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Questions tagged [solid-state-physics]

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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What would happen if we had a crystal structure but only gravitational interactions?

The idea is simple. Let's say we arrange similar bodies (call them planets, ions, anything) in an infinite crystal structure, but the only possible interactions are gravitational interactions. A ...
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Ising model with quantum magnetic field

Hamiltonian of the Ising model with an external magnetic field is written as $$H=-J\sum_{\langle i,j \rangle} s_i s_j + h\sum_j s_j$$ where $J$ is nearest neighbor coupling constant and $h$ is the ...
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Twisted bilayer graphene Hamiltonian

I am studying article about twisted bilayer graphene, and I am confused about the Hamiltonian of the problem. It seems that in momentum space the Hamiltonian is effectively infinite dimensional matrix ...
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How are the coefficients determined in the high temperature expansion of the 2D Ising model?

I have been studying the 2D Ising model lately and have been looking at high and low temperatures. But I'm having problems when trying to understand the high temperature one. The final expansion looks ...
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Why are 2N electrons allowed in an energy band?

In Solid State Physics, there are supposedly 2N electrons allowed in any energy band, with N being the number of atoms in the solid. Firstly, I understand why there should be N allowed states if ...
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Momentum Conservation for ARPES

I have a question about the principle of momentum conservation the modeling of ARPES: https://en.wikipedia.org/wiki/Angle-resolved_photoemission_spectroscopy#Theory We split the initial momentum of ...
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Highest occupied orbitals or bands

I am not a student of physics, but a student of nano-technology, hence I might sound extremely stupid, but I just want to clarify my doubt even if sounds very trivial. The no. of free charge ...
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Achiral system with Dzyaloshinskii-Moriya interaction?

From my tentative understanding, Dzyaloshinskii-Moriya (DM) interaction determines a certain chirality by its special mixed product form while its existence only requires the breaking of inversion ...
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What is the binding energy between conduction band and valence band of metals and insulators?

As far as my understanding of solid state physics goes, I can't see a clear connection between binding energy and band gap. But our teacher asked us the question as an assignment but i really can't ...
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Langevin theory does not consider the possibility of changing the orientation of orbits under an external magnetic field. Why?

In the classical Langevin theory of diamagnetism, an externally applied magnetic field $\vec{B}$ either increases or decreases the speed of orbital motion of the electrons. But there is yet another ...
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What does the concept of “free electron” mean in the context of band theory?

Often when conductivity is explained through band theory, the term "free" tends to crop up. As an example, I often come across descriptions of the valence band as a highest filled set of states ...
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Tight binding model and LCAO

What is the qualitative difference between the tight binding model and Linear Combination of Atomic Orbitals(LCAO) that is used in Chemistry? I have read that LCAO is a type of tight binding model. ...
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Kelvin solid and deformation in transverse direction with Poisson ratio

A Kelvin-Voigt material is a material with such a behavior : I'm wondering if there is a way to model in a similar way the deformation in the transverse directions $y$. Meaning we have for the ...
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Negative Miller indices and parallel planes

The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. https://en.m.wikipedia.org/wiki/Miller_index Does this mean, that parallel planes are generally ...
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Why the chemical potential of phonon gas in Einstein 's solid model is not zero

In Einstein’s model of solid, each atom in the solid is considered to be an independent three-dimensional quantum harmonic oscillator with characteristic frequency $ω$ that is constant. Each degree of ...
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Why don't marbles naturally arrange themselves like a crystal?

Most solids are crystalline in nature because the energy released during the formation of ordered structure is more than that released during the formation of disordered structure such that the ...
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Phase velocity of optical branch of lattice vibration at zone center

In a 1-D diatomic lattice, the dispersion relation for lattice vibration is given by: $\omega =\surd( \beta (1/M + 1/m)+\beta(\surd(1/M + 1/m)^2 -4sin^2ka/Mm))$ $v = \omega/k$ gives the phase ...
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Parallel Nature of Reciprocal and Real Lattice Primitive Vectors

In Michael Shur's "Physics of Semiconductor Devices" book, he asserts To satisfy $\exp (i\textbf{K}\cdot \textbf{a}) = 1$, the primitive vectors of the reciprocal and real lattices $\textbf{K}_i$ ...
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Solid foundation for obtaining the band gap from density functional theory

Looking around a lot of solid calculations, the band gap is usually estimated by DFT. But I have some doubts of that within my knowledge, so I'm asking the question. The usual process to generate ...
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Diffusion coefficient for electrons and holes in a semiconductor

I am trying to calculate the diffusion coefficient for electrons and holes in excess of each side of the junction p-n outside the depletion region. Silicon was used with electron mobility at 300 K, $\...
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1answer
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Energy band gap

I am studying from the Aschroft & Mermim. In the chapter 8 they prove the Bloch theorem and introduce the concept of band. they say that k is a quantum number that charactrize the eigenfunction ...
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How can there be an electric field normal to the surface in a surface plasmon in a metal

Ashcroft and Mermin's Solid State Physics, chapter one, has an exercise about surface plasmons. They give the electric field normal to the surface of the metal as $E_z=Be^{iqx}e^{-Kz}$ How can this be?...
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Plasma and helicon wave frequencies in iron according to Drude model

The first chapter of Ashcroft and Mermin's Solid State Physics discusses electromagnetic waves in metals. One of the exercises requires calculation of the plasma and helicon frequenies using the Drude ...
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Can amorphous solids have energy bands?

One can understand the formation of energy bands from the Kronig-Penny model which assumes a periodic potential. But I heard that even if the potential is aperiodic for example in amorphous substances ...
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Is exercise 4, part b of chapter one of Ashcroft and Mermin wrong?

This is from Solid State Physics. It is about helicon waves in a metal. When I take the curl of the given electric field it does not equal zero even though the magnetic field is static. Is this an ...
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Is there an English version of the book 'Festkörperphysik' by Rudolf Gross and Achim Marx?

I heard this book is very very nice, but too bad I cannot read German...yet..And I heard last year they published an English version, but I cannot find it anywhere. If anyone knows about it, it will ...
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Dispersion relation for one-dimensional linear chain with out-of-line vibration

I'm going to consider the effect of out of line vibrations in the dispersion relation of a one-dimensional linear chain of atoms (which is modeled as a harmonic oscillator in the x-direction). I ...
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A better understaing of drude model - derivation of the $\mathbf{p}$ ODE

In a few books (Simon, Aschroft and my univeristy course too) the ODE for the electrons $\mathbf{p}$ under the drude model assumptions is derived by taking an electron and saying: Let's say an ...
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Is the band theory valid for an electron with energy greater than the potential?

Consider Kroenig Penney model. Here there is a derivation that uses the following potential: One of the assumption is that the energy of the electron is $E<U_0$. Under this assumption (and others) ...
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Why is a dipole moment required for the polariton model to be applicable?

As stated in the first sentence of (https://en.wikipedia.org/wiki/Polariton) a dipole moment is a requirement for the polariton model to be applicable. Unfortunately I was not able to find an ...
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Why does ice freeze in feathery streaks on windows?

A twitter acquaintance asks: ...why does the ice form in feathery streaks like this?
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Coupling Coefficient of Piezoelectric Material

How is Coupling Coefficient of Piezoelectric Crystal measured? I found in an old lab manual that coupling coefficient of Piezoelectric Crystal equals $\frac{1}{Q_M}$ where $Q_M$ is the quality factor ...
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Why do covalent crystals typically have a much lower packing density than metal crystals?

I know the bond length and bond direction are much more important than the packing density but I'm stuck here.
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Weyl semimetal lattice model with real hoppings only?

Is there any lattice model of Weyl semimetal with real hopping amplitudes only? I was trying to find such a simplest model with only two Weyl points. As far as I've tried or read in papers, no ...
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Is 2D toric code dual to something?

I can understand 2D toric code as a quantum Z2 gauge theory defined on a lattice. Is this model dual to some simpler spin model? A bit of motivation to clarify my intention: I know 3D classical Ising ...
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Why does the 2D hexagonal lattice have a different tight binding band structure than Graphene?

Here you can find band structures for various tight binding models. I was wondering, why the 2-D hexagonal lattice has a different band structure than Graphene, even though they have the same lattice.
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How to determine the direction in reciprocal space from a given real space direction in an fcc(111) lattice?

Given a fcc(111) crystal and a real space direction of [011], what is the direction perpendicular to the [011] direction and how does this direction relate to the direction in the Brillouin zone (eg ...
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How to calculate conductivity / electron mobility from theory

Is there a way to make quantitative statements about the conductivity of materials with band theory? If not I should still be able to get information about the conductivity from Green-Kubo relations ...
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Calculation of density of states near a saddle point

I am trying to calculate density of states near a saddel point, where $$E(k) = E_c + \frac{\hbar^2}{2}\left( \frac{k_x^2}{m_x}+\frac{k_y^2}{m_y}- \frac{k_z^2}{m_z} \right)$$ Where, $E_c$ is the energy ...
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Analytic derivation of honeycomb lattice Brillouin zone

My goal is to analytically derive the first Brillouin zone of the honeycomb lattice. Geometrically it's clear how to do this by just finding the space on the lattice nearest to a particular point of ...
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Operator to find position of a particle in many body system

I am reading the following article by Raffaele Resta about modern theory of polarization The quantum-mechanical position operator and the polarization problem My question is not about polarization....
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Possible ground state wavefunctions of anti-ferromagnetic Heisenberg spin chains

What are the ground state wavefunctions of the anti-ferromagnetic (AFM) Heisenberg spin chains? Is that which of the following? $$| ↑↓↑↓ · · · ↑↓>$$ or $$| ↓↑↓↑ . . . ↓↑>$$ or $$| ↑↓↑↓ · · · ↑↓...
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What are phonon frequencies in solids? How are they related to the interaction potentials between the constituent atoms?

I was reading a paper on self-assembly of colloidal structures, where it was mentioned that only solids with real phonon frequencies are mechanically stable. And the authors go on to manipulate the ...
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transmission probability of eigenchannels as function of fermi energy

I am trying to understand how the fermi energy 'modifies the transmission probability for a number of high-transmission conduction channels,' which is mentioned here. I googled references and found ...
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Why does the hybridization occur between the orbitals that are even under a certain symmetry operations?

For example, in monolayers MoS$_2$, considering the prismatic coordination of the metal atom, the $d$-orbitals split into three categories: {$d_{z^2}$} {$d_{xy}, d_{x^2-y^2}$} {$d_{xz},d_{yz}$}. ...
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Understanding what the Bose-Einstein distribution

I'm currently studying Kittel's Solid State Physics and in his chapter on Phonon heat capacity, we need to first calculate the total energy $U$. Phonons have energy $E_n = (n+1/2)\hbar\omega$ and he ...
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The Griffiths of Solid State [duplicate]

I have recently started learning solid state at my university from an introductory graduate class. The professor is an absolute mess and his lectures are too incoherent and discontinuous. Due to my ...
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Attempt at proving $-i\ \langle{u_n|\nabla_k u_n}\rangle=-\dfrac{i}{2}tr[v^\dagger(k)\nabla_k v(k) ]$ from Kane and Fu's paper

I am trying to prove result (3.4) of the following paper: http://li.mit.edu/S/2d/Paper/Fu07Kane.pdf namely, that $$-i\ \langle{u_n|\nabla_k u_n}\rangle=-\dfrac{i}{2}tr[v^\dagger(k)\nabla_k v(k) ]$$ ...
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Points of symmetry in $k$-space

Can you relate a point in the reciprocal space with a vector in real space? How do I find the family of planes that represent a point of symmetry in the Brillouin zone? For example, germanium has ...
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Measurement of Pauli paramagnetism for conduction electrons in metals

To measure the paramagnetism of conduction electrons in metals, we can measure the shift of nuclei magnetic resonance frequency of the atom in metal (like sodium) compared with the frequency of the ...