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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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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Fate of acoustic phonons in incommensurate charge density wave states?

In most standard exposition of (the mean-field theory of) charge density wave (CDW), phase and amplitude fluctuations are introduced as the collective excitations. Kohn anomaly in the acoustic phonon ...
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GaAs Phonon Dispersion Spectrum understanding

I have a beginner question on solid state physics: GaAs has phonon dispersion spectrum that looks so: the horizontal axis parametrizes the wave numer values $k$, therefore it seems plasible that ...
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How to interpret stretching mode between two atoms in solid-state crystals?

I have a fundamental question about the definition of "stretching mode" obtained from molecular dynamics simulations. Is it the fourier transform of autocorrelation of bond lengths over a time period ...
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Difference between Debye frequency and highest phonon frequency

In my lecture it says that the Debye frequency is the cutoff frequency. So is this also the highest phonon frequency? And if not, what is the difference? A little background: I do have an exercise ...
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Surface States and Fermi Level

In work Gelmont, B. L., Shur, M., & Stroscio, M. (1995). Polar optical-phonon scattering in three- and two-dimensional electron gases. Journal of Applied Physics, 77(2), 657–660 when author moving ...
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Path a photon or phonon takes in a moving medium

Lets say we have a medium with refractive index n whose velocity is given as a function of height. $v_x(y)=ay$ How would we go about finding the motion of a photon or phonon in this space from the ...
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Treatment of electrons and phonons in condensed matter physics

I was watching the lectures by steve simon(oxford) on solid-state physics. In the course, he derived the dispersion relation for phonons(assuming spring between atoms) and dispersion relation for ...
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Speed of sound in Aluminum given the debye temperature

I am trying to calculate the speed of sound in aluminum given the Debye temperature $\theta_D=428 \;\mathrm{K}$, the mass density of Al is $\rho = 2.7 \cdot 10^3 \;\mathrm{kg}\cdot \mathrm{m}^{-3}$, ...
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Born van Karman periodic condition

Before getting deeper into the phonons. One of the conditions is that because of their quantization comes from the condition that system is invariant to translation. And length of the systems I can ...
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Prove that group velocity is the velocity of energy transport in wave

Generally, the group velocity $v_g = \dfrac{\partial \omega}{\partial k}$ of a wave is the velocity of energy transport. In "Introduction to Solid State Physics", Kittel following is stated: The ...
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Can we add the resistivity due to different scattering mechanisms?

Suppose there's a metal in which electrons interact with themselves and with the phonons. The hamiltonian might look like this \begin{equation} H= \sum_{k}\epsilon_k c^\dagger_k c_k + \sum_{k}\...
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Interpreting phonon dispersion relations

I have been working with phonon dispersion relations for a while now on the topic of metamaterials (phononic band gaps). However, I still do not feel that I have fully grasped how to interpret these ...
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Why does kinetic energy below molecule bond energy break bonds?

I was thinking about why bullet can break molecular bonds when it hits solid target despite the fact that the kinetic energy of the individual atoms that make up the bullet is less that the molecule ...
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Are sound waves in fluids also Goldstone modes?

One usually says that sound waves in a crystal, ie. phonons, are Goldstone modes of the broken translation symmetries. However, fluids have sound waves and also translation invariance. In fact, it's ...
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Questions about scattering matrix theory of non-free particles

Hi,I have a problem for scattering matrix theory. Currently, the book I've read is about collision between free particles. What if collision between non-free particles? For example, in lattice, only ...
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Why does silicon have 6 phonon modes instead of 24?

As is known, silicon has a structure made up of two intertwined face-centered cubic (FCC) lattices, with bases $[000]$ and $[\frac 1 4,\frac 1 4,\frac 1 4]$. This equates to $\frac{1}{8}\cdot 8 + \...
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How does heat is generated during nuclear reaction

In a nuclear reaction 235-U is being constantly divided under high neutron flux. After the division we get 2-3 neutrons with high energy and fission products with its own energy. My question is from ...
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How many atoms are in the primitive unit cell for diamond?

The primitive unit cell for diamond is pictured (the parallelepiped inside the cube). How many atoms are in the unit cell? My first guess is 3.5 and i know this must be wrong as the number of atoms in ...
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Phonons in quantum dots

If my understanding is correct, quantum dots are tiny crystals where the confined electronic degrees of freedom have discrete energy levels. In this paper Phys. Rev. B 65, 195313 (2002), and many ...
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High temperature phonon heat capacity and equipartition theorem

I have seen the derivation of the high temperature heat capatcity sing integration of the density of states. The heat capacity is $C=3Nk_B$ with $N$ the number of atoms in the lattice. According to my ...
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Why the phonon modes may not be horizontal at the brillouin zone boundary?

In the book Principles of the Theory of Solids by Ziman, it says: The exact behaviour then will be rather complicated. In general, (the phonon mode) $\nu_q$ bends over, as in the linear case, ...
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Harmonic Approximation for dynamical matrix in 3D fcc-lattice

I have maybe a basic misunderstanding of how the harmonic approximation is working. I have the following problem: Given a fcc-lattice with lattice constant $a$ and a radial-symmetric potential ...
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How do normal modes have group velocity?

Considering phonon dispersion curves in crystals, the group velocity is given by the derivative of frequency with respect to wave vector. But these modes on the dispersion represent normal modes, ...
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How can I meaningfully diagonalize the eigenvector subspace of a degenerate phonon mode?

It often occurs to find phonon modes which are degenerate by symmetry. In such occasions the eigenvector is usually not physically insightful, as is is a linear combination of the n degenerate ...
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Is the absorption of photons instantaneous?

I'd like to know if the excitation of chlorophyll by photons $$Chl+ h\nu \rightarrow Chl^*$$ is instantaneous. I imagine a photon arriving $0.5$ Angstroms away from the molecule, and then disappearing ...
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From a gravitational wave detector perspective, what is the difference between a gravitational wave and a phonon?

I already asked a question but it seemed that it was not precise enough. My problem is that I cannot see how gravitational waves have anything to do with spacetime. An EM wave or a phonon can put ...

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