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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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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Can anybody explain why was the additional mode excluded (Extract from Mckelvey)? I do not get it and Kittel gives the $N-1$ result only

The screenshot is from Mckelvey. He is trying to count the number of normal modes for a monatomic chain. The problem is that he gives the result of $N-2$ modes (after imposing the fixed ends ...
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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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How similar are phonons and photons?

If you go through the definitions for "phonon" (or for an explanation of phonon), most of the text or articles make the analogy to photons: A photon is a discrete quantum of light. A ...
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Why phonons are Goldstone modes?

I read this in the lecture notes by David Tong: "Gapless excitations often dominate the low-temperature behaviour of a system, where they are the only excitations that are not Boltzmann ...
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How do we know sound cannot travel in a quantum vacuum?

This is probably bad wording and I apologize. I mean the quantum vacuum in space that is made of a soup of emerging/vanishing pairs of particles. More generally, why sound (phonons) is assumed to not ...
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Linear chain Hamiltonian [closed]

In Ziman's Electrons and Phonons book, he starts describing phonons with a linear chain. On Page 7, Eq. 1.3.6, he gives the potential energy as $$ V = \frac{1}{2}g\sum_l{(n_{l+1}-n_l)^2} $$ where $g$ ...
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Can we add bosonic phonon in the Standard Model of Particles?

Nowadays, we describe phonon as “particle” of sound. They have zero spin but are thought to have mass and kinetic energy. Phonons are the smallest units of the vibrational energy that makes up sound ...
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Derivation of speed of sound in (diatomic) chain using Newton-Laplace formula

I am familiar with the derivation of the speed of sound done in the style of, for example, this question: Diatomic chain and speed of sound I would like to derive that same result $$ c^2=\frac{2ka^2}{...
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Infinite wavelength for the 1D harmonic chain of oscillators corresponds to a uniform translation, but why does it still have a finite phase velocity?

The dispersion for the 1d chain of harmonic oscillators is $\nu = \sqrt{\frac{\alpha}{m}} \frac{|\sin(\pi k d)|}{\pi}$ Where I'm explicitly not using angular frequencies ($\nu = \frac{1}{T}, k = \frac{...
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Mechanical mode (phonons) in cavity optomechanics

In the theoretical description of a cavity optomechanical system, it is described as the radiation pressure induced motion of a mirror by cavity optical field, where the moving mirror is described as ...
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38 views

State density in one dimension

For a phonon we took in our lectures the state density for a 3D crystal and in order to find the number of states with an energy value between $[0,E)$ we did the division between the volume of the ...
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Understanding the phonon

It is said that the phonon is the equivalent of the photon in Solid state physics. I cannot see how,when i try to give an interpretation to the phonon. What i am trying to say is the following: If we ...
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Why hot-electrons cool down through interaction with optical phonons (instead of acoustic one)?

I have been diving a bit on this topic but something is still not completely clear to me. If we generate hot-electrons in a semiconductor, these hot-electrons cool down (after thermalization) to the ...
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Do atoms always move in phase within the unit cell for acoustic mode phonons?

In my condensed matter book it says 'For the acoustic mode, all atoms in the unit cell move in-phase with each otehr (at $k=0$) whereas for optical modes they move out of pahse with each other (at $k=...
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What is the difference between pressure broadening and phonon broadening?

I have been reading chapter 5.2.2 Pressure broadening and chapter 5.2.3 Phonon broadening of the document Paper BIII: Diatomic Molecules & Laser Physics by Prof. Simon Hooker. Chapter 5.2.3 Phonon ...
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“Crystal electric field”, zero temperature, and the idea that the crystal electric field will have a “symmetry reflecting that of the crystal lattice”

I was searching for information on "phonon broadening" in the context of lasers. I found the document Paper BIII: Diatomic Molecules & Laser Physics by Prof. Simon Hooker, where chapter ...
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64 views

Boltzmann equation: how to estimate the relaxation time?

I am looking for qualitative/general explanations or references. A famous approximation of the full integro-differential Boltzmann equation is the so-called "relaxation time approximation", ...
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Vacuum catastrophy of the 1D harmonic chain

Consider an ion lattice of N atoms, modelled as a linear chain of length L $$ H = \sum_n \big( \frac{p_n^2}{2m} +\frac{m \omega^2}{2}(x_n-x_{n-1})^2 \big).$$ The Hamiltonian diagonalizes by going to ...
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Why does thermal conductivity of an alloy becomes nearly flat from $0.2<x<0.8$ composition?

I am trying to understand the effect of alloying on the thermal conductivity of an crystalline alloy. I have found a great many papers where I see thermal conductivity sharply decreases from 0 to 0.2 ...
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How to determine crystallographic directions from dispersion relation graph? [closed]

How does one determine the crystallographic directions in a phonon dispersion relation graph (e.g. see below)? I know it has something to do with the first Brillouin zone in reciprocal space (see ...
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How can Cooper pairs form in zero temperature, if there are no phonons?

Phonons behave like Bosons, so they have a Bose Einstein distribution. If you take the zero temperature limit, the distribution vanishes. So at zero temperature there are basically no phonons (up to ...
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Uniqueness of phonon vacuum

Consider a quantum harmonic chain, described by the Hamiltonian: $$\hat{H}=\sum_{j=1}^{N} \frac{\hat{p_j}}{2M} + \frac{1}{2}K(\hat{u}_j-\hat{u}_{j+1})^2,$$ where $\hat{p}_j$ is the momentum and $\hat{...
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What is the direction of wavevector in the real hexagonal phononic lattice?

Assuming we have a 2D hexagonal lattice and its reciprocal lattice. The difference between them is that the real lattice and its reciprocal lattice have 30° rotation. So if the following image is its ...
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Diagonalising the Hamiltonian phonon

I've been trying to derive the eigenvalues of the two mass atomic chain to get out both the acoustic and optic phonon dispersion curves. This is easy in classical physics but I wanted to see if I ...
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Physical meaning of constant zero phonon dispersion relation

Consider a 2D lattice model like this Assuming the mass of atom and force constant is 1, we could easily calculate the dispersion relations of the system. As there are four atoms per unit cell, there ...
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Solid state problems (phonons conductivity)

I took a quiz where i got two answers wrong and i want to know what the correct answer is and why. Q1) In a material where both phonons and electrons contribute to the thermal conductivity, the ...
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Lattice vibration and sound waves

In general, the acoustic branches of a crystalline solid has a nonlinear dispersion relation. For small values of the wavenumber $k$ or wavelengths large compared to the equilibrium lattice separation,...
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Why doesn't the acousto-optic frequency shift depend solely on the velocity of sound in the medium, if it is a form of Doppler shift?

Many optics books make the statement that the frequency shift of a laser beam from the acousto-optic effect can be thought of as a Doppler shift from a traveling index of refraction grating (pressure ...
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Raman Spectroscopy and Phonon Modes

How can someone use Raman Spectroscopy to obtain information for the phonon modes of a crystal? I am asking for some paper that contains information about Raman Spectroscopy and Phonons from an ...
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Why only the phonon with $k=0$ contribute Raman intensity?

I have read some literature to know that Raman intensity corresponds to the inelastic scattering of light with ion vibrations, and the positions of Raman peak correspond to the energy of phonon. My ...
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Electron phonon coupling within field integral formalism

Reading Altland and Simons' "Condensed matter field theory" I am stuck in the exercise called "electron phonon coupling" in section 4.5. The exercises is about integrating out the ...
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Any material that could help me calculate the surface/longitudinal/transversal modes in an isotropic semiconductor?

Basically a homework question, but I don't actually have a homework to give in. I just do it out of curiosity. I would like to know if there are any good materials out there that could ilustrate to me ...
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Phase velocity in monatomic chain

When considering a one-dimensional monatomic chain of atoms (identical masses $m$ & spring constant $\kappa$), one finds the following dispersion: $$ \omega(k) = \sqrt\frac{\kappa}{m}\cdot\left|\...
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Is Inelastic Neutron Scattering (INS) any good compared to synchrotron IXS for determining phonon dispersion relations?

Both INS and IXS can be used to study phonon dispersion relations. While INS requires large sample size due to low inelastic scattering cross section, IXS using synchrotron x-ray sources do not ...
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Why is crystalline graphite black yet shiny?

I am unable to find images of pure crystalline graphite with high confidence, but based on various sources I believe that it should actually be both black and shiny, in the sense that it reflects much ...
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Are the molecules of lattice in quantum entanglement when they vibrate as a phonon?

As all the molecules in the lattice are vibrating together to form a wave and the phonon is a quantum phenomenon, it makes sense to me that all the molecules inside the lattice are in the entangled ...
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189 views

Why do we need the quantization for lattice vibration?

I've been reading the Wikipedia article on phonon. So, my understanding is what they get is the discrete energy levels of vibration from quantization. But the discrete energy level is not only the ...
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What's a normalized coupling strength?

While reading about elctron-phonon coupling, I came across the term normalized coupling strength. It was defined as $$\eta = g / \omega$$ where $g$ is the coupling constant and $\omega$ the ground ...
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Why there is no ZA acoustic mode in bulk 3D materials whereas it appears in 2D materials (monolayer type)?

For each materials phonon band structure there are three acoustic phonon bands (2-LA and 1-TA for bulk or ZA,TA and LA for 2D materials). Now, I have this straightforward question that "Why there ...
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Phonons and Second Quantization

I have been reading David Tong's notes on Phonons: http://www.damtp.cam.ac.uk/user/tong/aqm/aqmfour.pdf I am quite interested in Section 4.1.4, where he quantises the vibrations. First, he defines the ...
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How did the author calculate the phonon energy?

I am currently studying Introductory Semiconductor Device Physics by Parker. Chapter 2.5 The concept of effective mass gives the following example: For GaAs, calculate the typical (band-gap) photon ...

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