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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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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Why is temperature vibration?

Why do the atoms in a crystal vibrate at finite temperature?
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Can the Fermi level go above the conduction band energy if doped heavily enough?

So for n-type Si with donor density $N_d$ and donor energy level $E_d$, $N_d^+ = N_d(1+\frac{1}{1+e^{\beta (E_d - E_f)}/2})$ is the number of ionized donors, so we get an relation between the number ...
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Why is the k=0 phonon neglected when calculating Debye-Waller factor?

When calculating Debye-Waller factor one gets the form: $e^{-2W} = ...
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Effective mass vs. cyclotron mass of electrons in graphene

Graphene possesses the highest charge carrier mobilities if the Fermi level is close to the Dirac point [see e.g. DOI 10.1103/PhysRevB.81.195434]. The band dispersion is approximately linear to 0.9 eV ...
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Coordination Number of a Bag of Marbles [on hold]

The problem is question 2.4 of Sidebottom's Solid State: ...
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Chemical potential and origin of pressure in a solid

Pressure of a gas is related to the rate of change of momentum of the particles; the temperature is the mean kinetic energy of the particles. Can the chemical potential be given a similar physical ...
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Goldstone modes of spin density wave

A spin density wave (SDW) is a phase in which a material suddenly shows a periodically modulated spin density $S_{\vec{q}}(\vec{r}) $ below a certain critical tempereature $T_C$. Obviously some kind ...
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Are the 14 Bravais lattices really distinct?

I have learned that there are 14 distinct Bravais lattices in 3D and any other thought lattice form could be reduced to or expressed in one of these 14 forms. But the primitive unit cell for f.c.c ...
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What are the possible reasons of deviation from Curie Weiss behavior well above Tc?

I think existence of other weak interactions which have higher transition temperature than the observed prominent interaction(ferro/antiferro) can perhaps lead to such result but I am confused when ...
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What material could be used to study magnetic phase transitions in a college laboratory exercise?

I am working to develop a simple laboratory exercise in solid state physics to be conducted by fourth year students of physics. The idea of the exercise is for the student to get some experience in ...
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22 views

Why is conductivity isotropic in a plane perpendicular to the z-axis of a tetragonal crystal?

Considering the symmetry of a tetragonal crystal, how can it be proved that conductivity is isotropic in a plane perpendicular to the z-axis?
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How to find dispersion relation for 1 d topological insulator?

Is it correct to write the dispersion relation for following Hamiltonian where $\sigma_{x}$ act in spin space and $\tau_{x}$ acts in pseudo spin particle hole spin $H_{BdG} (k)=(\xi_{k}+B\sigma_{x}+u ...
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$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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Trace part of Hamiltonian

Given an electron in one discrete dimension, the Hamiltonian is given by $H_{n,n'}\in Mat_{N\times N}\left(\mathbb{C}\right)$ acting on $l^2\left(\mathbb{C}^N\right)$ where $N$ is some integer ...
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How quickly is motion transferred in a solid object?

Just for example: assume an iron bar one foot in length. If you push on one end, the entire bar will move. This seems instantaneous. but actually, from my understanding, the atoms all push against ...
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Is Differential Geometry used in Solid State?

I'm an undergraduate in physics interested in a career in solid state. While I know that any additional math is helpful--I am on time constraints, and can only take a few supplemental classes. That ...
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Dual order parameters of superfluid and Mott insulator

In this paper of Leon Balents, Matthew Fisher, Chetan Nayak, they mention the dual order parameters of superfluid and Mott insulator in 1D and 2D. There are some statements which (I suppose) ...
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What is the boundary of restorable thermal expansion?

As every book indicates, thermal expansion is a linear process $\frac{\Delta L}{L}=\alpha \Delta T$. Upon heating an object the result is thermal expansion. If we cool it down it is restored its ...
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Resistance of a diode in different regime and the physics of recombination current

I would like to ask question about the resistance of a diode under different regime. Surely, in reverse bias, it has a breakdown voltage, and in forward bias,it rises exponentially according to the ...
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28 views

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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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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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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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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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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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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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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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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41 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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...