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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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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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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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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