Solid-state physics studies how macroscopic properties of solids (mechanical, electrical, optical, etc.) result from their microscopic structure. It usually deals with the scale where quantum properties of the particles are substantial.

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DOS behavior of Van Hove singularity in a line

When there are some points in momentum space give $|\nabla_k \varepsilon_k|=0$, they are called Van Hove points and give singularity in the desity of states (DOS). But what if $|\nabla_k \...
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DOS of Van Hove singularity in 2D square lattice tight binding model

For the simplest example, 2D square lattice tight binding model gives the energy band as $$\varepsilon_k=-2t(\cos k_x+\cos k_y) \, .$$ We know that $\vec{k}=(0,\pi)$ and related momentum points are ...
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129 views

How to get DOS of Van Hove singularity using quadratic dispersion relation

Take 2D case for example. We can first get the area in momentum space for all $k$ that satisfy $E_0<E(k)<E $, say $S(E)$. And the density of state (DOS) is $\rho(E)=\frac{\partial S(E)}{\partial ...
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How to get the asymptotic expression of DOS near Van Hove singularity [duplicate]

For the simplest example, 2D square lattice tight binding model gives the energy band as $$\varepsilon_k=-2t(\cos k_x+\cos k_y) \, .$$ We know that $\vec{k}=(0,\pi)$ and related momentum points are ...
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87 views

Fillings of dispersion bands (E-K diagram)

I struggle in understanding why in some references the bands filling by electrons in the E-k diagram is shown as an area delimited below by the dispersion curve and above by the Fermi energy (if in ...
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17 views

Dispersion in crystall for a random direction

Lets say one get a dispersion of electrons or phonons from this website: http://www.matprop.ru Usually dispersion in particular directions is drawn: as for wurtzite crystall it is A to L, L to U and ...
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29 views

Is it possible to hear trains when you live nothing near them? [duplicate]

So I live in Hollywood, California and last night I heard a single train horn blast through my neighborhood after that it was pretty quiet for the rest of the night. what I don't understand is I don't ...
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935 views

How can a material conduct heat but not electricity

Mica is a good conductor of heat but an electrical insulator. According to free electron theory (which applies only to metals) free electrons carry heat and electricity. Therefore, thermal ...
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37 views

What conditions are needed for Onsager reciprocal relations?

I often find a thorough discussion of the conditions that must hold for a theorem lacking, especially in the sense of what they actually mean physically. Could anyone write up what kind of systems ...
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57 views

Interpretation of the diode constant in a LED

For a real diode the current as function of the potential difference between its terminals (for big enough voltage) is given by: $$I=A e^{\frac{eV-E}{\eta k_B T}} \tag{1}$$ So in the case of LEDs ...
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82 views

Hopping on a lattice?

Usually hopping on a lattice written as $$H=-tc_i ^{\dagger} c_{i+1} + h.c$$ where $t$ represent hopping amplitude When we consider hopping on a lattice than, Do we need at least the empty orbitals ...
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170 views

Reflection, Transmission, and Plasma Frequency

Does anyone have a good, clear explanation of why and how this works? I don't understand the following. Say you have a piece of metal with a plasma frequency $\omega_p$. This is like a resonant ...
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57 views

Spectroscopy from a classical light wave or photon only?

In chemistry we mostly regard light/electromagnetic radiation as a beam of particles or photons. This is a very useful model to explain molecular excitations and ionisations from quantum interactions. ...
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113 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 ...
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1answer
47 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 ...
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102 views

Why Fermi level doesn't change with temperature?

We always draw f(E) vs. E crossing at $[E_F, 0.5]$ for any temperature. But a new temperature is a different steady state. So why the value of $E_F$ (Fermi level) doesn't change with temperature? No ...
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235 views

Total number of photons per unit volume in a box (extremely confusing)

This is a worked example from a text. a) Find an expression for the number of photons per unit volume with energies between $E$ and $E+dE$ in a cavity at temperature $T$. $$n(E)dE = g(E)f(E)dE = ...
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146 views

Why in excitation in indirect bandgap materials photon absorption is always before phonon absorption?

Why is it always photon->phonon? Why can't it be phonon->photon? (source)
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Understanding the quasiparticle lifetime

I have calculated the quasiparticle (QP) band structure in the GW approximation for an insulator and I'm trying to understand what the imaginary part of the self-energy represents. I understand how QP-...
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60 views

How to implement the form of current density in a Hall Effect related calculation?

Please consider the following; Question. A rectangular plate of semiconducting material has dimensions 10mm x 4mm x 1mm. A current of 3 mA flows along the length and a Hall Voltage of 13.6 mV is ...
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81 views

Einstein model for thermal capacity of solids and indistinguishability of the oscillators

Albert Einstein's theory of thermal capacity of a solids makes the assumption that a crystal is made up from oscillators which of course oscillate, in all three directions. Thus, for N atoms of the ...
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54 views

Asymmetric photoluminescence spectra

Why do photoluminescence spectra have asymmetric lineshapes as those here http://www.scielo.br/img/revistas/bjp/v37n4/a04fig01.gif or here: http://www.oxford-instruments.com/industries-and-...
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Specific Heat of Liquid Helium

At the lambda point, the specific heat of Liquid Helium diverges. After searching for a curve, I've found only measured curves. Is there a theoretical curve for this transition?
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234 views

Is there any other superfluid element except helium?

Is there any other superfluid element except helium? Everywhere we see and speak about superfluidity, we just speak about superfluid helium. but is't there any other element or material or system ...
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If 99% of an atom empty, and our body is made of atoms, does that mean 99% of our body is empty? [duplicate]

If 99% of an atom empty, and if we say that our body is made of atoms stacked together, then why is our body a solid object, rather than 99% hollow. I have one probable answer that I think might be ...
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128 views

Relation between energy band gap and atomic number

Is there any relation between energy band gap in group4 elements and their atomic numbers? It might be just a trivial observation but I noticed How from Carbon to Germanium the band gap went from 5....
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79 views

Textbooks or papers that clearly explain second harmonic generation?

I'm having trouble learning about Second Harmonic Generation. I've found a bunch of sources, but they all seem to expect a fairly advanced level of knowledge about it. For example, in the wiki section ...
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89 views

Derivation of the Kohn Effect

I'm working through a derivation of the Kohn Effect, as presented in Ziman's 'Principles of the Theory of Solids.' However, I find myself getting a somewhat different result. The book states that ...
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143 views

The Fermi Surface of the Free Electron Model for T>0K

For the Free electron model, we can easily describe the Fermi surface at T=0 due to the uniqueness of the Fermi-Dirac Distribution at T=0; below the Fermi-level, a state is definitely filled, above, ...
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71 views

The minimum possible energy for five noniteracting spin $\frac{1}{2}$ particles

Question What is the minimum possible energy for five (noniteracting) spin $\frac{1}{2}$ particles of mass $m$ in a one-dimensional box of length $L$? Answer: $$ 2 \times \frac{1^2\pi^2\hbar^2}{2mL}+...
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77 views

Energy levels in molecules

I apologize in advance if this turns out to be a duplicate question. As far as I can understand, if you bring two or more atoms together their wave functions begin to interfere and, since there ...
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32 views

Calculate characteristic frequency from atomic polarizability

With Lorentz model, the plasma frequency can be calculated from electron density $$\omega_p=\sqrt\frac{4\pi N e^2}{3m}$$ But I also found in this paper that it could also be calculated from atomic ...
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44 views

How close to the wavelength of light have to be to inter-planar spacing for diffraction to occur?

I'm doing past papers for my exam on Wednesday, and I've come to a question I'm stuck on. So, you have x rays of $\lambda = 0.25\,\mathrm{nm}$ incident on a cubic unit cell with lattice lattice ...
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Is it possible to have a line rather than a point where the three states of a substance can exist?

Most of us are familiar with state diagrams that define which of the three states a substance will take given the pressure and temperature. And that some substances, such as water for example, exhibit ...
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160 views

Reflectivity of Metals - real and imaginary part of k-vector and complex dielectric function

De electric field component of an electromagnetic wave that is traveling in the $x$-direction is given as $$E(x,t) = E_0 e^{i(kx - \omega t)} $$ with $E_0$ the amplitude and $k$ the wave vector. From ...
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What is the origin of the “polarization catastophe”?

According to the Clausius-Mossotti relation, $$ \frac{\epsilon_r - 1}{\epsilon_r + 2}=\frac{n\alpha}{3\epsilon_0} $$ So when $n\alpha = 3\epsilon_0$, the relative permittivity $\epsilon_r$ ...
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70 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 $U^{harm}=1/2 K \sum_{n} [u(na)-u([n+1]a)]^2$ (22....
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247 views

Is the photon truly not absorbed in Raman scattering?

In reading about Raman Scattering, I was thinking while reading it "okay, incident photo absorbed by molecule, molecule goes to higher energy vibrational state, molecule re-emits photon with either ...
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134 views

Is molecular vibration just phonon modes for a single molecule?

I'm reading about Raman Scattering, of which a big part is measuring the energy lost to/gained from Molecular Vibrations. I wasn't totally clear on exactly what is "vibrating" in vibrational modes (is ...
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Importance of thickness of SiO2-substrate for observing graphene's monolayer

I've discovered that one should use 300-nm-thick SiO2 substrate in order to effectively observe graphene's monolayer through optical microscope. If thickness differs even by 5%, i.e. 315 nm, then ...
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39 views

A book or paper on Fermi glasses

Can anybody recommend a good book treating the subject of Fermi glasses? A good review paper, preferably something relatively modern, would also be welcome. I know of Anderson's paper ("The Fermi ...
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228 views

Conduction in Solids

I have some text: I could understand it partially. My doubts are: What is effective mass $m^*$ (real meaning apart from explained in this text) and how can we calculate it/or what is it's value? ...
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125 views

Why is the ground state energy of a 2DEG higher compared to the 3DEG?

I am reading something about a 2DEG (2-dimensional electrongas model) and can not understand it. My book says the ground state of the 2DEG is higher compared to a 3DEG because the confinement to 2D ...
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77 views

Intuition for the density of states of the free electron gas model

The density of states as a function of energy for a free electron gas (inside some solid-thing where the electrons are modeled due to the free elecetron gas model) is in: 1D: D(E) ~ $\sqrt[-1/2]{E}$ ...
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Why graphene's substrate is important

I just have some feelings that somehow it is important what specific subtrate is used to grow graphene monolayer on. Some substrates are better, another ones are not so good. But I cannot completely ...
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878 views

electrical conductivity and resistivity tensor

By definition of the conductivity tensor $\hat{\sigma}$ and the resistivity tensor $\hat{\rho}$, we have \begin{equation*} \begin{split} & j_{\alpha}=\sigma_{\alpha \beta}E_{\beta} \\ & E_{\...
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can we have a phase transition from superconductor to the normal only by applying magnetic field?

for superconductors we have a phase transition diagram. according to that phase diagram in a temperature below Tc, we can only increase the applied magnetic field to make a superconductor a normal. ...
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91 views

How do you go from a sum over frequencies to an integral?

I am trying to figure out how to go, with help of a density of states function $g(\omega)$, from a sum like this $$K=\sum \limits_{j=0}^N f(\omega_j)$$ to an integral over the frequencies for $N \to \...
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88 views

Density of particles in hexagonal lattice

I need to calculate, in a 2D hexagonal lattice of point particles in which the nearest neighbours are a distance apart $a$, what's the density of particles. What I really need is, if $\rho$ is the ...
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217 views

How do the Fermi level, HOMO and LUMO change with doping?

I am a bit confused about solid state physics of organic materials because as I know the workfunction changes with the doping of a material but the Fermi level is constant with doping. So depend on ...