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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Why does chemical potential smaller than zero mean nondegeneracy and vice versa

In Mudelung's book, Introduction to Solid-State Theory, I have a confusion about the statement. Here, $x$ should be $\frac{\mu}{k_B T}$. I am cofused about his statement. Why does $x<0$ mean ...
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167 views

Why does $c_{-k,-\sigma}$ create a particle with momentum $k$?

In Mudelung's book, Introduction to Solid-State Theory, I am confused by the following statement. For many applications a further simplification is helpful. The concept of the hole presents us ...
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29 views

Explain Heat Transfer

I would like to know what are these formulas used for. There is no intro about it in my book at all, and I am reading Heat Transfer book. If needed Q. can be edited.
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50 views

Fermi level and conductivity

Can someone in a simple way explain me what the Fermi level is and what does it have to do with conductivity. My teacher said that Cu conducts electric current better than Al because of something in ...
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51 views

Getting nonphysical results when solving for the index of refraction of a slab?

I'm trying to computationally find the refractive indices (real and imaginary) for a thin slab suspended in air (so the only indices to deal with are air and my material's). I've experimentally taken ...
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56 views

Derivation of existence of energy band gap in semiconductor (solid State)

I am looking for both a mathematical and a physical reason for energy band gap in metals. For Physical reason, I was told that at each reciprocal lattice, you could have Bragg scattering, that would ...
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141 views

Why are free electrons free?

This is what I understand so far: in a conductor, the ions have a weak pull on the valence electrons. So when an electric field is applied, the free electrons are able to easily move about. Makes ...
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22 views

Vacancy Generation / Annihilation Time (Relaxation Time)

Vacancy Generation/Annihilation Time, Recombination Time and Relaxation Time ($\tau$) are all synonymously used in atomic physics literatures. They're defined as the time that it takes for vacancies ...
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39 views

Optical absorption — what are the common ranges and mechanisms?

So let's say you do some reflection/transmission spectroscopy of a material. It's clear that it's absorbing in some range. What would be your first step in identifying the source of the absorption? ...
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18 views

How to derive the exponential distribution for the Pool-Frenkel effect?

For the Pool-Frenkel effect, the external electrical field $E_{ext}$ reduces barrier by a potential energy amount $U_{ext}(r_{m})$, where $r_{m}$ is the distance maximizing the total potential enrgy ...
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21 views

Boundary effect on the Beer-Lambert for F-center/photon interaction

The Beer-Lambert law is: $ I=I_{0}e^{-n\sigma(\lambda) x} $, where $ n $ is the volume concentration and $ \sigma $ the "efficient" cross-section. For interaction with F-centers (kind of crystal ...
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37 views

What is the significance of the difference in the eigenvalue equations of Bloch functions for electrons vs photons?

any text on photonic crystals will highlight the almost perfect analogy between electrons in a periodic potential and photons in a periodic dielectric. The analogies are: $$V(\vec r + \vec R) = ...
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Separating the hamiltonian for a superlattice — is it this easy?

I've been banging my head against a wall trying to figure out what I'm sure is a very simple problem. I want to solve the Kronig Penney model for a superlattice, which is just a normal periodic 1D ...
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48 views

Molecules of a solid [closed]

Question: Molecules of a solid : (a) are always in a state of motion (b) move only when heated (c) move because they are loosely bound (d) do not move at all My attempt: I ...
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1answer
63 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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2answers
164 views

Dispersion Relation (e vs. k) clarification (crystal momentum or electron momentum)

If we get the dispersion relation from the Fourier transform of the lattice vectors then how do we get electrons information? Specifically, for the $k=0$ point of the graph, does this mean the ...
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37 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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118 views

Chronological and normal ordering

I've realized I'm little bit confused when I want to treat elements like this $$\left<\phi_0|T\{a_p(t)a_p^+(t')V(t_1)V(t_2)\}|\phi_0\right>$$ with $$V(t)=\dfrac12 \dfrac{1}{(2\pi ...
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1answer
53 views

Atomic nearest neighbor notation

I recently got a correction to a paper that I am writing. The correction references a section in which I talk about nearest neighbors. The comment says: Do you mean NN, NNN, etc., or NN, 2NN, 3NN? ...
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151 views

If you suddenly move a piece of metal, will that disturb the free electron density?

If we have a hollow pipe sitting at rest filled with gas and we moved the pipe suddenly along its length to the right, then the gas density will be momentarily higher near the rear of the pipe and ...
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130 views

A conceptual question about Green's function's treatment of interaction

Here we have electron gas and some other stuff. We expand the Hamiltonian to the 1st order of one single harmonic oscillator's displacement $\vec{u}$. Its equilibrium position is at the origin. Then ...
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63 views

Is crystal momentum an operator?

My teacher has for Bloch waves the notation $\langle \vec{r}|\vec{k} \rangle = e^{i\vec{k}\cdot \vec{r}}u_{\vec{k}}(r)$ and uses it consistently. However, does this not assume that there is an ...
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89 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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28 views

Reciprocal lattice and Bragg scattering

I know that there are two different ways to write the Bragg condition namely $k^2=(k+G)^2$ and $n\lambda=2d\sin \theta$ where $G$ is a reciprocal lattice vector, $\lambda$ is the wavelength and $d$ is ...
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Calculate 2D density of states from 3D density of states

I have a 3D DOS which is calculated by this formula: $$D(E) = \sum_n\int\frac{\mathrm d^3k}{(2π)^3}\delta(E−\epsilon_n(k)) $$ I do not have any analytical expression for kinetic energy. Is there any ...
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142 views

Silicon atom: How is it replaced by a Phosphorous (or Boron) atom?

My book says: A pure semiconductor at room temperature possesses free electrons and holes but their number is so small that conductivity offered by the pure semiconductor cannot be made of ...
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21 views

Is there a generic term for orbital groups such as $e_g$ and $t_{2g}$?

I am looking for a generic term for sets of atomic orbitals (viz. spherical harmonics) which are grouped by crystal symmetry. The most familiar examples would be $e_g$ and $t_{2g}$ (in cubic ...
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44 views

Bloch states at the zone boundary

How do I show that in 1D the Bloch states at the zone boundary $\left(k=\pm\frac{\pi}{a}\right)$ form standing waves? How is it clear, that there is a high- and a low energy state for a finite ...
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28 views

Simple examples for exchange and correlation

Is there an easy, in the best case intuitive, explanation of the difference of exchange and correlation? Is there a simple way to distinguish whether a certain contribution is due to exchange or ...
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1answer
58 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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1answer
62 views

Fermi Energy Variation

What would be a good Internet link that would properly explain Fermi Energy? How does the Fermi Energy of a material vary with external influence, such as doping of the material, and applied ...
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159 views

Manganese has more unpaired electrons than Iron so why is Iron ferromagnetic Manganese paramagnetic?

Manganese has five unpaired electrons, but Iron has four, then why is Iron ferromagnetic and Manganese paramagnetic? What's that property I'm missing?
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86 views

When can i separate spin from the wavefunction?

I am currently working on a Tight-Binding model and for the derivation of nearest neighbor spin interactions I have terms like $$ ...
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1answer
114 views

Group analysis forbids band-crossing in 1D?

Group analysis forbids band-crossing in 1D in terms of conventional band theory. I read this in a good solid state physics book. But there's no explanation at all. Can anyone help on this?
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55 views

what is the difference between binding energy and adsorption energy

I know the equations, but I am having difficulties to get the difference between this two concepts, binding energy and adsorption energy.
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3answers
105 views

Why can we quantize macro(meso)scopic harmonic oscillator?

It is well known that we have got many kinds of quantized macro(meso)scopic harmonic oscillators or so in tiny mechanical systems. People are talking about cavity cooling and so on. However, it is ...
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1answer
78 views

In a positively biaed 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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1answer
55 views

Why is more intrinsic carriers bad for high temperature semiconductors?

I'm taking a solid state course, and is currently on the subject of dielectrics. In one of the sections, concerning "Impurities in Dielectrics" the books says: "Impurities can also be used to make ...
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54 views

Fermi Energy and the Electric Potential

In an extrinsic semiconductor the electric potential is: $$\phi = \frac{1}{q}(E_{\mathrm{F}} - E_{\mathrm{Fi}})$$ where $E_{\mathrm{F}}$ is the Fermi energy, $E_{\mathrm{Fi}}$ is the intrinsic Fermi ...
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46 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
116 views

Overview and doubts about Bloch's theorem and the concept of partial density of states

So I have a large confusion with QM as applied to solid state. The following is a summary of what I know, what I think I know, and what I know I don't know. I hope to stir a discussion that will help ...
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854 views

Dielectric Constant or Permittivity of Metals

I'm wondering what the dielectric constant or permittivity of metals is --particularly copper. Do metals have an infinite permittivity?
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1answer
138 views

Divergent issue of Madelung's constant

This is a question triggered by this post Madelung's constant is defined to the coefficient of electrostatic potential energy in a ionic crystal. In the example of $NaCl$, \begin{equation} M = ...
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1answer
39 views

How do you justify neglecting electron-electron interaction in the Drude model?

I'm sure there's some way to justify it. Maybe a screening effect?
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1answer
82 views

Energy dispersion in graphene

Given that graphene has linear energy dispersion near the Fermi level and the dispersion is given by $E=\hbar \nu_F|\vec{K}|$, I would like to determine the density of states. I think it is equal to ...
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1answer
120 views

Questions about Statistical Mechanics

For grand partition ensemble, is it true that the introduction of chemical potential allows us to have the sum of number of the particles in each state to be the total number of particles ("On ...
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1answer
82 views

Density of states (treating states in continuum)

If we have a particle in a 3D infinite square well box, with length $L$, e.g. an electron in a conduction metal. By solving the Time independent Schrodinger equation, we can get the formula of ...
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Real and imaginary parts of dielectric constant vs refractive index?

So for a complex dielectric constant $\epsilon = \epsilon_a + i\epsilon_b$, the wave vector and index of refraction are related to it through $k = \frac{\omega}{c}n$ and $n = \sqrt{\frac{\mu ...
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67 views

The origin of contact noise?

I was trying to measure the noise of a device with metal probes. I was not sure whether I should trust the results because I was told contact noise might contribute to some degree. I am a little ...
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1answer
101 views

BCS Theory of Superconductivity

I'm currently taking an introduction to Solid State Physics class, and is now on the subject of superconductivity (SC). Currently I'm reading about the BCS theory, and how this works on a microscopic ...