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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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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What is the difference between crystals and solid? [on hold]

In condensed matter physics, what are the differences between crystals.
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177 views

Problem with derivation of phonons in crystal

In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental ...
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3k views

Melting diamond and cool down as diamond

Is it possible to melt diamond? And if possible while let it cool will it became diamond again?
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Can Non-Magnetic Dust Particles become magnetic if their particle size is decreased (by grinding them probably)?

Problem: Take some dust particles whose size is big. Bring a magnet near them. They do not get attracted to the magnet and thus we conclude that they are non-magnetic. However, when you grind the ...
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147 views

Energy conservation of permanent magnets engine

How to explain the fact that magnet can attract an object (apply a work W) without losing a (significant) part of its internal energy? How to apply the energy conservation principle? Please think to ...
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108 views

What do DFT band structure plots actually show?

In a lot of the literature, we see plots of the energy band structure from DFT simulations. How are these eigen-energies obtained as function of crystal momentum within the DFT framework? Are they the ...
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Why Weyl fermion in Weyl semimetals(WSM) have high mobility only at low temperature?

I read several papers reporting high Weyl fermion with very high mobility in WSMs such as TaAs, NbAs, WTe2 and so on. However, this high mobility looks like (=Weyl fermion) always appears at only low ...
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50 views

Could dark matter possibly be anti-matter?

Considering the broken symmetry after the big bang - what I understand as there being a huge surplus of matter and a lesser presence of anti matter - is it possible that dark matter could be anti-...
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Resistance increase with length because of more scattering?

I am referring to one of the answers to this old question. I can't add comment to it because I don't have enough reputation. So here I rephrase the question: does resistance increase with length ...
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288 views

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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226 views

Tight binding Hamiltonian for 2D finite dimensional lattice and nanowire

The Hamiltonian of a 1D lattice having finite $N$ atoms, (if we consider one basis per atom) is given by the following $N\times N$ matrix- Here $E$ is the onsite energy and $t$ is the hopping ...
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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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How do i calculate leakage current in passivation layer of GaN HEMT?

I want to calculate the leakage current between the passivation and encapsulation layers of the GaN HEMT which will give me information about the material
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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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409 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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39 views

Why does AC Conductivty in Drude Theory have an Imaginary and a Real Part?

In the Drude Model the direct current (DC) conductivity is given by the following formula: $$\sigma_0=\frac{ne^2 \tau}{m}$$ where $\tau$ is the relaxation time. Furthermore, the AC conductivity in ...
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Third Brillouin zone for a quadratic 2D lattice

As far as I understand, the construction of Brillouin zones stems from the relation $$ 2 \vec{k}\cdot \vec{G} +G^2 = 0$$, where k is the wave vector and and G is the reciprocal lattice vector. This ...
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108 views

Simple questions about reciprocal lattice and brillouin zone

I have few simple questions about Brillouin zone. I will take the example of a 1D lattice with a period of "a". If I have well understood, the reciprocal lattice shows all the point in "k-space" ...
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Landau Diamagnetism and Pauli paramagnetism

In the conventional definition of Landau's diamagnetism we ignore the effect of spin-electron coupling and vice versa for the derivation of Pauli's paramagnetism. I want to know what would happen if ...
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687 views

Peierls substitution vs minimal coupling

In the presence of vector potential (let's assume it's uniform), a tight-binding Hamiltonian will be changed according to the Peierls substitution: $$t_{ij}c_i^{\dagger}c_j \to t_{ij}e^{iqA|i-j|}...
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Speed of sound in solid — temperature dependence

Let $v$ denote the speed of sound in a fixed solid, at a fixed temperature $T$. This will depend on properties of the solid (such as the bulk modulus and density). Given an increase in $T$, does $v$ ...
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How can I derive the Phonon Density of Normal Modes in two and three dimensions?

The density of normal modes in 1D has already been discussed in another post (LINK) In essence, the formula is: $$D(\omega) = \frac{1}{2\pi}\int\mathrm{d}q\,\delta(\omega-\omega(q))$$ resulting in ...
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Out-of-plane electronic band structure for 2D materials?

There's been much recent interest in 2D materials since they can form monolayer-thick films. Since their crystal structure is periodic along the in-plane directions, the electronic band structure ...
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Solid state physics: When do I use classical laws?

Let's say I am given the dispersion relation for nearly-free electrons: $$ E(k) = \frac{\hbar^2}{2m}(k^2+c\,k^4)$$ Where $c$ is a small constant of appropiate dimension. How do I calculate the ...
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How do signals go through solid objects? [closed]

So many types of signals pass, or seem to pass I don't know, through solid objects. How do they do this?
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How to prove Bloch function is periodic in reciprocal lattice?

How to prove Bloch function is periodic in reciprocal lattice? I saw in some textbooks this formula: $$ \Psi_{\mathbf{k}} (\mathbf{r}) = \sum_{\mathbf{G}} c_{\mathbf{k}+\mathbf{G}}e^{i(\mathbf{k}+\...
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54 views

Intuition for defining basis for Hamiltonian in momentum representation

I am going through Quantum information approach to the Ising model: Entanglement in chains of qubits by Stelmachovic et al. In Section A.4, the authors determines the eigenvalues and eigenstates of ...
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118 views

Question regarding NaCl equilibrium separation

So I am tutoring someone later and one of the problems is from Eisberg/Resnick Ch 12. The potential energy $V$ of NaCl can be described emperically by $$V = \frac{-e^2}{4\pi\epsilon_0 R}+Ae^{-R/\...
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792 views

Phonon Momentum

I am reading Charles Kittel's solid state physics and wondering what's the mechanism that neutron waves and photons can interact with phonons and the process obey the generalized momentum-energy ...
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Deriving Reciprocal Lattice Definition

The derivation of reciprocal lattice vectors in terms of the direct space lattice vectors starts by applying expanding a translationally invariant lattice function $f(\bf{R_k}+r)$ in plane waves $f_k ...
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Bosonization for unequal left/right Fermi velocities

The standard exposition of bosonization/Luttinger liquid theory in textbooks treats the case that left and right channels share the same absolute value of Fermi velocity. Is it possible to relax this ...
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768 views

How is current produced in semiconductors or metals?

I think current is the movement of electrons through the wire or semiconductor, thus when I press the switch of the light bulb the electrons go from positive part to tungsten and light is produced. ...
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How to confirm experimentally the effect of momentum space Berry curvature in solids?

I'm studying spin-orbit coupling and Berry curvature effects, especially on the spin Hall effect. However, Table 3 in a review paper http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.87.1213 ...
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Why polymeric solids are said to be intermediate between crystalline solids and amorphous solids?

Crystalline solids have ordered arrangement and amorphous solids do not. Polymeric solids are simply formed by the joining of some monomeric units. It has nothing to do with ordered or not ordered ...
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Particle density in k-space

Question: Given a many particle wave function $|\Psi\rangle$, how can I calculate the occupation numbers in k-space? Setup: I have a 1D chain of molecules which contains 4 sites per unit cell. Let'...
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168 views

Why is the density of states in $k$-space constant?

Why are the allowed states in $k$-space equidistant in every direction? As a consequence of this, the density of states for phonons in 3D is $$\frac{V}{(2\pi)^3}$$ while for electrons it is $$2 \frac{...
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The d-orbital splittings in WS2 monolayer

According to this paper (and many others), the formely degenerate $d$ orbitals of the tungsten atoms in the $WS_2$ monolayer are split into three groups: (1) $d_{z^2}$, (2) $d_{x^2-y^2}, d_{xy}$ and (...
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C libraries for Solid State Physics

During last year I've attended courses of solid state physics, and I studied methods for bands structure calculations in the Hartree Fock framework. However, I know only theoretical aspects of these ...
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111 views

What is the difference between Fermi level and Fermi edge?

Just as in title: What is the difference between Fermi level and Fermi edge? My friend makes some research about XPS and he encountered this term. He knows what is Fermi level, but never heard about ...
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865 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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163 views

Coordinate system for crystallographic groups

In the International Tables for Crystallography for each crystallographic group an asymmetric unit is supplied (mathematicians call this a fundamental domain of the group). This region is a bounded ...
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39 views

Bands in semiconductors: $E$ vs. $k$ diagram

I always thought that in a semiconductor there was one gap, one conduction band and one valence band. However, reading a book I came across this picture And now I'm very confused. Apparently there ...
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Pauli paramagnetism for electrons with external magnetic field

Apparently it is to be shown that for electrons under an external magnetic field, in the limit as $B\to 0 $ $$ \chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)} $$ ...
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Question about electron-hole pair generation in depletion layer for a p-n junction photodiode

At the heart of operation of p-n (or p-i-n) junction photodiodes is the absorption of photons leading to generation of electron-hole pairs. If the diode is, e.g., reverse biased, then the motion of ...
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Connection between fractional charge and Schrodinger's cat

In the FQHE, it is said that one electron splits into three 1/3-charged entities. Is it like the Schrodinger cat?
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At most $N$ gapless charge/spin modes in a system of $N$ coupled 1D chains?

Leon Balents and Matthew P. A. Fisher claimed the following without any further explanation ($N$ is the number of chains) For a system of $N$ coupled 1D chains, the number of gapless charge modes ...
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Non-constant Bandgap in a semiconductor

For a material made of two different intrinsic semiconductors (SC); $SC_A$ on the left, and $SC_B$ on the right, such that $E_{gap,A}>E_{gap,B}$, the energy band diagram would look like so: Note: ...
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Density of States for a separable hamiltonian

There are $N$ non interacting electrons in a potential well: \begin{align} H&= -{1 \over 2 } \nabla^2 + U(x,y,z) \\ U(x,y,z)&={1\over2}\omega^2z^2 \; \mbox{for} \; (x,y) \in [0,L]\times [0,L]; ...