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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The reciprocal lattice of HCP lattice

There is a very similar question here Reciprocal Lattice of a non-bravais lattice, but I don't fully understand the answer, and the question is now obsolete so I feel that I should ask it again. How ...
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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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Wannier Functions as Discrete Basis

In solid state physics, using Bloch's theorem we know that the one-electron energy eigen-function can be written as $\psi_{\lambda,\vec{k}}(\vec{r})$ where $\lambda$ indexes eigenvalues of $\hat{H}$ ...
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Wannier Hamiltonian in Momentum Space

In connection to a previous question, We can write the one-particle Hamiltonian in the Wannier basis working on a general vector $v$ as : $$ \langle\vec{R},\,\lambda|\hat{H}|v\rangle = ...
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Thermal healing of defects in crystals

Thermal treatment can heal point defects due to the diffusion of atoms towards empty points. In a solid crystal structure, atoms do not diffuse at room temperature (correct?) Energy of thermal ...
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76 views

Why doesn't topological phase transition break any symmetry? Hidden symmetry?

This question may be superficial. However why all people saying this without a proof? Just like the "hidden variables" assumption in quantum mechanics, can one disproof that there is no hidden ...
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244 views

How do the effects of semiconductor doping affect the Hall effect?

For instance, consider number 4 and 5 in the following sample: Using the right hand rule, B points downwards, conventional current points to the right (because of the 5V battery), and therefore, ...
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316 views

How is Meissner effect explained by BCS theory?

Someone says we can derive the GL equations from BCS theory, which can explain Meissner effect, but I want a more clear physical picture of this phenomena.
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Real materials described by the fermionic Hubbard model?

I was always curios what real material are described by the fermionic Hubbard model. $$H = \sum_{\left< i, j\right> \sigma} t_{ij} c^{\dagger}_{i, \sigma} c_{j, \sigma} + \sum_i U_i ...
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279 views

What is the difference between spin glass and spin liquid?

What is the difference between spin glass and spin liquid? Do they both originate from frustration?
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232 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
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85 views

How does a band gap arise from the 3D Kronig Penney model?

The Kronig-Penney (KP) model is a classic model that is used to show that a periodic lattice of finite well potential sites will give rise to a band gap. The typical process in solving the KP seems to ...
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How to compute matsubara frequency summation over computer?

Matsubara frequency sum usually takes the following form: $S_\eta = \frac{1}{\beta}\sum_{i\omega_n} g(i\omega_n).$ But in my problem, $g(i\omega_n)$ is a lengthy expression, which can not be ...
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112 views

How to get conductivity from Green function $\mathcal{G}(x_1,x_2,\tau)$ of inhomogeneous system?

I'd like to study an inhomogeneous system, i.e., momentum is not a good quantum number therein. Therefore, I tried to calculate temperature Green functions like $\mathcal{G}(x_1,x_2;\tau)$, or its ...
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15 views

Proton energy distribution after Si layer

I've been using SRIM to get an approximation of the energy distribution that a beam of monoenergetic incident ions will have after a thin layer of silicon. However, for my purposes it would be better ...
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19 views

Which thin Layer deposition method is the best? [closed]

Based of the material to be coated one technique may be more suitable than the other.I want to know how the techniques can be classified on 'most suitable for a given material coating' basis.
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How does a knife cut things at the atomic level?

As the title says. It is common sense that sharp things cut, but how do they work at the atomical level?
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138 views

Do indirect optical transitions “cool” the material a little?

So I'm reading in Ashcroft and Mermin about indirect optical transitions: So, a photon comes in, and it only excites the electron across the indirect band gap if a phonon with the appropriate wave ...
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48 views

Wannier functions on a ring

Let's say I have a single particle hamiltonian in a periodic potential, for example a 1D lattice such that: $$H = -\frac{\partial_x^2}{2m} + V(x) $$ with $ V(x+a) = V(x)$ where $a$ is the lattice ...
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80 views

Volume of Brillouin zone is the same as Fourier primitive cell?

In Kittel's solid state text, problem 2.3, he says that the volume of the Brillouin zone is the same as a primitive parallelepiped in Fourier space. Somehow I can't see why this is true. Can someone ...
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43 views

How to understand the unitary? [closed]

In the page 219 of Mahan's Many Particle Physics(3ed), there exists a transform $$ S=c^{\dagger}c\sum_q\frac{M_q}{\omega_q}(a_q^{\dagger}-a_q)$$ In order to prove that the transformation relating to ...
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30 views

Why do pores make ceramic opaque?

I want to know how a ceramic transparency is mostly affected by the pores, grain boundary, second phases etc. present inside of it, but the major contribution is due to the pores. Let's consider the ...
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Lecture notes of many body theory of solids [duplicate]

Can anyone help me to get a complete and comprehensive lecture note of the "many body theory of solids" according to the book written by John C. Inkson, please?
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Hamiltonian governing liquid to a solid transition

What is the Hamiltonian 'H' (at the atomic or molecular level) that governs the phase transition from a liquid to a solid state? Actually, I want to explicitly verify the Hamiltonian 'H' admits the ...
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71 views

What's the difference between hopping and tunneling?

My professor made a distinction between electron hopping (the closest wikipedia had an article on) and tunneling, saying that one (he didn't say which, but I assume hopping) was temperature dependent ...
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50 views

Lattice geometry and dispersion relation

Is there a general theorem which gives some information about which influence have the lattice geometry (for example sub-lattice structure, square lattice, honeycomb lattice, lattice symmetries, ...) ...
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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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182 views

Are they the same thing: Wigner distribution in quantum Boltzmann equation and Wigner function in quantum optics?

We know that quantum Boltzmann equation (QBE) is an equation of motion for the interacting Green's function $G^<(\vec{x}_1,t_1;\vec{x}_2,t_2)\equiv\mathrm{i}\langle ...
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113 views

Kronig-Penney model

I am studying the Kronig-Penney model as treated in the book by Kittel: Introduction to Solid State Physics. In this model one considers a period potential which is zero in the region $[0,a]$ ...
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173 views

Adiabatic approximation

The adiabatic approximation for solid state systems is rather radical. I was wondering in which cases it breaks down. As it is based on the idea of the nuclii being much heavier than the electrons I ...
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71 views

Photoelectric Effect - How are the electrons regained?

When the photons with enough energy impinge on a photocathode, it emits electrons. Does this mean that the solid will lose all its electron at one point? If not, how are electrons restored?
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30 views

A problem about solving energy bands by the method of second quantization

In hopping model, we can get the Hamitonian as $H_0=-t\sum a^\dagger_ia_{i'}$. Then we take the fourier transform and put the operator which are in momentum space in the Hamitonian above. However, I ...
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207 views

Why does the Fermi Surface cross the Brillouin zone boundary at right angles?

I'm not sure why the fermi surface crosses the Brillouin zone boundary at right angles. I understand that this is normally the case, but not necessarily always. I'm aware that the fermi surface is a ...
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50 views

Bragg diffraction and lattice planes

Crystalline substances show, for certain sharply defined wavelength and incident directions, very sharp peaks of scattered X-ray radiation. From the illustration below we see that we get constructive ...
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74 views

Can you explain why crystals form without thermodynamics?

I know that the basic reason that solid crystals form is because it's the lowest energy configuration (i.e. this). I am looking for an intuitive explanation for this process, one that does not involve ...
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64 views

Thomas - Fermi screening

I read in Ashcroft & Mermin's Solid State text that for the Thomas-Fermi approximation to be applicable, the external potential needs to be "slowly varying," What does it mean for a function (in ...
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1answer
74 views

What is $\epsilon_\infty$ in this equation and why can it be neglected in the IR?

I'm reading this paper (warning, PDF) and they mention that the complex permittivity $\epsilon$ and complex conductivity $\sigma$ are related through the equation $$\epsilon - \epsilon_\infty = (4\pi ...
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134 views

In a positively biased PN junction, where do the injection carriers come from?

I am not quite understand i-v character of PN-junction diode. Here is the model in textbook. The PN junction diode can be divided into three regions. They are One depletion region near the PN ...
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What is the the real world interpretation of the high dimensionality of quasicrystals?

One of the examples of the problems of 5-fold symmetry is that pentagons tiled on a 2D plane do not completely fill that plane, leaving voids. This may be solved by "folding" it into 3D space, and ...
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116 views

Temperature in a Voltaic Cell

The potential difference across a voltaic cell varies with temperature. But my question is whether the voltage increases or decreases as temperature rises. According to the Nernst equation, the two ...
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115 views

Why are most ferromagnets metals while antiferromagnets are insulators?

This seems to be experimentally true, but I don't quite have an intuition as the why. In the Ising model, we usually consider an insulating ferromagnet if $J>0$, where $J$ is the exchange coupling. ...
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Symmetry of amorphous thin films

I'm wondering whether amorphous thin films have point group symmetries? Landau's Statistical Physics Vol. I writes: The highest symmetry is that of isotropic bodies (bodies whose properties are the ...
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288 views

What is crystal field anisotropy or effect ? It forces the magnetic moment to point in particular local direction..

Can you give a basic explanation of what is crystal field anisotropy ? What is the reason to arise ? In spin ice it forces the dipoles to point in the local 111 direction. For partially filled rare ...
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42 views

Electron density in metals at non zero temperature

When computing the electron density in metals, the usual crude result is computed for zero temperature. That is, we integrate \begin{equation} n=\frac{8\sqrt{2}\pi m^{3/2}}{h^{3}} ...
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Disclinations, dislocations, lattices, Displacement fields and scaling

I am looking up Frank, and Burger vectors and associated material on dislocation/disclination. It seems straightforward describing a lattice and what dislocation means. It is even possible to restrict ...
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2answers
203 views

Why a mono-atomic crystal layer (2D) can't be stable?

According to Peierls and Landau, 2D crystals were thermodynamically unstable. They can't exist! Of course, this theory was disapproved in 2004 (example: graphene). What is the general definition of ...
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143 views

Are there materials that get softer with temperature decrease?

Could be there material that begins melting/softening when it's temperature is lowered? I would say no, but I've seen enough physics to know that not always life is so easy. Moreover I think I've ...
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Why aren't base-centered orthorhombic Bravais lattice simple monoclinic?

I am learning 7 crystal systems and 32 Bravais lattices. I am quite confused about why a base-centered orthorhombic Bravais lattice is not a simple monoclinic one, if we take two edges and a half ...
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54 views

Why is the law of the p-n junction valid under forward bias?

I'm currently studying the physics of the PN junction. I went though the derivation of the built-in potential in the PN junction under equilibrium: $$ {Diffusion\ current\ density} = {Drift\ current\ ...
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How can one reasonably theoretically model polycrystalline materials?

Many techniques are taught in advanced solid state courses but they are almost all derived for perfectly crystalline materials. For example, band structure really only appears theoretically when you ...