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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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Reciprocal lattice points and diffraction peaks

I am having a issue with the concept of what this question is asking. Question For a FCC crystal describe all the reciprocal lattice points corresponding to the two diffraction peaks. Here is my ...
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Interchanging $\epsilon_F$ and $\epsilon$ when deriving Density of States (DOS) of Free Electron Fermi Gas (FEFG)

When deriving the Density of States for a Free Electron Fermi Gas, Kittel seems to flamboyantly interchange $\epsilon$ and $\epsilon_F$ when going between equations. I am specifically puzzled as to ...
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Why isn't the dispersion of the phonon spectrum of two atomic basis with equal masses the same as for the one atomic basis?

The solution for the two atomic basis is given by \begin{align*} \omega^{2}=\gamma\left(\frac{1}{M_{1}}+\frac{1}{M_{2}}\right) \pm \gamma\left[\left(\frac{1}{M_{1}}+\frac{1}{M_{2}}\right)^{2}-\frac{...
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Dispersion relations in 2 atom and above

I am having a little trouble understanding this information of dispersion relations show below for a two atom basis. So it states that there should be in total 6 dispersion branches but there only 4. ...
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How is the effective mass of electrons related to the specific heat of an electron gas? (in uniform magnetic field)

Just to make it clear, this is related to solid state physics. QUESTION How is the effective mass of electrons in uniform magnetic field related to the specific heat of an electron gas? DETAILS ...
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Hamiltonian is given of ising model in picture calculate the quantities [on hold]

How to solve this problem please help and help enter image description here
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Confusion about average KE in free electron model via Density of States (DOS)

Assume a low temperature regime in which levels up to the Fermi Level, $E_F$, are populated. I have evaluated the density of states in energy space as $$D(E)=\frac{L^3}{\pi^2\hbar^3}(2m_e^2E)^{1/2},$...
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Fourier transformation of a discrete function; conclusion of having a finite sum [migrated]

For a function $g$ defined at discrete points $x_n = n a$ with $n \in \{0, \ldots, N\}$ with periodicity $g(x_0) = g(x_N)$ the discrete Fourier transformation reads $g(x_n) = \frac{1}{Na} \sum_{q \in ...
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Slater-Koster parameter for SC

I want to use SK method to calculate the interatomic matrix element for $P_{y}$ and $P_{z}$ for the nearest, second and third neighbors in simple cubic crystal. based on paper written by Slater-Koster ...
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45 views

Why an insufficient overlap cause vanishing exchange interaction?

Why should the exchange interaction vanish if the atoms do not have sufficient overlap in their overfunctions? For exchange interaction not to vanish, the only requirement seems to be that the ...
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35 views

How can i show mathematically, that adding few electrons to a conductor almost does not change the chemical potential

The Fermi-Dirac distribution is given by: $$f(\varepsilon)=\frac{1}{e^{\left(\varepsilon-\mu\right) / k_{\mathrm{B}} T}+1}$$ The Fermi-level (or chemical potential) $\mu$ is in the center of the ...
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How to derive the energy of a parabolic confining potential in a wire [closed]

I couldn't find any sources or help on other websites with regards to this question... Anyways, how to derive the expression for energy of parabolic confining potential in a wire as shown below? I ...
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Why do purely harmonic interatomic interactions result in infinite thermal conductivity?

When interatomic interactions are purely harmonic, normal modes cannot interact, and therefore no phonon scattering occurs, thus resulting in infinite thermal conductivity. But why is anharmonicity ...
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DFT Local Density Approach. Please, help me to understand some formulas [closed]

First of all i'd like to apologize for my poor English. In general im quite bad in physics, but it turned out that i have to carry out some band structure calculations. I've already done some with ...
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Why are magnon/phonon/photon velocities linear response quantities?

On page 2 of this paper, Onsager reciprocal relation for linear response is introduced as $$K_{AB}(q,\omega,B)=\epsilon_A\epsilon_B K_{BA}(-q,\omega,-B)$$ where $\epsilon_A,\epsilon_B=\pm1$ specifies ...
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How are atomic orbitals ascribed to crystal bands?

It is possible to understand band formation by considering a free electron dispersion relation $E(\vec{k})=\frac{{\hbar}^2k^2}{2m}$ which is modified when a periodic potential $V(\vec{r})$ is ...
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Diffusion current and depletion region with doping

I've been told that depletion region width decreases when we increase doping in a P-N junction. But doesn't this contradicts the fact that diffusion current increases with current? I'm probably mixing ...
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Why would $B_{1g}$ Raman mode still exist under $D_{4h}$ where $xx = yy$?

I come across some issues about Raman tensors under high symmetry , e.g. $D_{4h}$. A preliminary thought tells me that $x$ and $y$ are supposed to be equivalent in this point group therefore the Raman ...
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40 views

Mossbauer effect: neglectable recoil or absolute no recoil?

I stumbled on the Mossbauer effect. From the wikipedia article, I cannot tell for sure if the momentum of recoil is really zero, or only neglectable. From what I do (think I) understand, the ...
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24 views

Actual width of surface charge layer in conductors

In routine calculations we consider the width tending to zero and instead let volume charge density become a one-dimensional (radial) delta function. Thinking classically in lieu of quantum reality, ...
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62 views

Should phonon energy be undefined at zero frequency?

The energy carried by phonons of frequency $\omega$ is given by $$ E = \hbar \omega n_b(\beta \hbar \omega) = \hbar \omega \frac{1}{exp(\beta \hbar \omega) - 1} $$ So when $\omega = 0 $, the energy ...
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Hot point probe

How does the hot point probe method actually helps to determine the doping of a given wafer? Why the electrons move from hot to cold when the wafer is N doped and from cold to hot when the wafer is P ...
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How do you calculate the electric field from conduction and/or valence band energy?

I am currently using a program to calculate the band diagram of a semiconductor structure in 3D. I am wondering if its possible to use the finite difference method to calculate the electric field. ...
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Low energy electrons occupy holes

In Tipler's Physics it is said that for a temperature $T>0$ the only electrons that can gain energy from collisions are the ones with initial energy greater than $E_F-K_BT$. I understand that, ...
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Heat capacity due to Phonon Vibrations

Why does the speed of sound come, in the expression of Heat capacity, from phonon vibrations?
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Calculate phonon density of states

I need to calculate phonon density of states for a cuprate superconductor. I know there is a general formula for the calculation of phonon density of states by Einstein models like this $$D(\omega)=(\...
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Why do the $C_v$ of gapless systems have a power law behaviour?

The functional dependence of the heat capacity $C_v$ of systems with gapless excitations (e.g., lattice with acoustic phonons, Heisenberg ferromagnet with spin waves etc) is like a power law $$C_v\sim ...
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45 views

Optical and acoustic branch

Does a diatomic crystal posses both optical and acoustic branch simultaneously; Or, whether the vibration is either optical or acoustic?
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Conductive properties of oxidation depleted metals

When oxidation occurs on the surface of a metal it is know that there has to be diffusion of metallic elements from the bulk of the metal to the surface to react with oxygen, creating a concentration ...
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1answer
33 views

Closed and open orbit of electrons

What is exactly the difference between closed and open electron orbits?. Is it that, when crossed electric and magnetic field is applied, the electron in the real space does not complete an orbit, and ...
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57 views

Why optical phonons are called “optical”? [duplicate]

In diatomic lattice vibration, acoustical phonons correspond to vibration. But I could not understand the relevance of term optical in this context.
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1answer
25 views

An Expression for $\Delta T$ for a Thermal Conductivity derivation

In kinetic theory, the thermal conductivity of a gas is $$K = \frac{1}{3} C vl.$$ In deriving this formula, why is the following equation valid? "Now $ \Delta T$ between the ends of a free path of ...
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How does a basis affect the nearly free electron model?

Lets say I have a monatomic chain of atoms in which the electrons are nearly free. I know how to solve this, we end with energy gaps at the Brillouin zone boundaries. Now lets say every other atom ...
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Vibrational Energy at T = 0 K using the Debye model

I mm trying to estimate the vibrational energy at $T=0$ for a 3-D lattice using the Debye model. My plan is to sum over all the frequencies using: $$U = \int_0^{\omega_D} d\omega D(\omega)\epsilon(...
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Dynamics of the Ising model and its Monte Carlo sampling

The Ising model is a statistical mechanical model of ferromagnetism that defines the energy of a collection of magnetic dipoles arranged in a lattice, hence, through the Boltzmann distribution, also ...
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Can we numerically find ground-state of a 1D tight binding Hamiltonain with odd sites at half filling?

We can numerically find ground state energy and wavefunction of a 1D Hamiltonian at half-filling ($L = \#$ of sites and $N = \# $ of particles) using exact diagonalization. i.e at $L = 10$ and $N = 5$,...
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How to find the structure factor for the BCC lattice?

why is the value of structure factor zero when value of exponential is -1?
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How do irrational numbers give incommensurate potential (in lattice models)?

I am trying to understand Aubry-Andre model. It has the following form $$H = \sum_n c_n^\dagger c_{n+1}+H.C.+V\sum_n \cos{(2\pi\beta n)}c_n^\dagger c_n$$ This reference (at 3rd page) says that if $\...
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1answer
24 views

How to prevent recombination of carriers?

Let say we have a contact of an electron conductor and a hole conductor. How is it possible to prevent recombination of the carriers nearly completely? So, electrons do not suppose to fly or tunnel ...
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1answer
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Why a softer phonon is easier to get excited

In Kittel's book, "Some other structure B may have a softer or lower frequency phonon spectrum than A. As the temperature is increased the phonons in B will be more highly excited (higher thermal ...
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2answers
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Madelung energy

I was reading Solid State Physics by Charles Kittel, and equation (19) (in the image above) aroused my confusion. For non-nearest neighbours (indicated in equation(19) as "otherwise") why is the ...
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Symmetry Operation in Reciprocal Space

I have a set of k points spanning the entire Brillouin zone and I want to reduce it to the irreducible BZ. So for reduction, I use the point group symmetry operation. To verify, I use quantum espresso ...
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1answer
59 views

Einstein solid: one or three dimensional quantum harmonic oscillator?

The Einstein model for solids assumes all atoms vibrate with the same frequency $\omega$, each atom being modeled as a quantum harmonic oscillator. The thing is: solids are three-dimensional objects, ...
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1answer
25 views

Relevance of electromagnetic multipole transitions

In what kind of systems higher electromagnetic multipole transitions (like electric quadrupole transitions) become important or at least measurable? Is it for antennas in radiofrequency? Is it in the ...
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1answer
19 views

Does the band gap increase or decrease in this case? [closed]

Suppose I deposit a thin layer of a material A (with band gap Ea, say) on a material B (having band gap Eb) to form the film AB. What will the band gap of AB be? Will it be equal to Ea or Eb? Or will ...
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1answer
74 views

When will a cubical shaped diamond in outer space transform in a spherical shaped one?

Suppose we were able to build up a diamond (it could also be another material, but the structure of a diamond is very solid, literally) with the form of a cube in outer space. Will the diamond remain ...
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70 views

Why do we take the volume of quantum state as $\left(\frac{2\pi}{L}\right)^3$

If we consider this as volume of quantum state, and if I take length as 1 Ångström, then this volume will become something like $10^{30}$!!! Why do we take such a big volume to represent a quantum ...
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59 views

Density of states change in basis

I have my density of states (continuous energy) in some basis $|l\rangle$ given by $g_l(\epsilon) = \sum_l \delta(E_l-\epsilon)$ And I want to express it in terms of $|j\rangle$ where I have the ...
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3answers
55 views

An ohmic contact

It is claimed that Schottky type of contact between low work function p-type semiconductor and higher work function metal creates an ohmic contact in which current can flow both sides almost fluently ...
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1answer
43 views

Seebeck coefficient of metals

In some metals such as Platinum Seebeck coefficient is taking for 0 conditionally. https://en.wikipedia.org/wiki/Seebeck_coefficient#Seebeck_coefficients_for_some_common_materials Or graphite. How ...