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22
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2answers
3k views

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). ...
11
votes
2answers
586 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 ...
9
votes
3answers
1k views

Phonon carries zero spin. Why?

photons and phonons both have polarization, we attribute spin 1 for photons but spin 0 for phonons. Why?
7
votes
1answer
613 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
votes
2answers
163 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
votes
2answers
1k views

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 ...
6
votes
1answer
300 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 ...
5
votes
2answers
360 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
votes
1answer
220 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
votes
1answer
219 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
votes
3answers
395 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
votes
1answer
87 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
votes
1answer
3k views

Why the name “optical phonon”?

Why do we have two different types of phonons, optical and acoustical? Why are they called optical phonons?
3
votes
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.
3
votes
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
votes
1answer
656 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
votes
1answer
231 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 ...
3
votes
2answers
338 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
votes
3answers
1k views

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? ...
3
votes
0answers
153 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 ...
2
votes
3answers
645 views

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 ...
2
votes
1answer
59 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
votes
1answer
202 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
votes
1answer
252 views

What is the experimental evidence for quantization of lattice vibrations?

Is there any direct experiment to show the quantization of lattice vibrations?
2
votes
1answer
185 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
votes
1answer
313 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
votes
1answer
46 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
votes
1answer
37 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
votes
2answers
83 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
votes
1answer
129 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
votes
1answer
127 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
votes
1answer
73 views

What is the first paper to report observations of polaritons?

I am seeking references to the first articles regarding the observation of polaritons.
2
votes
0answers
51 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 ...
2
votes
0answers
70 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
votes
2answers
73 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
votes
0answers
94 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 ...
2
votes
0answers
88 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
votes
0answers
62 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
votes
1answer
105 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: ...
2
votes
0answers
117 views

Phonon-polariton literature resources? [closed]

What is a good resource for studying phonon-polaritons?
1
vote
3answers
802 views

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 ...
1
vote
1answer
85 views

Understanding EM Fields

I am an electronics engineering major and some questions arise when studying communications technology that utilizes wireless technology. In particular, I am more of a complete picture kind of person, ...
1
vote
2answers
31 views

When do optical phonon branches arise?

As far as I understand from what I'm studying, only when you have more than one kind of atom in the lattice structure, will the phonon have an optical branch, or else it should not have an optical ...
1
vote
2answers
229 views

Reciprocal lattice and phonon

As we obtain a reciprocal lattice for a given crystal we see that discrete values of wavevectors are allowed but a phonon wavevector spectrum is a continuum. Is there a relation between reciprocal ...
1
vote
1answer
23 views

Help with the analytical solution for the dispersion relation of an elastic wave with wave vector k

I was studying Phonons and Lattice vibrations and came across the equation. I want the mathematical solution for this. $$M\frac{d^2u_n}{dt^2}=C[u_{n+1}+u_{n-1}-2u_n]$$ from here it is argued that ...
1
vote
1answer
26 views

Do the characteristic vibrational modes of a material define how much will a material heat up upon radiation excitation?

Do, and if yes how, does the intensity and energy of the Raman modes of a material make it to heat more by radiation excitation. I see phonons and vibrations of the lattice as heat, but maybe I'm ...
1
vote
1answer
100 views

Laser excitation of Phonon Modes

Can a laser only excite optical modes? The name appears to have historical significance in terms of the sodium ion, but I presume it must be true when looking at the dispersion relationship (the ...
1
vote
0answers
22 views

phonon dispersion with random masses

In order to see how phonons should be affected by disorder, I've been playing around with a model involving a 1D chain of masses linked by springs, where the spring strengths are all the same but the ...
1
vote
0answers
30 views

Monte calro, Non-polar optical phonon scattering?

I have a question on electron and non-polar optical phonon scattering in GaAs. Is it allowed to consider intravally electron non-polar optical phonon scattering in L-valley of GaAs ?. I found in the ...
1
vote
2answers
85 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 ...