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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Is this a valid way for deriving the ODE for a lattice vibration of a one dimensional crystal?

Consider the following lattice: I want to derive a differential equation that describes the forces acting on the $n$-th atom in the lattice. Each atom is coupled to its neighbour ($n+1,n-1)$ by a ...
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3answers
204 views

How does crystal lattice explain electrical conductance?

From http://education.jlab.org In a metal, the atoms are arranged in a crystal-like configuration. ... Now, in a metal, the valence band is relatively close to the conduction band - ...
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22 views

Why can the dispersion relation for a linear chain of atoms (connected by springs) be written as $\omega(k)=c_s \lvert k\rvert$?

On the german wikipedia site (right under "Akustische Moden"), the dispersion relation for a linear chain of atoms (connected by springs): $$\omega(k)=2 \sqrt{\frac{K}{M}} \left \vert ...
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23 views

MOS junction physics [on hold]

Why when apply a voltage $V>0$, the acceptor ions tends to appear at junction though the electrons and holes are changing at the same rate? assume it to be p channel MOS junction
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11 views

How one can count how many phonon modes is there in the crystal?

I'm reading the review on phonon and Raman scattering in 2D transition metal dichalcogenides (2D TMDCs). At the beginning of Section 2.1 it is said that, since there are two X-M-X units in the ...
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16 views

finding the plane of cleavage in crystals [on hold]

The crystal can be clear such as diamond or shiny like germanium or metallic like galena or fools gold. I would like to cut some of these cleanly along natural cleavage lines. I would also like to ...
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1answer
142 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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2answers
168 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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2answers
51 views

bare Phonon and Symmetry Breaking

In condensed matter physics, the phonon is considered as a quasiparticle which is a result of the quantization of lattice vibrations. In many textbooks on solid state physics, it can be done if we ...
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1answer
62 views

Springs, elastic potential energy, kinetic energy

If a ball with some kinetic energy collides with a spring, the ball doesn't lose its kinetic energy in an instant, right? it loses kinetic energy as the spring gains potential elastic energy. Right? ...
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20 views

Derivation of effective mass equation in carbon nanotubes

I am trying to reproduce the calculations in the paper here by Ando and Nakanishi and am already stuck on equation 1. It is stated that in the vicinity of $\epsilon=0$ the amplitude of the ...
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3answers
421 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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200 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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114 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 ...
5
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1answer
661 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 ...
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18 views

What is the name of basis states of bulk k.p Hamiltonian?

A k.p Hamiltonian for a bulk material can be represented by 8x8 matrix in basis of $|S\uparrow\rangle$, $|S\downarrow\rangle$, $|X\uparrow\rangle$, $|Y\uparrow\rangle$, $|Z\uparrow\rangle$, ...
4
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1answer
45 views

quantum and thermal fluctuations in 1D, 2D, 3D

Why do thermal and quantum fluctuations destroy long-range order in 1D and 2D? Why not in 3D? If the answer is quite elaborated (with many formulas) perhaps a reference would be better. Sorry if this ...
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1answer
60 views

Why thermal conductivity increases with temperature?

what is the molecular mechanism with which thermal conductivity increases by increasing temperature? at least for metals? I know that heat increases the oscillations of the atoms in the crystal. But ...
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1answer
127 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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1answer
192 views

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}} ...
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22 views

What's the conductivity of graphene nanostructres (nanoribbon, nanomesh)?

As we know, the conductivity of graphene can be expressed with Kubo formula,including intra transition and inter transition. But does graphene nanoribbon or graphene nanomesh have the same ...
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1answer
135 views

Do solids have translational energy?

Along with having vibrational energy, do both crystalline and amorphous solids also have translational energy? I ask because I've always understood solids to have just vibrational motion/energy. But ...
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389 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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2answers
393 views

What is the significance of Fermi temperature?

The Fermi temperature of a solid is related to Fermi energy by relation $$ { E }_{ F } ={ k }_{ B }\times{ T }_{ F } $$ where $ { k }_{ B } $ is Boltzman constant. But what is the significance of ...
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2answers
371 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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21 views

P-n junction diode under forward bias configuration

Why there is exponential growth in current with respect to voltage in p-n junction diode under forward bias configuration?
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275 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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1answer
35 views

Is Mott insulator the same as non-compressible quantum fluid?

In the field of ultracold quantum gases we study the so called Bose-Hubbard model given in second quantization: $$\hat{\mathcal{H}} = -t\sum_{\langle i,j\rangle}\hat{a}^{\dagger}_{i}\hat{a}_{j} + ...
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2answers
1k views

Sign of the hopping integral in tight binding model

The Hamiltonian of tight binding model reads $H=-|t|\sum\limits_{<i,j>}c_i^{\dagger}c_j+h.c.$, why is there a negative sign in the hopping term?
4
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1answer
60 views

Is diamagnetism a static or dynamic effect?

When we put a diamagnetic material in the presence of an external magnetic field $\vec B_0$, the magnetic field inside the material decreases to $$\vec B=(1+\chi_m)\vec B_0,$$ where the magnetic ...
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3answers
54 views

Is there a way to measure the thickness of a metallic plate of order of micrometers?

I have a $5 cm×5 cm×? \mu m$ copper plate. Where '$?$', the thickness of the plate, is really small (about 30um). Is there anyway using physics to calculate the thickness? Update: Sorry I forgot ...
3
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1answer
748 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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67 views

It it true that the Fourier transform of the return probability can be written as the product of the retarded propagator & the advanced propagator?

I know the retarded green's function $G(r,r; E)$ is expressed as $$G(r,r; E)=\sum_n \frac{|\mu_n(r)|^2}{E-E_n+i\eta}$$ with the eigenvectors/eigenvalues $\mu_n(r)/E_n$. This expression of $G(r,r; E)$ ...
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183 views

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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1answer
158 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 ...
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31 views

Microscopic interpretation of magnetization in a 2D electron gas

I'm studying the de Haas-Van Alphen (dHvA) effect in a 2D free electron gas, and I have a problem to interpret the microscopical meaning of the flip of magnetization during the dHvA oscillation. My ...
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24 views

What many-body physics book is taught in universities of europ and USA? [duplicate]

Please suggest me a standard many-body physics book for teaching to PhD students of solid state physics. as i know "many particle physics" by mahan is a great book in this field but cant be taught in ...
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1answer
828 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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2answers
330 views

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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0answers
27 views

What is space charge Capacitance of diode?

Most of the books say that $p$-type and $n$-type materials of diode act as parallel plates of space charge capacitance were as the depletion charges (uncovered) act as dielectric. Then why do these ...
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0answers
46 views

How should I interpret the x-axis of an electronic band structure diagram ? Is it the direction an electron is moving?

Recently I've come in contact with electronic structure diagrams for my thesis and I have some difficulties getting an intuitive interpretation of reading these diagrams. What I think is happening: ...
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3answers
661 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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27 views

Is disturbance propagation velocity equal to wave velocity in a solid body?

How do the disturbance propagation velocity and wave propagation velocity relate to each other? To explain my question in details I will describe the following situation from the theory of acoustic ...
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1answer
777 views

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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2answers
278 views

What kinds of behavioural anomalies can a zero-field-cooled (ZFC) / field-cooled (FC) split indicate?

If a material shows a spiltting in the ZFC and FC curves, is it necessarily superparamagnetic, or could there be any other reason for the irreversibility? I have heard spin glasses also show ZFC-FC ...
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2answers
51 views

Can conducting electrons in a metal be modeled at all as classical particles?

I have seen computational models that treat the highest energy electrons in a conducting metal as classical particles in a plasma, the ions being held in place with some sort of heuristic ...
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17 views

Free charges inside a conductor and propagation of EM wave

In Griffith's book on Electrodynamics, while discussing the propagation of electromagnetic wave in a conducting medium, he set $\rho_{free}=0$. He argues that, any extra charge given to the conductor ...
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9 views

Calculating the matrix element for interband absorption

I am reading the book by Fox 'optical properties of solids'. In chapter 3, he considers the interband absorption of photons in an direct band solid. It is necessary to calculate the matrix element ...
2
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1answer
198 views

Perturbation theory in second quantization

I am dealing with electron/phonon interaction in QM. In particular, given the Hamiltonian of a solid, $$H=H_\text{el}+H_\text{ion}+H_\text{el-ion}$$ we have that the el-phonon Hamiltonian is treated ...