamical matrix without inversion
Assume throughout this question that we are working with non-relativistic phonons in the harmonic approximation.
The Hamiltonian for phonons in the harmonic approximation is usually taken to be the ...
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Normalization of phonon density of states
Analogous to electronic structure calculations, we can solve for dispersion band structure of phonons for lattices using harmonic lattice approx. And we can find the so-called phonon density of states ...
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Book recommendation: Does anybody know a book adopting a more intuitive approach to the topic of Crystal Vibrations (phonons) than the Book by Kittel?
I have tried Simon's 'Oxford Solid State basics' and Kittel 8th edition but I am not impressed by both (I mean the content covered through Chapters 4 and 5 in Kittel)
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Why isn't the quantization of the phonon wave vector due to quantum mechanics?
My text book in solid state physics (Kittel) states that the quantization of the phonon wave vector arises due to boundary conditions (periodic or hard wall) for the modes of oscillation, and I can ...
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Picturing Phonons
Consider vibrations of a One-dimensional monatomic chain of atoms. What I'm trying to do is to picture phonons?
First where I am? So I have a one-dimensional monoatomic chain. With little calculation, ...
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Writing down a Hamiltonian that couples spin and phonons
I am studying spin dynamics and am trying to write down a Hamiltonian that couples the spins with the phonons. I have the following interacting spin Hamiltonian
$$H_{s}=\sum h_{i}S_{i}+H_{\text{...
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