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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What is a phonon?

I am trying to understand intuitively what a phonon is, but for the moment I find it quite difficult (having a limited background in quantum mechanics, an undergraduate course in non-relativistic QM). ...
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2k views

Phonon carries zero spin. Why?

photons and phonons both have polarization, we attribute spin 1 for photons but spin 0 for phonons. Why?
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657 views

Number density of LO and LA phonons as a function of temperature?

I'd like to know the how the number density of longitudinal optical (LO) and longitudinal acoustic (LA) phonons varies as a function of temperature of the material. Is there a simple expression for ...
10
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How to get an imaginary self energy?

The Lehman representation of the frequency-dependent single particle Green's function is $$G(k,\omega) = \sum_n \frac{|c_k|^2}{\omega - E_n + i\eta}$$ where $n$ enumerates all the eigenstates of the ...
8
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2answers
259 views

Has a phonon, a formal quasi-particle, ever been observed as a point particle?

Phonons are a nice tool to simplify the quantum-mechanical description of lattice vibrations by identifying the ladder operator of normal modes as creation operators of a certain quasi-particle. In ...
7
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1answer
775 views

Lagrangian of 2D square lattice of point masses connected by springs

Zee's QFT book mentions the Lagrangian of a square 2D horizontal lattice of point masses, connected by springs, and considering only vertical displacements $q_{i}$, as $ L = \frac{1}{2} ...
7
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370 views

Why does the conductivity $\sigma$ decrease with the temperature $T$ in a semi-conductor?

We performed an undergrad experiment where we looked at the resistance $\rho$ and Hall constant $R_\text H$ of a doped InAs semiconductor with the van der Pauw method. Then we cooled it down to around ...
6
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What is a Zero-Phonon Line (ZPL)?

I am trying to understand the electronic structure of the negatively charged NV centre in diamond, where there is a so-called Zero-Phonon Line (ZPL) in the spectrum. Can anybody explain what a ZPL is? ...
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How is Mössbauer spectroscopy so resistant to thermal motion?

Mössbauer spectroscopy detects tiny shifts (on the order of $\mu$eV or meV) in a gamma ray's energy due to the chemical environment of the nucleus. The scan consists of moving a source of excited ...
5
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2answers
60 views

What do we know about the strength of the electron-phonon coupling in high-temperature superconductors?

I would like to clarify the situation of the electron-phonon coupling in high-temperature superconductors (or considering only the cuprates). The main question is what do we know about the strength of ...
5
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2answers
132 views

How should I be thinking about phonons?

I have started learning solid state physics and i am struggling with the concept of phonons. I understand how the vibrational wave can be quantised (because of quantum oscillators) and thought of as ...
5
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429 views

Higgs vs phonons

Jim Baggott's "Higgs" quotes David Millers' prize-winning one-page explanation of the Higgs mechanism (the one that evokes Margaret Thatcher crossing a room). I've heard that part many times, but not ...
5
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257 views

Real World measurements related to phonon dispersion [closed]

I hope no one objects to the style of this question. Let me explain my motives in asking the question first. Condensed matter physics is one of the most beautiful subjects around. But those who are ...
4
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1answer
4k views

Why the name “optical phonon”?

Why do we have two different types of phonons, optical and acoustical? Why are they called optical phonons?
4
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1answer
323 views

How does Cooper pairing work?

Cooper pairs are one of the models how superconductivity is explained. What still baffles me is how a vibration of the crystal lattice (the so-called phonon) can interact with the electron (an actual ...
4
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1answer
241 views

Coupling of matter field with gauge boson and Goldstone boson:

What's the fundamental difference between the way a gauge boson gets coupled to a matter field, preferably a Fermionic field and the way a Goldstone boson gets coupled to the matter field ? In ...
4
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583 views

What is the mathematical justification for the quadratic approximation to the energy of a spring in a one-dimensional lattice?

It follows easily from this draw, the length $l$ of this spring as a function of the vertical distance $x$, as $l(x)=\sqrt{1+x^{2}}$ Now, $l$ can be expressed as a MacLaurin expansion: $$l(x) = ...
4
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1answer
100 views

Where to learn Temperature Dependent Conductivity induced by Electron-Phonon Interaction? [closed]

I want to learn how to calculate the temperature dependent conductivity induced by electron-phonon interaction. I know in low temperature, the resistance in metal $\rho$ is proportional to $T^5$, $T$ ...
3
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4answers
2k views

Do we say that phonon has effective mass through its dispersion relation?

The effective mass is proportional to the second derivative of the dispersion relation d2k/dE2. Do we say that phonon have effective mass through it ? Spin wave have.
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2answers
3k views

Are there devices which convert thermal energy to electric energy?

Converting optical energy to electric energy is a huge business based on the photovoltaic effect. Is there an analogous effect for phonons? Are ther devices which convert phonon energy to electric ...
3
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730 views

Why must phonon-phonon interaction be anharmonic?

I'm learning about phonons and this is really interesting. Why can't I describe two phonons colliding as a harmonic oscillation? Why does it have to be anharmonic for the phonon model to work?
3
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1answer
1k views

Question about the quantization of lattice vibration (phonons)

In my syllabus about solid state physics they state that lattice vibration is quantized, analogous to the harmonic oscillator: $$E = (n+\frac{1}{2})\hbar\omega$$ So the lattice vibration has ...
3
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1answer
251 views

Why does the creation operator take a continuum value for the momentum?

Imagine that you have a lattice and a set of masses. Each mass at a lattice point. Now each two neighbouring masses are connected with spring. Now in Classical Mechanics (CM) the ground state is the ...
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71 views

Is it possible to efficiently extract phonons from a lattice?

The population inversion generated in lasers occurs in multi-level atomic systems. As an example, the Nd:YAG energy diagram is shown below. The pump pushes the Nd ions up to the upper levels, and ...
3
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2answers
154 views

Problem with derivation of phonons in crystal

In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental ...
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Raman vs. Brillouin Scattering

In my class notes, I have the two types of inelastic scattering described as follows. (Note that the "difference in energy" here is the difference between the incident frequency of the light and the ...
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1answer
76 views

Why is the number of phonon modes in a solid restricted to a finite value?

Kittel's Thermal Physics (Amazon link) makes the statement: There is no limit to the number of possible electromagnetic modes in a cavity, but the number of elastic modes in a finite solid is ...
2
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1answer
302 views

Difference between the 'phonons and virtual photons'

I understand what are virtual photons and the difference between the real and virtual photons. However, I am not able to clearly distinguish the difference between the 'phonons and virtual photons'. ...
2
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1answer
321 views

What is the experimental evidence for quantization of lattice vibrations?

Is there any direct experiment to show the quantization of lattice vibrations?
2
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1answer
226 views

Phonon-phonon interaction

I have been told that phonon-phonon Interaction is an anharmonic effect so only arises if terms of third and higher order in the displacement of the ions the Hamiltonian for the nuclii is taken into ...
2
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1answer
423 views

Explanation of Superconductivity

I can't get a definitive explanation of why superconductivity happens and I am getting mixed explanations from my textbooks. I will tell you what I know and hopefully you can correct any ...
2
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1answer
39 views

Localized Phonon Vibrational Modes and Thermal Conductivity

I chanced upon this 1D chain Mass Impurity model: At the end of all the derivations, it concludes that Case 1: $ 0 < M_0 < M$ The impurity is lighter than the host atoms. The frequencies ...
2
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2answers
52 views

Are there materials that strongly (macroscopically) vibrate under light of certain frequencies? If so why?

Picture an imperfect plane of loose particulate matter like sand or silt. Are there materials where if I shine light (not isotropically) on the plane I could get the particles to vibrate with large ...
2
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1answer
90 views

What is a single-phonon?

From what I understood from wikipedia, as well as some other resources, each phonon corresponds to a normal mode oscillation, and the creation operator to create a phonon of wavevector $k$ is: $$ ...
2
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1answer
52 views

How does phonon scattering change the distribution function?

For a one-dimensional structure, we know that the modified distribution function has the following energy dependency in equilibrium: \begin{equation} Z(\varepsilon)\,f(\varepsilon) = ...
2
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187 views

Phonon spectrum

I had a question regarding phonon spectrum in condensed matter. Consider a cubic lattice with '$p$' atoms per primitive cell. Consider the lattice plane used for derivation of the phonon spectrum to ...
2
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2answers
219 views

What's the relationship between sound speed and acoustic phonons?

In the textbook, it says that the slope of the acoustic branch of phonons equals to the sound speed. There are 3 kinds of acoustic phonons including TA and LA phonons. Does it mean that there are also ...
2
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1answer
175 views

How does a sonic black hole (or dumb hole) work?

I came across this term and I heard they used sonic black holes to detect something analogous to hawking radiation, but I have failed to find sources which explain how exactly they work and how they ...
2
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1answer
222 views

Help needed to understand the dispersion curve of a 1D lattice with diatomic basis

I am trying to understand the dispersion curve (as shown below) of a 1D lattice with diatomic basis. Here are my questions: Can both optical and acoustic branch of phonon simultaneously exist in ...
2
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1answer
178 views

Phonon scattering process in raman spectroscopy

I am trying to understand diagrams that involve showing phonon scattering processes that contribute to raman spectroscopy peaks. For example, I drew the one at the bottom of this post. This is ...
2
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1answer
75 views

What is the first paper to report observations of polaritons?

I am seeking references to the first articles regarding the observation of polaritons.
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How do phonons and spinwaves interact? [closed]

What governs the coupling of acoustic phonons to transverse and longitudinal spinwaves? Is there a simple picture?
2
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105 views

Proof of equivalence between soundwaves and phonons in large wavelength limit (Ashcroft-Mermin, ch. 22)

In chapter 22, Ashcrof and Mermin argue that the normal modes of a harmonic crystal are not only formal but precisely equal to the large wavelength limit of acoustic phonons (which sounds, of course, ...
2
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2answers
106 views

Potential Energy in solids: Why are different equations used for deriving lattice constants and for deriving the properties of phonons?

While deriving the equilibrium lattice constants we use expressions for potential like Lennard-Jones potential which have 6th and 12th order terms or Madelung energy for ionic crystals. While ...
2
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125 views

Force constant of metals - Kohn anomaly

In Introduction to Solid State Physics (Kittel), it assumed the force constant between plane $s$ and $s+p$ $C_p=A\frac{\sin pk_0a}{pa}$ in metals to represent a Kohn anomaly. It says such a form is ...
2
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0answers
101 views

How do I determine resistivity from electron defects of high purity gold?

I am trying to create a plot for the electrical resistivity of high purity gold from 1 K to 1000 K. I found gold's resistivity at 300 K using the Wiedemann-Franz Law based on thermal conductivity data ...
2
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1answer
138 views

Out-of-Plane Phonons

I am trying to derive the out-of-plane phonon dispersion relation for a membrane. As far as I can tell, one of the simplest ways to do so is with a Lagrangian of the form: ...
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1answer
38 views

How do phonons affect the work function?

How do phonons affect the work function? Could phonons that are directed towards a single atom, such as in a body-centered cubic crystal, increase the amount of thermal excitation and thus decrease ...
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3answers
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Can someone explain LO-TO Splitting?

LO-TO splitting occurs in an ionic (i.e. polar) solid such as GaAs or NaCl. What happens is that the degeneracy of the transverse optical (TO) and longitudinal optical (LO) phonons at $k=0$ is broken ...