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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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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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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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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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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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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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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47 views

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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44 views

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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32 views

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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56 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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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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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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22 views

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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19 views

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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604 views

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 ...
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Does a list of errata for Ashcroft and Mermin's Solid State Physics exist?

I have tried Googling a list of errata for A&M, but it does not seem to exist. Has anyone found one?
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What is the Difference Between BCS Theory and Ginzburg-Landau Theory?

What is the Difference Between BCS Theory and Ginzburg-Landau Theory? I have been studying Superconductivity and I know that Both of the theories (BCS Theory and Ginzburg-Landau Theory) can be used ...
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Definition Of Dark Current In PhotoDetectors

What is The Definition of Dark Current In PhotoDetectore. How Can I Eliminate This Effect. I Think When Electrons Near The Conduction Band Are Excited Into It By Thermal Effect Then Dark Current Is ...
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Hole, solid state physics

In n-type semi conductor, when hole is created, which starts to move, but not in p-type semi conductor, hence, is a hole a static or dynamic? hole is absence on electron, absence means nothing, then, ...
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Exciton in semi-conductor

I don't understand why an exciton describes only the interaction between an electron hole and an electron in the conduction band? How is this interaction different from the interaction between an ...
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29 views

Hamiltonian for electron hole

I found in lectures notes that the Hamiltonian containing the energy of a electron hole without any interaction is given by $$H = \sum_k d_k^{\dagger} d_k \left( \frac{\hbar k^2}{2m_V} - E_{0,V} ...
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Bloch's theorem for Semi-Infinite Lattice

If we have a lattice Hamiltonian $$ \sum_{n'\in\mathbb{Z}}H_{n,n'}\psi_{n'} = E\psi_{n} \,\forall n\in\mathbb{Z} $$ such that $ H_{n,n'} = H_{n+q,n'+q}$ for some $q\in\mathbb{N}$ and for all ...
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Two state Hubbard modell

I am given the two state Hamiltonian $$ H = U \sum_{j \in \{L,R\}} n_{j \uparrow}n_{j \downarrow} - t \sum_{\sigma \in \{\uparrow,\downarrow\}}(a_{L \sigma}^{\dagger}a_{R \sigma} +a_{R ...
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What does the Equation $E_s = -dF$ mean in terms of a Rydberg Atoms Dipole Moment and its Energy?

Could someone explain what the equation $E_s = -d$•$F$: Where, '$d$' is the Rydberg Atoms Dipole Moment, '$F$' is The Electric Field Strength and '$E_s$' is the Energy of the Rydberg Atom. In terms ...
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35 views

How can I determine the convergence of self energy in Green's function

I want to solve for the Green's function (in the context of many body theory) but I have a question. After the determination of the retarded Green's function and the lesser Green's function we ...
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States in valence and conduction band

I often see a Hamiltonian in second quantization written for the valence and conduction band. Now, I was wondering: What are the single-electron states that form the prouct state they act on? So what ...
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Horrifying electron gas model

I am given the Hamiltonian, in an exercise called plasmons, and where $\langle, \rangle $ denotes the expectation value. $$ H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_{k_1,k_2,q} V_q ...
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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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Why are (most) solids periodic?

Is there a rigorous proof that periodic arrangements minimize the energy of a group of particles?
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Origin of High-temperature Superconductivity

What is the mechanism that causes certain materials to exhibit superconductivity at temperatures much higher than around 25 kelvin?
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Symmetry breaking and band gaps?

Can the discontinuity in the E-K dispersion relation of a periodic lattice (at the boundary of a Brillouin zone) be understood as a consequence of breaking continuous translation symmetry into ...
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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 to discretize a finite crystal?

I am trying to find a general method to discretize a finite crystal system. How I have been discretizing systems so far (using Wannier functions): When you have an infinite crystal, you may apply ...
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Why does Pressure Increase the Tc (Critical Temperature) of a Superconductor?

Just a heads up - please make this answer understandable to around 1st year degree level physics - not PhD research. So I can understand it - thanks. I was wondering why they Critical Temperature ...
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Why isn't doped silicon a strongly correlated electron system?

Most books on strongly correlated electrons claim that when the number of itinerant electrons is small and the screening length is large, that the system becomes "strongly correlated", (i.e. the ...
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Crystal in Magnetic Field

When you have a 2D crystal in a uniform perpendicular magnetic field, you can use the Peierls substitution to convert one tight-binding before-magnetic-field-band into a $q$-bands under the influence ...
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Binding forces in crystalline solids

I am referring to rocks in this instance. Individual crystals grow together in an igneous rock as it solidifies. I know that the SiO4 tetrahedron is the basic building unit of silicate minerals, and ...
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Coupling a ferromagnet to an antiferromagnet

Consider a system composed of a thin film of FM material on top of an AFM material. From my research I found that pinning of the FM material occurs when we cool the system from $T_N<T<T_C$ to ...
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The correspondence between real space and reciprocal space

From what I've learned, a point $P=(h\ k\ l)^T$ in the real space can be expressed as a linear combination of the primitive vectors $$A\left(\array{n_1\\n_2\\n_3}\right)=P$$ Where $A=(a_1a_2a_3)$ is ...
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How does current flow in superconductors if Cooper pairs have zero momentum?

I've been reading a lot of condensed matter textbooks, which state both that the net momentum of a Cooper pair in a superconductor is zero, and that Cooper pairs have momentum when they carry current. ...