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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Thermal propagator for free phonons evaluation
I'm trying to evaluate the thermal propagator for free phonons $$-D(\bar{x}\tau, \bar{x}'\tau') = \left\langle \mathcal{T} \varphi(\bar{x}\tau)\varphi(\bar{x}'\tau') \right\rangle $$
where its ...
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Why does the Schriefer-Wolff transformation works for phonons?
One way to derive a Hamiltonian with attractive electron interactions is to start from the Hamiltonian with a part quadratic in electrons, quadratic in phonons, and a standard electron phono coupling ...
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What is the displacement of E$_g$ mode of SrTiO$_3$ in tetragonal phase? [closed]
In the tetragonal phase, SrTiO$_3$ belongs to the D$_{4h}$ point group and possesses two Raman-active modes with the symmetry rep of A$_{1g}$ and E$_g$. However, in most books only 7 modes (normal ...
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Are phonon position and momentum operators self-adjoint?
I am currently doing a calculation which involves phonons and decided to try to follow every detail regarding the quantization of the phonons.
Lets suppose we have a collection of atoms in a crystal, ...
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What is the material with the highest mass enhancement factor?
The electron phonon coupling mass enhancement factor $\lambda$ is a measure of the strength of this coupling. This quantity can be measured experimentally. For instance, Pb has a factor of 1.55 ...
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What is the criteria of forming a phonon polariton?
It is well know that, phonon polariton is a quasiparticle formed by the interaction between photons and optical phonons. But, does it mean that, any photons that are resonant with phonons can form ...
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Quantization into Phonon in a multi-basis crystal
I am quite frustrated in quantizing the vibration of a multi-basis crystal.
The specific point that confuses me is the potential term, which hinders me from decoupling the Hamiltonian as the sum of HO-...
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How many distinct phonon branches will I see for 3 atoms in the unit cell, along the [100] direction?
Silicon (Si) crystallises in the fcc cubic structure with two atoms in the primitive unit cell.
How many acoustic and optical phonon branches does it have?
How many distinct branches in the ...
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Longitudinal and Transverse phonons
I was looking at this demonstration of acoustic and optical phonons and it seems to me that the animation has 'transverse' and 'longitudinal' upside down.
Am I correct? For instance the picture below ...
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How do I find the eigenstates of the dispersion in a diatomic linear chain with two different spring constants?
This is my first post.
I've got a problem with finding the eigenstates of the diatomic linear chain. Let me show you guys what I already did. The equations of motion are:
$$
M_1\ddot u_n^1=-C_1(u_n^1-...
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Will every material with strong electron-phonon coupling ($\lambda > 1$) have polarons?
Does polaron formation need only strong electron-phonon coupling? Or does it need something else?
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What is the difference in Debye heat capacity formulas?
In my textbook I have a Debye formula for the heat capacity (without derivation), and it looks like this:
$$9Nk_b [4(T/T_D)² \int_{0}^{T_D} \frac{x³}{e^(x)-1} \, dx - \frac{T_D}{T} \frac{1}{e^(T_D/T) -...
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Phonon dispersion and what wave it represents
To start things off, I'm doing a semestral project on phonons and I'm to find a dispersion relation of a crystal (with the use phonopy). I chose to do hexagonal boron nitride.
From my understanding, ...
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Can we use Density Functional Theory (DFT) to calculate the second and third-order force constants of a slab?
If we aim to compute the surface phonon lifetime of a Cu(111) surface, the second and third-order force constants are essential (to put in Boltzmann transport equation). However, to my knowledge, it ...
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Phonon and the coupling to electrons
I am new to looking at phonons, especially in relation to their use in coupling to electrons.
Phonons can be defined as the treatment of vibrations in a crystal lattice. There can be different types/...
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Why don't we see the transverse waves with a phonon lattice dynamic while we see them with linear elasticity theory?
Let's say that we have a lattice with particles sitting on the nodes. Each particle $n$ has neighbors $\bar n$:
$$\dfrac{d^2\boldsymbol u_n}{dt^2}=-K\sum_{\bar n}\boldsymbol u_{\bar n}\tag{1}$$
The ...
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Exploring Phonon Dispersion in Two-Dimensional Materials: Analytical Techniques and Mode Identification
How can one analyze the phonon dispersion of 2D materials like graphene to discern specific curves corresponding to particular phonon modes, such as acoustic or optical, as well as longitudinal and ...
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Evaluate convergence of force constants in crystal with increasing cutoff
I have a crystal with 2 atomic species, A and B. I'm interested in the interatomic force constants (IFCs) and I have a program that computes them for a given supercell. Basically, I have to provide ...
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What is the relation between linear elastic theory and phonon transport?
I am reading about Boltzmann equation and I am having a hard time making a link between elastodynamics and phonon equations. Clearly there should be a limit where both are one and the same, isn't it? ...
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Can one experimentally confirm whether the effective attractive interaction is retarded and its relation with superconductivity?
It's widely believed that in convential BCS superconductors, only after taking the retardation effect into consideration the weak attractive interaction mediated by phonons can overwhelm the strong ...
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Why acoustic phonon dispersion cross $\omega=0$ at $k=0$?
When I am learning about phonons, it is taught that acoustic phonons necessarily have $\omega=0$ at $k=0$. while optical phonons have a finite $\omega$ at $k=0$.
But I am confused about two things:
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Born Oppenheimer approximation and screening
In the Born-Oppenheimer approximation we take the full Hamiltonian of a solid, given by
$$H = T_e + T_{ion} + V_{ee} + V_{e-ion} + V_{ion-ion}$$
where the T are the kinetic energy of electrons and ...
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Phonons from Born-Oppenheimer approximation vs plasma oscillations
I'm trying to connect to different pictures used when talking about phonon dispersion relations in metals. Both can be found in standard textbooks, for example Ashcroft & Mermin.
In the first, one ...
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Why does the phonon displacement have an overall factor of $i$?
I'm going through Mahan's book on Many Body Physics, and I'm a bit confused about one of his claims. First he expresses the position of an atom as
$$\textbf{R}=\textbf{R}_{i}^{(0)}+\textbf{Q}_i$$
...
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Sound as an energy source [closed]
A sound wave is a massless packet of energy much like a photon. Would it be feasible to use these energy packets to generate electricity in the same way as solar panels. I am thinking of panels about ...
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Do certain quasi-particles really have negative mass?
Do phonons for example really have negative mass or does it just seem like they have negative mass? Could one use the negative mass of certain quasi particles to meet the negative energy requirements ...
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Why each normal mode is treated as a harmonic oscillator in Debye's calculation of specific heat?
So in Einstein's calculation of specific heat each oscillator is assumed to be vibrating with same frequency and its average energy is given by hv(n+1/2) where n is bose factor. Debye said that ...
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How is the energy of phonon modes $\left(n+\frac{1}{2}\right)\hbar \omega_k$ when each atom in the mode has $\left(p+\frac{1}{2}\right)\hbar \omega$?
I'm having trouble understanding the quantisation of energy in normal modes of lattice vibrations. Stating Kittel :
The energy of a lattice vibration is quantized. The quantum of energy is
called a ...
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Can continuous translation of Wigner crystal be described by charge neutral density excitations?
In a two-dimensional electron gas (2DEG), under conditions where electron-electron interactions predominate over kinetic energy contributions, the ground state is a Wigner crystal. This crystalline ...
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Picturing a normal mode of vibration of the monoatomic lattice in 1D that is either in-phase nor completely out-of-phase
For a monoatomic lattice of $N$ atoms in one-dimension, the ratio of the displacements of two consecutive atoms at the $(n+1)$th and the $n$th site is given by $$\frac{u_{n+1}}{u_n}=e^{ika}$$ where ...
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What are soft phonon modes?
In chapter 4 of Charles Kittel's Introduction to Solid State Physics, a problem titled "soft phonon modes" asks us to derive the dispersion relation for the following setup: a 1d crystal ...
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Soliton in non-degenerate polymer
I just started reading about the conduction mechanism in polymer. From what i read, polarons are used as method of charge transportation in non-degenerate polymer. While for degenerate polymer, both ...
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Mermin-Wagner theorem and SSB in 2D: is there sound in low dimensional solids
The Mermin-Wagner theorem states that there cannot be any spontaneous symmetry breaking happening in systems with short range interactions below dimension 3. Moreover, we know that Goldstone boson, ...
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Lennard-Jones potential can be valid at 0.2 Angstrom Distance between two particles?
I have modeled a graphene-vacuum-graphene system. Here two graphene sheets connected by L-J potential through vacuum gap (Phonon transfer through vacuum). I have simulated it considering 0.2 to 10 ...
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Debye-Waller Factor in the case of isotropic fluctuations
I am reading through Girvin & Yang Ch. 6 (pg. 91), they mention that the Debye-Waller factor
$$-2\Gamma(\vec{q})=-\langle\langle(\vec{q}\cdot\vec{u}_j)^2\rangle\rangle$$
(where the positions of ...
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Possibility of calculating phonon dispersion from crystal structure
Is it in principle possible to calculate the dispersion relation of phonons in a crystal from the crystal structure?
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The definitions of coherent phonons and acoustic phonons
I found that the definition of coherent phonon: A femtosecond laser pulse can initiate collective, in-phase atomic motions in solids called coherent phonons.
My question is: what is the difference ...
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At temperature $T>0K$, are all normal vibrational modes present simultaneously in a one-dimensional solid?
I am studying Debye theory of Specific heat.
hyperphysics has this picture and there it says
"Considering a solid to be a periodic array of mass points, there are constraints on both the minimum ...
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Kink in Dispersion Relationship due to Electron Phonon Coupling
How can I start from a Hamiltonian with electron-phonon coupling and show that a kink should show up in the energy dispersion relationship?
In a brief communication called "Universal Nodal Fermi ...
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Phonon eigenfrequencies under time reversal
In G. P. Srivastava's "The Physics of Phonons", 1e., the ansatz which solves Newton's second law in the harmonic approximation is taken to be
$$
u_\alpha(\ell b;t)
=\frac{1}{\sqrt{m_b}}\...
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Why haven't we found thermal superconductors?
First of all I want to apologize if this is a stupid question. I'm a layman who's merely very interested in physics, without a degree to my name.
I was trying to research electric superconductors ...
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How to interpret huge number of phonons?
In my condensed matter class we have seen how to treat the problem of vibration in a lattice in quantum mechanics. After heavy calculation we derive that the number of phonons with a given crystal ...
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How phonon emerges from the quantum mechanics of the lattice?
In all textbooks and lecture notes I've seen so far, a phonon is introduced by imposing the (second) quantization condition on the classical Hamiltonian of the bodies connected with springs.
However, ...
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Question about Debye's and Einstein's Heat Capacity Theory
I am reading the phonon part of Omar's textbook, but
I am a bit confused over the way through which the distribution of the frequencies of oscillators are determined. In Einstein's model all ...
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Are there phonons in air?
Phonons are typically used to describe quantised vibrations in solids. However, is it legitimate to talk about phonons for e.g. a sound wave propagating in air?
Contrary to photons that are particles ...
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Does bubble-phonon-bubble diagram matter for conductivity of electron-phonon system?
In linear response, electrical conductivity due to electron-phonon coupling (EPC) is calculated by using the Kubo formula. Typically, electronic self-energy due to such coupling is included, and such ...
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Acoustic phonons & Debye model, optical phonons & Einstein model
In our class today we spoke about the Einstein and Debye models. We associated the Einstein model with the optical phonons and the Debye one with the acoustic phonons. But I have a question:
what is ...
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Calculating the nr. of phonon modes depending on atom nr. in a crystal and dimensions
I am trying to understand how we can determine the correct nr. of phonon modes of a crystal lattice, because I am trying to show that the volume of a state in reciprocal space is $(\frac{2\pi}{L})^3$. ...
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Conceptual understanding of the phonon and its mode
As stated in Wikipedia, the phonon is a quasiparticle, it's the representative of the collective oscillation of the particles which build a crystal. These particles can be atoms, ions etc. The ...
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How to differentiate longitudinal and transverse phonons from the phonon dispersion curve?
I know that there are two kinds of phonons: acoustic and optical. Acoustic phonons have zero frequency at the $\Gamma$ point, whereas optical phonons have a non-zero frequency at the $\Gamma$ point.
I ...
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