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.
1
vote
1answer
21 views
Why isn't the dispersion of the phonon spectrum of two atomic basis with equal masses the same as for the one atomic basis?
The solution for the two atomic basis is given by
\begin{align*}
\omega^{2}=\gamma\left(\frac{1}{M_{1}}+\frac{1}{M_{2}}\right) \pm \gamma\left[\left(\frac{1}{M_{1}}+\frac{1}{M_{2}}\right)^{2}-\frac{...
-3
votes
0answers
58 views
Is it possible that gravitons don't exist, but are actually something like phonons? [on hold]
Why or why not? String theory says that gravity arises due to spin 2 closed strings. If gravitons were actually phonons, is it against the possibility that gravitons are actually closed strings? How ...
0
votes
0answers
20 views
Deriving effective interactions, e.g. phonon-mediated electron-electron interaction
Upshot of the question: how can I derive the effective electron-electron interaction brought about by the electron-phonon interaction?
I've read derivations of the electron-phonon interaction and ...
2
votes
1answer
41 views
Why do purely harmonic interatomic interactions result in infinite thermal conductivity?
When interatomic interactions are purely harmonic, normal modes cannot interact, and therefore no phonon scattering occurs, thus resulting in infinite thermal conductivity.
But why is anharmonicity ...
1
vote
1answer
40 views
Mossbauer effect: neglectable recoil or absolute no recoil?
I stumbled on the Mossbauer effect. From the wikipedia article, I cannot tell for sure if the momentum of recoil is really zero, or only neglectable.
From what I do (think I) understand, the ...
0
votes
1answer
61 views
Should phonon energy be undefined at zero frequency?
The energy carried by phonons of frequency $\omega$ is given by
$$
E = \hbar \omega n_b(\beta \hbar \omega) = \hbar \omega \frac{1}{exp(\beta \hbar \omega) - 1}
$$
So when $\omega = 0 $, the energy ...
5
votes
2answers
72 views
The difference between optical phonons and acoustic phonons in terms of energy absorption
Why can the energy of a photon be directly absorbed by an optical phonon but not by an acoustic phonon？
0
votes
1answer
36 views
Heat capacity due to Phonon Vibrations
Why does the speed of sound come, in the expression of Heat capacity, from phonon vibrations?
0
votes
0answers
20 views
Calculate phonon density of states
I need to calculate phonon density of states for a cuprate superconductor. I know there is a general formula for the calculation of phonon density of states by Einstein models like this
$$D(\omega)=(\...
0
votes
1answer
43 views
Optical and acoustic branch
Does a diatomic crystal posses both optical and acoustic branch simultaneously; Or, whether the vibration is either optical or acoustic?
1
vote
0answers
57 views
Why optical phonons are called “optical”? [duplicate]
In diatomic lattice vibration, acoustical phonons correspond to vibration. But I could not understand the relevance of term optical in this context.
0
votes
0answers
25 views
Vibrational Energy at T = 0 K using the Debye model
I mm trying to estimate the vibrational energy at $T=0$ for a 3-D lattice using the Debye model.
My plan is to sum over all the frequencies using:
$$U = \int_0^{\omega_D} d\omega D(\omega)\epsilon(...
2
votes
0answers
21 views
Approximations in article on phonon-assisted emission
I am trying to reproduce the calculations from an old article by J.J. Hopfield (J. Phys. Chem. Solids, vol.10, pp.110-119 (1959) - A theory of edge emission phenomena in CdS, ZnS and ZnO - found here)....
1
vote
0answers
55 views
Elastic X-ray diffraction: Where does the Photon Momentum go to?
lately I was discussing the following situation. Let's suppose you are doing X-Ray diffraction experiments on a crystal. So what you basically do is shooting a high energy photon with a wave vector $k$...
2
votes
1answer
57 views
Why phonon density of state depends on velocity autocorrelation?
We know that if we take the Fourier Transformation of velocity autocorrelation function, we will get the phonon density of state. But why phonon density of state depends on this? What is the physical ...
1
vote
0answers
10 views
Thermalizing bulk superconductors
I have been discussing with some friends whether or not (or how) bulk superconductors thermalize when placed in an environment far below their transition temperature.
Suppose you have a cube of pure ...
0
votes
1answer
40 views
Derivation of the dynamical matrix
I am following a derivation of the dynamical matrix given at http://physik.uni-graz.at/~pep/Lehre/PP/DynMat.pdf. Here T and W are kinetic and potential energies.
$T=\sum_{n\alpha i}\frac{M_{\alpha}}{...
2
votes
0answers
78 views
How does Bohmian Mechanics explain superconductivity?
I'm looking for sources that discuss how Bohmian Mechanics explains superconductivity. Are there still Cooper pairs? Phonons? I saw one vague reference to vortices, but no details. This is my first ...
0
votes
1answer
17 views
Is this equation for the density of states of an elastic isotropic material an approximation?
The density of states of phonons can be calculated with
$$
Z(\omega)=\frac{V}{(2\pi)^3}\int_{\omega=\text{const}}\frac{d\vec{f}_\omega}{|\vec\nabla\omega|}
$$
where $\omega$ is the phonon frequency ...
0
votes
0answers
14 views
Doppler shift in Acousto-Optic modulators
The interaction between a beam of light and an acoustic wave is commonly modelized as a photon-phonon scattering phenomenon. Applying the conservation of energy we have that
$$ \hbar\nu_1=\hbar\nu_0\...
0
votes
0answers
25 views
Long-ranged Coulomb Interaction $\Rightarrow$ Longitudinal Plasmon Modes?
I am currently taking a lecture on quantum theory of condesed matter systems. In the lecture notes it is stated that
For long-ranged Coulomb interactions only longitudinal plasmon modes are ...
1
vote
1answer
46 views
Can we consider oscillation of air column in the wind instruments as phonons subject to Bose- Einstein statistics ?
A flute is a wind instrument, which could be modelled as a resonance cylinder open at both ends. Any cylinder resonates at multiple frequencies. A skilful player produces a standing wave in the flute ...
1
vote
1answer
241 views
Why the chemical potential of phonon gas in Einstein 's solid model is not zero
In Einstein’s model of solid, each atom in the solid is considered to be an independent three-dimensional quantum harmonic oscillator with characteristic frequency $ω$ that is constant. Each degree of ...
1
vote
1answer
53 views
Understanding what the Bose-Einstein distribution
I'm currently studying Kittel's Solid State Physics and in his chapter on Phonon heat capacity, we need to first calculate the total energy $U$. Phonons have energy $E_n = (n+1/2)\hbar\omega$ and he ...
0
votes
1answer
30 views
Understanding the technical bits of quantising elastic waves
I'm reading Kittel's Solid State book and I have a number of 'simple-ish' questions regarding phonons. He starts with the hamiltonian
$$H=\sum_{s=1}^N\left[\dfrac{1}{2M}p_s^2+\dfrac{1}{2}C(q_{s+1}-q_s)...
4
votes
1answer
88 views
Spontaneous symmetry breaking in fluids
BACKGROUND:
One can think of solids as spontaneously breaking translational symmetries in the sense that each atom in a lattice has to pick a particular position. Yet, as with everything in our ...
2
votes
1answer
151 views
What is the phonon/lattice interaction?
To my understanding, phonons in solids are an excited state of a lattice, i.e., a lattice of atoms oscillate at a certain frequency. Phonons are quasipartices.
But what should the phonon/lattice ...
3
votes
1answer
193 views
Debye Temperature for Copper
I am trying to calculate the Debye temperature, $\theta_D$, of copper using the following:
$$
\theta_D = \frac{\hbar v_s}{k_B} \left( \frac{6\pi^2N}{V} \right)^{1/3}
$$
I have the following values: $...
0
votes
1answer
16 views
Why does acoustic imepdance increase when mass density and bulk modulus increaes?
If we take some material and (somehow) increase its mass density or bulk modulus then its acoustic impedance will increase as $z = \sqrt{\rho \kappa}$. That is, it What is the physical reasoning ...
1
vote
0answers
50 views
Allowed k value for maximum and minimum phonon frequency in a diatomic lattice
I've got an expression for the phonon frequency in a diatomic lattice where the atoms are of mass $m$ and $5m$. The expression is $\omega^2=(12Cm\pm\sqrt{(144C^2m^2-20m^2C^2(1-\cos(ka)})))/(10m^2)$. I ...
3
votes
1answer
61 views
Can light cool down materials?
I was studying Raman scattering and I computed the probability of anti-Stokes scattering (with density of states n, at the numerator) over Stokes (n+1 at denominator). The densities are based on the ...
1
vote
2answers
89 views
In phonon theory, what is the physical significance of the force constants tensors?
I want to compute phase equilibria of crystalline solids using First-principle methods (DFT in particular). The methodology for this computation is described in this chapter.
In order to calculate ...
1
vote
0answers
57 views
Can the periodicity in k-space of the electronic band structure be understood as a result of aliasing?
Discrete sampling in the case of phonons
In the case of phonons in periodic solids, the picture is quite intuitive. The motion of the atoms in the lattice is described as a continuous wave (amplitude ...
0
votes
1answer
158 views
How many types of phonons are there, and what are their characteristics?
I've skimmed through Wikipedia's article, as well as as PSE question What is a phonon?, but I am still entirely left in confusion as to the types of phonons and their corresponding characteristics and ...
2
votes
1answer
100 views
Pauli principle for “Phonons”
I'm reading in Feynman's "Statistical Mechanics" Chap. 6.4 about a system of $M$ interacting particles, they may be bosons or fermions. Let the hamiltonian be
$$ H=\sum_i^{3M}p_i^2+\sum_{ij}^{3M}U_{...
1
vote
0answers
66 views
Phonons to solve solid mechanics problems?
From what I understand, phonons can be used to solve acoustics or optics problems, but can we used phonons to solve a solid mechanics problem?
The first answer I expect is :"Acoustics wave are solid ...
3
votes
1answer
120 views
In a material, how does the heat equation arise from phonons? And from electrons?
What would be the starting point to derive the heat equation in a material?
Generally, in insulators the heat is mediated via phonons while in metals (conductors), electrons are the main responsible ...
1
vote
1answer
62 views
Phase-shifting by Acousto-Optic modulators
I am working on a project where I need to be able to introduce a phase-shift to a light pulse, without any mechanical parts involved. One of the options is to use an acousto-optic modulator:
...
0
votes
3answers
68 views
How do phonons impact the way heat is transferred between two solids?
If we assume that in a system heat is only transferred by conduction (between two different solid of different materials), what role do phonons play in this phenomenon?
0
votes
0answers
24 views
Perowskit: Why is oxygen moving “up”?
I have a question concerning the "Perowskit Structure". First of all, a displacement of positively and negatively charged ions happens. So far, so good. But why is oxygen considered to move upwards? ...
0
votes
0answers
28 views
Quasi-elastic electron-phonon scattering
When does electron-phonon interaction become quasi-elastic as opposed to inelastic and why does this happen at high temperatures? Also, which factors influence the temperature at which this crossover ...
3
votes
2answers
125 views
Misunderstood of wave-particle dualism? [duplicate]
Reading about dual nature of light, and atomic transitions, it seems to me, maybe wrongly, that the dual nature depends on the way we look at the phenomena.
Suppose a water wave travels and reach ...
1
vote
0answers
32 views
D-peak of Raman Spectra of Graphite explanation
The D peak in the Raman Spectrum of Graphite is attributed to the breathing mode of $A_{1g)$ symmetry involving phonons near zone boundary. The explanation is the following:
The change of bond ...
1
vote
0answers
46 views
Energy and momentum conservation argument for electron-phonon transitions in Bilayer Graphene
I'm reading a paper which says that the interband transitions ($\pi_1^* \rightarrow \pi_2^*$) involving phonons at $q= 0 $ and $ q = K$ in Bilayer Graphene are prohibited by energy and momentum ...
1
vote
0answers
64 views
Fourier transform to decouple pairwise interacting harmonic oscillators
To solve a Hamiltonian below $$H=\sum_{i}\frac{p^{2}_{i}}{2m_{i}}+\frac{1}{2}\sum_{j}k_{jj+1}(x_{j}-x_{j+1})^{2} $$ one can do fourier transform to decouple the harmonic oscillators. $$p_{m}=\sum_{q=1}...
0
votes
1answer
40 views
Solid State Phonons at the edge of Brillion zone
Bose-Einstein statistics tell us that the number of phonons with energy k at temperature
T via the bose einstein distribution.
My question is regarding phonons in the low energy regime.
My notes ...
0
votes
1answer
19 views
Velocity changes due to crystal anharmonicity?
What is the effect of cubic and higher anharmonicities of a phonon hamiltonian on the velocity of phonons?
0
votes
2answers
89 views
Difference between Phonons and heat?
1, if these two were the different then how we differentiate with one another?.
2, if these two were the same, then what is really vibrating?, atom in the lattice or electron in the atom or the bond ...
1
vote
0answers
28 views
Lattice to continuum transformation in one dimension (arbitrary range interaction)
Please help me convert the ionic displacement $u_l$ of the $l^{th}$ ion to a continuous field $u'(y)$ in the following problem. I am trying to derive the Hamiltonian of a 1-D lattice (spacing $=n_0^{-...
0
votes
1answer
98 views
Beyond the frequency cutoff in Debye model
I understand when wavelength is smaller than the atom interval, sound waves can't travel; hence, we need a frequency cutoff in the Debye Model.
But surely when it is the case, atoms are still ...
