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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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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How does gravity-spacetime interaction modulate the Casimir force? [closed]

Suppose there is a point source of strong gravity. Far away from this point source in terms of the speed of light, there exists a vacuum in space where no dust is. This vacuum nonetheless can ...
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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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How exactly do the electron and phonon interact for the process of recombination to occur?

I am currently studying Introductory Semiconductor Device Physics by Parker. Chapter 2.5 The concept of effective mass says the following: Figure 2.8 shows two hypothetical energy-momentum diagrams ...
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Effect of the number of atoms in the basis to the heat capacity (component of the phonons)

I am wondering what's the effect of the number of atoms in the basis onto the heat capacity (phonon part). I've found this post: How the number of atoms in the basis affects the density of states? ...
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Generalisation of the density states of phonons

Is it possible to generalize de density of states for phonons $\left( \left(\frac{L}{2\pi} \right )^3 \int \frac{dS_\omega}{v_g}\right)$ to a density of states which is also applicable to Bloch ...
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X ray diffraction and the band theory

I was look around stack exchange and couldn't find a good answer to this: What is the relation of the band theory of solids and the X-ray diffraction? We know that it EM wave is scattered (the process ...
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Feynman's Diagram contribution in Green's Function

I was reading Many Particle Physics by G. Mahan and they calculated the Green's function for electron-phonon interaction using Feynman's Diagram. It was written that Green's function contribution by ...
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What does phonon exchange do in the theory of superconductivity?

In the theory of superconductivity, the phonon-mediated electron-electron scattering leads to an effective interaction, the BCS hamiltonian,$$\hat{H}_{\rm BCS}=\sum\limits_{\vec k,\sigma}\epsilon_{\...
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Dispersion relation with damping force

We consider a linear chain of atom connected by springs with constant $K$. We have the usual elastic force and we add damping force such that the dispersion relation is: $$ \omega = 2\sqrt \frac K m \...
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distribution of atomic displacements in two-dimensional materials

In 3-dimensional materials, the thermal vibration of atoms can be described by mean-squared displacement values $\langle u_i u_j \rangle$ (where $u_i$ are displacements from equilibrium positions for ...
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Phonon density of states

How can I easily calculate phonon density of states from phonon dispersion? I want to compare DOS of graphene and Si from phonon dispersion. Is there a better alternative to Debye DOS = $\frac{w^2}{2\...
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What contributes to the specific heat of a magnetized ferromagnetic solid?

In general, for small wavenumber, $k$, the dispersion relation of ferromagnetic spin waves is $\omega\propto k^2$ and that of phonons is $\omega\propto k$, and in 3D, the low-temperature behaviour of ...
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Melting point of solids from phonon dispersion

Is there a way to predict the melting point of a solid from phonon dispersion curves, measured experimentally or via DFT?
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Acoustic phonons velocity of GaN

Phonons dispersion is presented at figure below: T. Ruf. “Phonon Dispersion Curves in Wurtzite-Structure GaN Determined by Inelastic X-Ray Scattering”. In: Physical Review Letters 86.5 (2001), pp. 906–...
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How many optical and acoustical branches are in a primitive cell?

I am reading Introduction to Solid-State Physics (by Kittel) and I don't understand how he counts the optical and acoustical branches in a primitive cell. It says that if there are $p$ atoms in a ...
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Electron-Phonon Hamiltonian and One-particle Approximation

Consider a hamiltonian with electron-phonon coupling, for instance, a very simple version of Holstein hamiltonian: $$t\sum_k \hat{c}^\dagger_k \hat{c}_{k+1}+\text{h.c.}+\hat{b}^\dagger \hat{b}+\alpha ...
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Quantum confinement effect of phonons

I wonder what length scale is necessary to observe quantum confinement effects of phonons. I am supposing the situation of quantum wells (two dimensional). In case of electrons, by knowing Bohr radius,...
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How to understand spin-phonon coupling in any material? Differs from electron-phonon coupling?

Spin-phonon coupling is an interesting phenomena, especially, in the case of multiferroic materials. Its origin is said to be the exchange interaction of magnetic ions. In that case, any magnetic ...
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Why we can use $\frac{1}{V}\sum_{k \in 1BZ} \approx \int_{k\in 1BZ} \frac{dk}{(2\pi)^d}$ for phonons?

Why can we use $$\frac{1}{V}\sum_{k \in 1BZ} \approx \int_{k\in 1BZ} \frac{dk}{(2\pi)^d}$$ where $d$ is the dimension of the lattice, for phonon related integration? I know the above sum converted ...
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Can we understand the strong reflectivity of metals from band theory?

I know that solids, including metals, have electronic bands and bandgaps. If we consider some typical metal such as copper, we know that it strongly reflects visible light. From the point of view of ...
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Lattice vibrations in one-dimensional monatomic crystals vs. diatomic crystals

A one-dimensional diatomic crystal (with two distinct atoms A and B arranged in a line) can exhibit two types of collective motions. In one type, the consecutive atoms move in-phase and in the other, ...
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Physical momentum of phonon [duplicate]

I have read in the book 'Introduction to solid state physics' by Kittel that phonons do not carry any physical momentum. But what is the reason for phonons not having any physical momentum?
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Why is the ground state energy of a linearly perturbed quantum oscillator always lower than its harmonic counterpart?

I am concerned with a QHO that is linearly perturbed in $x$, i.e. $$ H = \hbar \omega \left(\hat{n} + \frac{1}{2}\right) + \lambda \underbrace{\left(\hat{b}+ \hat{b}^\dagger \right)}_{\propto \hat{x}}....
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Energy and location during quantum coherence

Can the energy of of a system during quantum coherence be thought of as smeared across the coherence domain (e.g. coherent phonons)? Is the location of the energy during quantum coherence uncertain? ...
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Are phonons accepted particles by mainstream physicists?

I just encountered the wikipedia article on phonons, which says that these quasiparticles represent vibrations through matter. Wikipedia says that Phonons have negative mass and negative gravity. But ...
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How do solids transfer heat?

We all know heat transfer occurs via energy carriers (electrons, photons, bulk flow of molecules, phonons, etc.). In many materials, phonons are the major contributors to heat transfer. Classic ...
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Number density of phonons in superfluid

I'm reading Superfluidity and Superconductivity by Tilley & Tilley. In section 2.4, the argument is made that the normal component of superfluid helium consists of phonons and rotons. The ...
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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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Why doesn't the phonon theory reproduce a Debye-like curve for $C_V$ vs. $T$?

Debye's theory is a model of specific heat in which a high-frequency cut-off $\omega_D$ is put in by hand. The resulting curve of $C_V$ versus temperature $T$ grows as $T^3$ at low $T$ and saturates ...
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Can you calculate the static lattice/potential energy given a phonon dispersion curve?

Let's say I determine a material's dispersion relation from experiments. Would it then be possible to use the information contained within the dispersion relation to calculate the material's static ...
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Conduction Theory [closed]

Why the conductivity of Metal increase with a decrease in temperature, semiconductor increase with an increase in temperature and alloys remains the same ? Is it due to the following reasons? ...
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Usually, how much does a phonon travel without scattering?

Phonons propagate without problems in a lattice, until they scatter on something, like a defect, an electron, or other phonon. But in a typical solid at room temperature, how much (or how long) is the ...
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Lattice stability

If one calculates the phonon dispersion function for cubic lattice in 3d or quadratic lattice in 2d, then it is seen that there exist impulses for which the frequency becomes imaginary. So it seems ...
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Photon-phonon scattering problem

I have to calculate the following: a) The speed of the acoustic phonons b) Which phonons(frequency and wavevector) can be observed for scattering angles between 0° and 180° and how much of the ...
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What are the types of polarons?

It is said that an electron and its virtual phonon is called as polaron. There is large and small polarons. What type of the polarons are there? Are large polarons due to lattice defects and ...
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What is the temperature at which one-half of the oscillators in a Debye solid are expected to be in the ground state?

This is a slightly reworded question picked up from Pathria and Beale's textbook on Statistical Mechanics. I'm unable to even get started on the problem. Any ideas?
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Green function for bosons in ground state

I have to obtain a one-particle Green function for phonons at $T=0$ $$D^{0}(\mathbf{x},t)=\frac{1}{iV}\sum_{\mathbf{k}}\frac{\omega_\mathbf{k}}{2}\big(\theta(t)e^{i(\mathbf{kx}-\omega_{\mathbf{k}} t)}+...

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