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Sum of powers of complex exponentials

EDIT: Amusingly enough, this same question was asked (and answered) 4 days ago by someone else. The link is here I encountered the identity $\sum_{j=1}^{N} {e^{ikja}} = N\delta_{k,0}$ when reading ...
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1answer
29 views

Phonon modes in one-dimensional monoatomic chain

I am familirazing myself with the lattice dynamics reading Ashkroft-Mermin (p2 ch 22). My question is what it the mathematics behind the deriviation $U^{harm}=1/2 K \sum_{n} [u(na)-u([n+1]a)]^2$ ...
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0answers
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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 ...
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9 views

Why is forward brillouin scattering difficult to observe?

Generally we talk of only the backward Brillouin scattering. And I just know forward scattering is difficult to observe? Why is it so? Does it have something to do with phonon life time? Is it ...
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21 views

What is the difference between finite displacement and linear response for calculating vibrational properties?

I see these concepts appearing in the context of calculating phonons and other vibrational properties, but I can't find a concrete explanation of the differences between linear response (DFPT) and the ...
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24 views

Why the lifetime of acoustic phonons is larger than that of optical phonons?

for example, in GaAs, the LA phonon lifetime can be ~850 ns, while LO phonon lifetime is only about 5 ps. Why such huge difference occurs? Thanks!
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46 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 ...
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1answer
56 views

What is the relationship between Raman peaks and phonon vibration modes?

I've seen Raman spectra, such as here, where peaks at certain wavenumbers were identified with phonon vibration modes (TO, LO, TA, LA). What is the relationship behind this, and how could I make such ...
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2answers
59 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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1answer
50 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 ...
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0answers
32 views

What does a 'complex displacement' of phonon mode mean?

I'm trying to interpret the phonon mode output file from a phonopy/vasp calculation, and this webpage talks about the 'complex displacement' of atoms in the system, and I'm not quite sure what it ...
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29 views

How to calculate phonon decay rate?

Here, the authors calculate the quality factor for a resonator. They take it as one over phonon decay rate, given by (24). Simplified, (24) looks like this: \begin{equation} \Gamma = \gamma_{N-1,N} - ...
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2answers
66 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 ...
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0answers
62 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, ...
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1answer
45 views

Why does a thermal memory need a thermal bath?

In the article "Thermal Memory: A Storage of Phononic Information Phys. Rev. Lett. 101, 267203 – Published 29 December 2008" it's said that a thermal memory need a thermal bath, similar to a power ...
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138 views

A naive question on the “continuously” degenerate ground states of 1d phonons?

In general, the gapless Goldstone mode is related to the "continuously" degenerate ground states. The Mexican hat potential is an example (see the logo of this SE website), where the bottom circle is ...
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43 views

Why is the k=0 phonon neglected when calculating Debye-Waller factor?

When calculating Debye-Waller factor one gets the form: $e^{-2W} = ...
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0answers
59 views

How to deal with coupled fermion boson operators?

I am a beginner in field theory and I have an exercise where I have a product of coupled fermion boson operators? $$ \hat{b_{l} }^{\dagger}\hat{c_{l^{'}} }^{\dagger}\hat{a_{q} }\hat{b_{l} ...
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1answer
111 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 ...
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1answer
124 views

How to define the heat current in an isotropic continuum material

I'm doing a FDTD (finite difference time domain) simulation of an isotropic continuum material. And I have several questions. How do you define the energy transferred through an isotropic continuum ...
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136 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
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1answer
117 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 ...
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2answers
67 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 ...
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1answer
238 views

Non-trivial solution for a linear set of coefficients involved in the phonon modes of a semiconductor quantum dot

I am trying to use the method outlined in this linked paper (T. Takagahara, Journal of Luminescence, 70 (1996), pp. 129-143) to find the phonon-exciton coupling in a spherical PbS quantum dot. In Eq ...
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1answer
560 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 ...
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88 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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1answer
83 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, ...
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1answer
25 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 ...
2
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1answer
180 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'. ...
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2answers
250 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?
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1answer
27 views

Why does a phononic gas require that to reach equilibrium phonon waves need to lose momentum when colliding?

I'm learning about phonons and I read that for a phononic gas to reach equilibrium the phonon waves need to lose momentum when they collide. However in an ideal gas the momentum is always preseved. ...
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1answer
90 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 ...
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3answers
532 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 ...
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77 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 ...
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0answers
55 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
92 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
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1answer
112 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 ...
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1answer
189 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 ...
2
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1answer
172 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 ...
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0answers
129 views

Do I understand measurement of dispersion relation in a solid correctly?

I'm currently doing an introduction to solid state physics course and have a quick question about measurement of the dispersion relation of phonons in a solid: The way I understood it is the ...
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1answer
1k views

Photons and phonons

A few months ago I asked about phonons. I got some very good answers but I still have difficulty getting an intuition for phonons, while somehow photons, which in many ways are similar and which I ...
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2answers
199 views

Debye temperature for the steel?

I'm looking for data on Debye temperature of steel (ideally with a known carbon concentration, structure, and set of phases), but find only data on elements. Do You happen to meet the data in papers, ...
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1answer
292 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 ...
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1answer
614 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 ...
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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? ...
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0answers
81 views

What is the physical meaning of group velocity for elastic waves through crystals?

In a chapter about phonons they define group speeds for elastic waves in crystals as the derivative of the dispersion relation: $$v_g = \frac{d{\omega}}{d{k}} $$ I wonder though how they come to ...
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1answer
31 views

What are degenerate transversal oscillation modes?

This is just a question about terminology that is used in the beginning of a chapter about phonons. In a simple cubic crystal, we can consider elastic oscillations in f.i. the [100] direction. In ...
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2answers
2k 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). ...
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1answer
2k views

Why the name “optical phonon”?

Why do we have two different types of phonons, optical and acoustical? Why are they called optical phonons?
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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?