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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neglect of lattice potential for conduction electrons

Why is it true that in nearly free electron compunds, complete neglect of the lattice potential is usually a good approximation as long as one considers crystal momenta remote from the boundaries of ...
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Charge density waves: site-centering v.s. bond-centering

Question about charge density wave (CDW): From this Ref. page 13, why bond-centering charge density wave is naturally compatible with the observed coexistence of charge ordering and ...
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Floquet and Bloch's theorems : connection?

It is often stated that Bloch's theorem and Floquet's theorem are equivalent, even the Bloch's theorem is often referred as Floquet-Bloch theorem. However, it seems quite confusing to me since the ...
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Spontaneous breaking order and the Peierls order

From this this Ref, several types of orderings are considered. Question: What are the Hamiltonians which support the Peierls order? Do they necessarily break translational symmetry or break the ...
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314 views

What is crystal field anisotropy or effect ? It forces the magnetic moment to point in particular local direction..

Can you give a basic explanation of what is crystal field anisotropy ? What is the reason to arise ? In spin ice it forces the dipoles to point in the local 111 direction. For partially filled rare ...
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81 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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Why are crystals so useful for quantum isolation?

Some implementations of quantum gates (in the hopes of building a quantum computer one day) use crystals to isolate the qubits (to prevent decoherence). Why is a crystal so much better than an ...
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Nuclear spin relaxation, quasi-particle energy and spin spectral density

Below is a measurement of the longitudinal nuclear spin relaxation ($1/T_1$). Ref: Fig 4 of page 24 Competing ground states in low dimensions. My question concerns the statement in this Ref that: ...
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planewave Ansatz for modelling phonon dispersion in crystals

From Ashcroft's "Solid State Physics", for one-dimensional monatomic Bravais lattice, the equations of motion of ions are: \begin{equation} M\ddot u(na)=-K[2u(na)-u([n-1]a)-u([n+1]a)] \end{equation} ...
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How is potential energy actually stored in a steel spring at the atomic level?

Elasticity is one the most intriguing phenomena, wiki gives a summary explanation of what happens in a steel spring: the atomic lattice changes size and shape when forces are applied (energy 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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Real materials described by the fermionic Hubbard model?

I was always curios what real material are described by the fermionic Hubbard model. $$H = \sum_{\left< i, j\right> \sigma} t_{ij} c^{\dagger}_{i, \sigma} c_{j, \sigma} + \sum_i U_i ...
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264 views

How do the effects of semiconductor doping affect the Hall effect?

For instance, consider number 4 and 5 in the following sample: Using the right hand rule, B points downwards, conventional current points to the right (because of the 5V battery), and therefore, ...
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Difficult school decision: last year in school, should I take 2 math courses or 2 physics courses? [on hold]

I know this maybe off topic, but you guys are the best people out there to answer this for me. If you had the choice to choose between option 1) Group theory, and Differential Geometry, versus 2) ...
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33 views

What can we learn from a band structure diagram?

Other than the band gap and its magnitude, what are the things that we can immediately learn about the properties of the material just by glancing at its band structure? Can we say something about ...
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93 views

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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19 views

In what order will the magnetic quantum number be filled

For example, the electron configuration for Cu(II) ion is [Ar]3d9. So only the 3d shell matters to the total orbital angular momentum of the ion. For 3d shell there are 5 possible values of $m_l : ...
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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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LOCAL Temperature Gradient and Stress

I'm investigating the thermo-migration failure mechanism in nanoscale ICs interconnects. Typically, a nano wire under thermal stress suffers from material/mass migration or void nucleation if it ...
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Parity of magnetic susceptibility $\chi(\omega)$

It is well known that real and imaginary parts of magnetic susceptbility, defined as $\chi=\chi'(\omega)-\mathrm{i}\chi''(\omega)$, ought to be even and odd to frequency $\omega$ respectively, ...
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Difference between energy levels and bands of energy

As per the notes of my Solid state physics, band gap arises when the two atoms come close to each other so that their discrete energy levels split and become continuous which gives rise to bands of ...
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32 views

Kittel solid state physics handbook - Plasma oscillation of a ball - Am I solving this right?

I'm self learning nanotechnology undergraduate and I'm trying to solve a problem from chapter "plasmons, polaritons and polarons". This is it: Frequency of uniform mode of plasmons in a ball is ...
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Spectral properties in Solid state physics

So assume we have a periodic 1d Schrödinger operator $$- f'' + V(x) f(x)= \lambda f(x)$$ and we want $V$ to be periodic. Now if we assume that we are on a finite interval and that we have periodic ...
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36 views

Origin of band Gap

I know that in the Kronig Penney model there are values of the energy $E$ for which solutions to the Schrodinger equation don't exist. I understand that these forbidden values of $E$ form the band ...
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62 views

Lattice geometry and dispersion relation

Is there a general theorem which gives some information about which influence have the lattice geometry (for example sub-lattice structure, square lattice, honeycomb lattice, lattice symmetries, ...) ...
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244 views

Intro to Solid State Physics

I didn't see this listed on the books page so here it is. I'm currently in an introductory Solid State course, and we are using Kittel's book. I have been having a rough time with this book although I ...
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Kronig Penney Model Delta potential

I am finding it very hard to understand the implications of the equation obtained for the Kronig Penney Model from Solid State Physics by Kittel. The equation he obtained by using delta potential is ...
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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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There must be free positive charges, moving oppositely to electrons for the wire with current to stay neutral

All popular expositions (e.g. these ones) of relativistic electromagnetism claim univocally that electrons in motion become more dense due to the speed. They teach that Lorentz contraction of charges ...
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149 views

Do indirect optical transitions “cool” the material a little?

So I'm reading in Ashcroft and Mermin about indirect optical transitions: So, a photon comes in, and it only excites the electron across the indirect band gap if a phonon with the appropriate wave ...
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57 views

Condensed matter physics: the concept of holes [duplicate]

Is it possible to see an analogy between the holes and positron particle behavior? The holes are particles that behave oppositely to the electron in current conduction. So it is not the electron ...
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69 views

Why according to Hund's first rule all electron with same spin should occupy orbitals when partially filling?

I get that because of coulomb repulsion initially all the electrons will not occupy the same site but will single occupy the orbitals.But while doing so how do they know to keep their spins aligned ...
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65 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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51 views

Heisenberg Hamiltonian for spin-spin system

I wonder how we should conclude the following Hamiltonian (I mean the 32-18 in the picture below, written in solid state physics by Ashcroft & Mermin.) for spin-spin system? (It is in chapter 32 ...
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85 views

Photoelectric Effect - How are the electrons regained?

When the photons with enough energy impinge on a photocathode, it emits electrons. Does this mean that the solid will lose all its electron at one point? If not, how are electrons restored?
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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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364 views

Why does the n=0 Landau level in graphene have half the degeneracy of the other levels?

I've looked through several papers that talk about the anomalous integer quantum Hall effect of graphene (such as http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.95.146801), and they all state ...
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Why is Graphene Transparent?

Graphene is always in the news now a days and its key features are that it is; very strong, conductive and transparent. It is so transparent that each layer of graphene will only absorb 2% of Light ...
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Does carrier concentration at thermal equilibrium depend on doping concentration?

I came across a general equation at thermal equilibrium for carrier concentration that seems to be independent of doping concentration: $$n_0= 2\left( \frac{2\pi m_n^* k_BT}{h^2} \right)^{3\over 2} ...
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53 views

Why is Graphene So Strong?

There has been a lot of news about Graphene since its discovery in 2004. And as we are all told it is a revolutionary material which is very strong, conductive and transparent. But what is it about ...
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Why the mobilities of holes and electrons are not identical in an intrinsic material?

In an intrinsic material, the lifetime $\tau$ of electrons and holes is the same, so in the equation for mobility, $$\mu = \frac{e\tau}{m^*}$$ the only difference between mobility of electrons an ...
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piezoelectric in quartz

Does any one know if it is possible to find the relation between the ac current frequency applied to a piezoelectric and the change in the crystal lattice due to this current BY USE OF HAMILTONIAN (in ...
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107 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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Semiconductors and energy bands

The valence and conduction band of a semi-conductor are often drawn as here click. This plot has essentially two features and I would like to understand them. The peak and the valley of the two ...
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What does $m^*>m_e$ imply? (the effective mass of electron is larger than its rest mass)

From what I understand, the concept of effective mass is just something people come up with to make electrons and holes obey the equation of motion $$ \vec{F}=m^* \vec{a} $$ without dealing with the ...
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3D Density of states

I have the following dispersion relation: $$\epsilon(\vec{k})=\frac{\hbar}{2}\left(\frac{k_x^2}{m_1}+\frac{k_y^2}{m_2}-\frac{k_z^2}{m_3}\right)$$ (note the minus sign in the third term). And I am ...
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159 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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How to calculate the speed of electrons in a metal

According to the Sommerfeld model, the electrons on the Fermi level has the relation $$ \epsilon_F=\frac{\hbar^2k_F^2}{2m_e}=\frac{1}{2}m_ev_F^2 $$ i.e. $\hbar k_F=m_ev_F$ with $k_F=(3\pi^2n)^{1/3}$ ...
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Periodic momentum space in band structure

I often see pictures like this in physics, this one for Silicon band structure. (source, NB: it's the German page for Silicon). There you see the plot of the energy in terms of the momentum $k$. ...
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In Ashcroft and Mermin SSP, is 18.28 wrong?

I have been going over LEED in Ashcroft and Mermin independently. I believe equation $(18.28)$ has a factor of $2 \pi$ which should not be included. It would be in the dot product of $a$ and $b$, then ...