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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Number of classical oscillation modes of a Lattice and number of quantum phonons

In solving the Classical model for lattice dynamics [Rossler pag 38] we find that the lattice admits $$d\cdot N\cdot r = \#modes$$ where $d=$dimension of the problem $N=$ number of atoms $r=$ ...
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Double groups in Crystallography

I'm currently studying double point groups and their applications in condensed matter physics. Let me start by giving you the definition of the double group that is used in my textbook: Let $G$ be a ...
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What causes the Shubnikov-de Haas Oscillations?

If I have a 2DEG with a voltage in the $x$-direction and a $B$-Field in the $z$-direction (so I also get a hall-voltage in the $y$-direction (classicaly)). But if I do this stuff at low temperatures I ...
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Why do we assume electrons experience lattice potentials in solids?

Why don't we assume the protons wave function spreads out uniformly and just provides a uniform background potential?
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Resistance of a cloud of free electron gas by Kubo formula?

How much is the resistance of a cloud of free electron gas, if at all? How much is the resistance of a cloud of free electrons in a periodic potential? Did anyone calculate it using the Kubo ...
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Topological insulators literature

I started learning things on topological insulators and I got lost in dozens of existing papers on this topic. Could anyone recommend me appropriate literature that explains deeply enough what ...
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Nature of photoluminescence at a semiconductor heterojunction

Do I understand it correctly that photoluminescence at a semiconductor heterojunction occurs because of intralayer recombination? If so, why can't photoluminescence occur because of interlayer ...
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e-e scattering time in graphene

I think its worth writing my second question in this post as a separate one. In normal Fermi liquid, the electron-electron scattering time $\tau_{e-e}$ is about: $$ \tau_{e-e} \approx \frac{\hbar ...
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Repulsive component of intermolecular interaction

Intermolecular interaction mainly consists of 2 components: (a) Dipole vs dipole (permanent & induced), which is more likely to be attractive (b) Pauli exclusion, which is always repulsive The ...
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Basic questions about the Kitaev chain

I am trying to understand the first 5 pages of Introduction to topological superconductivity and Majorana fermions http://arxiv.org/abs/1206.1736 I read it 2-3 times and thought about it but a few ...
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Matsubara Green function of anderson impurity model

I am currently having trouble computing the imaginary-time Green's functions of a model similar to the single-impurity anderson model. The hamiltonian is given as: \begin{equation} H = ...
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How can crystal symmetry operations be used to reduce the number of unique properties of a solid?

Can anyone please give an example or a reference which shows how crystal point groups and symmetry operations can be used to reduce the number of parameters describing the property of a crystal, ...
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e-e scattering rate in normal fermi liquid and in graphene

In Ashcroft/Mermin's solid state physics, in equation (17.64) they argued that: We expect from lowest-order perturbation theory (Born approximation) that $\tau$ will depend on the ...
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About the definition of the spin current

People have been talking about the spin current for a while. But there is a fundamental problem. Unlike charge, or mass, spin is not conserved. Let us take the 1d spin-1/2 Heisenberg chain as an ...
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Why are bandstructures plotted only along certain symmetry points?

Why is it that bandstructures are usually represented along certain symmetry points ? What determines these symmetry points ?
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DOS integral when surface is not closed

According to the density of states (DOS) formula $$\rho(\varepsilon)\propto \int_{\varepsilon=\text{const}}\frac{dS}{|\nabla_k \varepsilon_k|}$$ Since there is an integral on the constant energy ...
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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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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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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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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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174 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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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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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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51 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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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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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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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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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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35 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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93 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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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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Exercises about solid state physics ( free electron, tight binding approximations)

I'm doing a (first) course in solid state physics following the book of Ashcroft/Mermin , the classes are quite theoretical and we have practically no examples. The problem that I'm having is that I ...
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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 ...
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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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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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How to calculate the dispersion relation of graphene?

Graphene is a well investigated two-dimensional material in nano-physics. My teacher asked me to calculate its phonon dispersion with interactions between the first and second nearest neighbors, both ...
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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: ...
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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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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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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 ...
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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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53 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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43 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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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 ...
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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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Klein paradox in graphene

When considering the Klein paradox in graphene Katsnelson, Novoselov and Geim introduce a potential barrier (see http://www.nature.com/nphys/journal/v2/n9/full/nphys384.html). But I cannot understand ...