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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Diffusion and Drift currents in a PN junction

In a forward-biased PN junction, the potential barrier decreases, allowing more majority carriers from one side to diffuse to the other side where they are minority carriers. After they cross the ...
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Tight binding in the limit of large system size

Suppose that one has a continuous Hamiltonian with spin-orbit interaction, for example $H=-\dfrac{\mathbf{p}^2}{2m} +\kappa({\boldsymbol\sigma}\times\mathbf{p}) + U(x)$ and want to approximate this ...
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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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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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28 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 $U^{harm}=1/2 K \sum_{n} [u(na)-u([n+1]a)]^2$ ...
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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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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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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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what is the difference between mictomagnetism and spin glass?

What is the difference between mictomagnetism and spin glasses? I mean what are the distinguishing characteristics of them which makes them separate?
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38 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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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 ...
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band structure of Topological insulators

The above figure is Rashba-split free electron-like surface state in a projected bulk band gap. The bellow figure is the band structure of Topological insulators. x axis is the wave vector, y axis ...
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why is DFT(Density Functional Theory) weak in evaluating semiconductor and insulator bandgaps?

we say that the DFT (Density Functional Theory) is to obtain the ground state properties of a quantum system and then we say: so, we can not use it to obtain the semiconductors and insulators band ...
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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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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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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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55 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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Chemical potential

This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at ...
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164 views

Is this a correct description of bonding in a metal?

I am reading the paper "Twenty five years of Finnis-Sinclair potentials" by Graeme Ackland, Adrian Sutton, and Vasek Vitek, Philosophical Magazine 2009, 89, 3111-3116. It is a review-type article ...
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191 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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$T$-invariant Hamiltonians

If $T$ is time-reversal transformation $t\mapsto -t$, Why do $T$-invariant Bloch Hamiltonians obey $$H(-k) = T H(k) T^{-1}$$ and not $$H(k) = T H(k) T^{-1}$$ Somehow I understand the word "invariant" ...
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47 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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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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101 views

How to obtain the asymptotic behavior of Green's function?

This question arose from Eq.(9.135) and Eq.(9.136) in Fradkin's Field theories of condensed matter physics (2nd Ed.). The author mapped quantum-dimer models to an action of monopole gas in $(2+1)$ ...
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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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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} \\ & ...
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129 views

Is carrier charge density and carrier mobility constant in a given material?

If we assume the semi-conductor is doped by a variable amount, is there some way I can look up carrier charge density for the material in a reference somewhere? What about carrier mobility?
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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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30 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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Combining a p and n type semiconductor

According to my textbook, when a p and n type semiconductor combine the following happens: Electrons from the n type semiconductor will migrate into the p-type semiconductor at the junction (so the ...
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23 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 ...
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what is the influence of Normal (N-processes) to thermal resistivity?

i can't seem to get a proper understanding on what is the role of N-process on thermal resistivity. As far as I know it conserves total phonon momentum. While U-processes (Umklapp) changes the phonon ...
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I have negative slop of Williamson-Hall plot, XRD data. Is this right?

I have Ag (silver) powder sample. I measured xdd of the sample and got very good 2theta peak. Since I want to know bulk modulus and Young's modulus of Ag(silver), So, I got williamson-Hall plot ...
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Relation between Fourier Transform of potential $v(x)$ and |r| in Born approximation

I'm doing an exercise about Kronnig Penny model and I'm asked to do the following: If $t=|t|e^{i\delta}$ and $r=\pm i|r|e^{i\delta}$ are respectively the transmission and reflection coefficients. And ...
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What's an intuitive understanding of diffusion capacitance?

Diffusion capacitance often comes up in transistor design. It is one of the two main capacitances you see, the other being the depletion layer capacitance. The depletion layer capacitance (per unit ...
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35 views

Why is graphene stronger than graphite?

Why is graphene stronger than graphite when graphene is just a single layer while graphite is multiple layers of graphene? And can't we say that diamond and coal also consist of layers of graphene as ...
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Bimolecular recombination in few words

I'm making a short seminar about VERY broad topic of fullerenes in photovoltaics, but I'd like it to be educational (not just full of words hard to audience to make them think I'm smart). In one of ...
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43 views

Are there any units involved in the partition function for a classical particle system?

Is the output of a partition function dimensionless or are there units involved? The question as it is: $$E_1\text{=0}K_B\text{,g=1}$$ $$E_2\text{=0}K_B\text{,g=3}$$ $$E_3\text{=0}K_B\text{,g=5}$$ ...
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Energy dependence of integrating dosimeters

The graph shows the relative response of a dosimeter at different energies, normalized to 1.25 MeV Co-60 gamma rays. Curve A is the graph of the equation $$ ...
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Conceptual explanation of the Single particle partition function

The Single particle partition function is defined mathematically as $$\text{Z=$\sum $}g_ie^{\left(\frac{-E_i}{K_BT}\right)}$$ But what is the physical interpretation of the partition function and ...
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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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Why do some materials have a negative coefficient of thermal expansion in all directions?

Those materials are especially ceramic-glasses. I've found some studies about how does it happens in one dimension (for example a nanocrystalline has a silica helix that works like twisting spring, ...
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Ground State energy as a function of $N$ and $B$, $E_0(N,B)$

The one-particle Hamiltonian is given by: $$\hat{H}=\frac{1}{2m}\left(p+\frac{e}{c}A\right)^2$$ where $p=\hbar\vec{k}$ with $e > 0$ and vector potential $A=(0,x,0)B$, such $B=\triangledown ...
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Applying Schrodinger equation to find the energies of a free electron model in a metal [closed]

The one-particle Hamiltonian is given by $$\hat{H}=\frac{1}{2m}\left(p+\frac{e}{c}A\right)$$ with $e > 0$ and vector potential $A=(0,x,0)B$, such $B=\triangledown \times A=(0,0,B)$ Question: "I ...
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21 views

What causes triboluminescence in quartz?

I have already read this question about triboluminescence but it doesn't really cover my question. I am trying to understand what causes quartz crystals to glow when mechanical pressure is applied ...
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Sum in the reciprocal lattice

I have to use this property but I don't understand at all the deduction, so I was wondering if someone could help me. We have a crystal lattice with vectors to each atom from one of them $R_j$, and ...
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Atomic orbitals

I just studied atomic orbitals in a theoretical QM class, and I'm left with several questions, that are probably more questions in quantum chemistry: Many orbitals seem to have a preferred axis - ...
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98 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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Understanding electronic band structure diagrams

Currently I'm trying to understand electronic band structures such as depicted below: And following questions were arisen. Why are there multiple lines in valence side and conduction side? Where ...
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Intuition behind modeling quantum impurities as two-level systems

I've been trying to get a basic understanding of quantum impurity problems, starting with the Anderson model. The Wikipedia article (along with some review articles) seems to explain the simplest ...