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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Effective Hamiltonian in Heisenberg model

How can we divide the whole matrix into submatrices that we can write effective Hamiltonian on the Heisenberg model Based on Fundamentals of the Physics of Solids book (Volume I) written by Jen˝o ...
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How can we obtain Heisenberg Hamiltonian $H = J S_1\cdot S_2$ in Patrik Fazekas's book?

Actually I cannot understand how he wrote this Hamiltonian (how using of (2.56), (2.52) and (2.53) to combine into a single expression)? and also How and why he wrote (2.56) identity? (2.52) is $E_{...
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Deriving relations for a hard sphere phase diagram

In Torquato's Random Heterogeneous Materials, he has written $$\frac{p}{\rho kT} = 1+2^{d-1}\eta g_2 (D^{+})$$ where $g_2(D^+)$ is the contact value from the right-side of the radial distribution ...
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Microscopic Point Defects Interaction with Dislocation Motion

I am currently studying material science and we had been going through strengthening lately. One thing I never thoroughly understand is how exactly does point defects such as vacancies and ...
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Simple formula for conductivity in an insulator

I have seen cited without explanation the fact that an insulator with band gap $\Delta$ has conductivity $$\sigma = C e^{-\Delta / kT}$$ at temperature $T$. Could some one provide a derivation of this ...
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Converting Hamiltonian of a 2-atom basis tight binding model to k-space and finding its hopping factors (using Fourier transform)

Hi could someone please help in finding the hopping factors of this Hamiltonian and also explain how to do it. H = sin(Kx)/σx + sin(Ky)/σy + (m-2 (2- cos(Kx)- cos(Ky )) /σz 0<m<4 4<m<8
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How to prove the flat region for density of states $D(\epsilon)$ in tight binding electron model in 3D

The density of states for tight binding electron, $D(\epsilon)$, with respect to $\epsilon$(electron energy) followed an inverse cosine, a flat region ,and inverse cosine function in 3D. It was easy ...
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What is the direction of wavevector in the real hexagonal phononic lattice?

Assuming we have a 2D hexagonal lattice and its reciprocal lattice. The difference between them is that the real lattice and its reciprocal lattice have 30° rotation. So if the following image is its ...
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Find binding energy of NaCl-crystal with compressibility $\kappa$

I have tried to solve the following exercise, but my solution doesn't match the solution-sheet. It is given that the binding energy of a NaCl-crystal can be approximated with $E(r) = -N\left( k\dfrac{...
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Dielectric constant or permitivity of copper

I'm trying to simulate a capacitor made of copper plates in comsol multiphysics. What is the value that I should use for the dielectric constant or permittivity of the copper plates? I've read that ...
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Deriving a simplified expression for geometrical structure factor

I am interested in deriving a simplified expression for the geometrical structure factor $F_{hkl}$ for the alloy $Cu_3Au$. At high temperatures, there is an order-disorder phase transition, but lets ...
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Energy of exciton formation in semiconductors

Many sources I've seen have alluded to: An exciton can form when a material absorbs a photon of higher energy than its bandgap I looked at absorption enhancing effects of excitons, and am aware of ...
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What is the relation between the short-/open-circuit current and the band gap energy in solar cells?

For the VOC it is: VOC = E_g - something, where something is positive and depends on the Urbach energy. Otherwise it should be linear: https://aip.scitation.org/doi/pdf/10.1063/1.49397 For the ISC I ...
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Electronic specific heat capacity using free electron theory

While considering the contribtution of the electronic specific heat capacity, it is stated that, when the temperature increases from 0 K , only the electrons with energy range of the order of $k_bT$ ...
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Dipole moment in primary polarization mechanism in a dielectric

The question I have is regarding material from an old University book I am currently reading, Chapter 13, "The Solid State", Third Edition, H.M Rosenburg. And it states that the first ...
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How to understand Bragg rods?

From reading this PRL, I came across the idea of the reciprocal lattice of crystals being spread out in diffraction to "Bragg rods". Is there a good intuitive explanation of this? I'm ...
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Find the density of states in X points of Silicon

The problem statement is given verbatim In Si, the dispersion relation at the [001] X points is: $$E=\frac{\hbar^2}{2}\left(\frac{k_x^2+k_y^2}{m_t}+\frac{(k_z-G)^2}{m_l}\right)$$ where G is the ...
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Is the $E=E(k)$ dispersion relation periodic across Brillouin zones?

I am quite confused by the Brillouin zones. I know there is a dispersion relation $E=E(k)$ for the first Brillouin zone. But is this dispersion relation periodic across different Brillouin zones? ...
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Conductance of an interacting quasi one dimensional wire using the method for a 1D Fermi gas?

Assuming the electrons are non interacting and spin degenerate, the conductance of a quasi one dimensional quantum wire is quantised in units of $2\frac{e^2}{h}$. For small voltages, we simply count ...
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Show reciprocal lattice vectors are normal to direct lattice planes [closed]

Given a direct lattice: $\textbf{R}=m\vec{a}+n\vec{b}+p\vec{c}$ where $m,\ n,\ p$ are integers and a reciprocal lattice: $\textbf{G}=h\vec{a^{*}}+k\vec{b^{*}}+l\vec{c^{*}}$ where $h,\ k,\ l$ are ...
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Why can it be important to engineer band alignments/offsets (e.g. CdS buffer layer in CIGS)?

I would like to ask this question by the example of the CdS buffer layer in CIGS solar cells. One paper (https://pubs.rsc.org/en/content/articlelanding/2017/se/c7se00348j#!divAbstract) says that CdS ...
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Why are standing wave solutions discarded in conduction models

In electron conduction models like the Sommerfeld model, why are only the running wave solutions of the Time independent Schrodinger's equation considered for analysis. If the only application out of ...
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Which volatile ices are hardest below 100 K?

In the context of planetary science, some elements and compounds are informally called volatile instead of refractory, such as H2O, HCN, CO2, NH3, HCHO, CH4, CO, N2. At conditions found near planetary ...
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How to understand the anti-ferromagnetic picture for Slater insulator?

The Mott insulator is "local" picture and comes from strong interaction. This means single electron stays at their own site, and results in anti-ferromagnetic(AFM) order via super-exchange ...
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Effective density of states $N_c$ at different temperature for $\rm Si$

For Silicon at room temperature, Nc = 2.8x10^19 per unit volume. For 300K, m*/m = 1.81 for Silicon. Now Nc is proportional to 1.5th power of both temperature and m* (effective mass). So, at any other ...
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Excitons - Increase in absorption

I have consulted a book by Mark Fox on Optical Properties of Solids, and it states: " The absorption of a photon by an inter-band transition in a semiconductor or insulator creates an electron in ...
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What happens to the space group of a crystal when introducing a non-trivial basis?

I am trying to understand crystallography and the space groups of crystals, but I have one major question bugging me. The book I am using adresses different lattice symmetries and applications of ...
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What's the relation between degeneracy and $\pi$-flux

Ring with magnetic flux Assuming a particle locates in a ring which circle a magnetic flux, the Hamiltonian is: $$\hat{H}=\frac{1}{2 m}(\hat{p}-A)^{2} \rightarrow \frac{1}{2 m}\left(-i \partial_{\phi}...
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Low temperature resistance of metal

Is there any intuitive explanation of why resistivity of metal goes as $T^5$ at low temperature? The Debye theory gives that the phonon distribution goes as $n(\omega)\sim T $ at higher temperature ...
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Heat capacity of solid metals at room temperature

Estimate the molar heat capacity of gadolinium at room temperature, given it's Debye temperature $155 \ K$. $C=2.4\pi^4 N_A k \left(\frac{T}{T_D} \right)^3\approx13000\ \frac{J}{molK}$. I didn't think ...
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Classical Hall-Effect: Sign of the Hall Constant [closed]

In our lecture, we considered the classical Drude-Sommerfeld model and considered the following definition for the Hall constant: $$R_H := -\frac{1}{ne},$$ since we assume that only negatively ...
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First superconductors’ failure to follow BCS theory

Which superconductors were the first to fail to follow BCS theory? And in what year was it?
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Where do interactions enter the composite fermion theory in the fractional quantum Hall effect?

The question is, in short, where in the composite fermion argument are electron-electron interactions used? I know that interactions, namely Coulomb repulsion, between electrons are crucial in ...
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If a quantum state occupied by an electron has a $m^*_e>0$, will the same state if unoccupied have $m_h^*<0$ and vice-versa?

For electrons in a periodic potential, the effective mass of an electron in an energy band can be positive or negative depending on its quantum state specified by $n,k$ i.e. its energy $E_n(k)$ and ...
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What is so special about semiconductors?

In high school, I hear a lot about semiconductors. Semiconductors are used to make transistors and diodes. A semiconductor material has an electrical conductivity value falling between that of a ...
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Why does Einstein's theory of specific heat fail only at one extreme of temperature?

Why does Einstein's theory of specific heat of solids work well at high temperatures but fail at low temperatures?
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Can Metals Have an Energy Gap?

It's a very silly question, but sill: Can metals have an energy gap in their bandstructures? I would say yes, because the band gap is just $E_g = E_{c} - E_{v}$, I thought, where $E_c$ is the minimal ...
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DOS for anisotropic 2D electron gas dispersion

If we start with the simple 2D isotropic-parabolic dispersion, \begin{align} E\left(\textbf{p}\right) & \approx\tilde{\varepsilon}_{0}+\alpha p_{y}^{2}+\alpha p_{x}^{2}, \label{1} \end{align} ...
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How do you observe “silent” quantum vibrations?

In the theory of quantum vibrations (aka phonons) it is useful to divide up the vibrational normal modes of a crystal based on their representation within the symmetry group of the crystal. The ...
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Fermi-Surfaces of Alkali-Metals

I think I am a bit confused if I look at the following image of Fermi-surfaces for different metals: Li, Na, K, Rb and Cs have only one valence electron. Hence, if one calculates the Fermi-vector $...
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High symmetry point formulas for energy bands in empirical tight binding

I have a question about some intriguing formulas that I found. I am following ...
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Determine Phase and Group Velocities for Monoatomic Lattice

I have a question about determining the phase and group velocity for a monoatomic lattice. I know from various reference texts that $$v_p = \frac {\omega}{q}$$ $$v_g = \frac {\partial \omega}{\partial ...
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How could wavefunction be the same and yet it has degenerate eigenvalues?

In solid state physics, the schrodinger equation $$H \psi_{\vec{k}} = E_{\vec{k}} \psi_{\vec{k}}$$ has solutions $\psi_{\vec{k}}(x)$. In the near free electron approximation, I was told that $$\psi_{\...
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A question on reciprocal space for effective mass relation

The effective mass is defined as $$ \frac{1}{m_{ij}^*} = \frac{1}{\hbar^2} \frac{\partial^2\epsilon}{\partial k_i \partial k_j} $$ where, $m_{ij}^*$ is the effective mass, $\hbar$ is the Planck's ...
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Solid state problems (phonons conductivity)

I took a quiz where i got two answers wrong and i want to know what the correct answer is and why. Q1) In a material where both phonons and electrons contribute to the thermal conductivity, the ...
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Electron trap states

Some researchers claim that electron trap states in graphene (and I suggest in other materials) contribute to overall capacitance of a supercapacitor. https://www.researchgate.net/publication/...
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Retarded van der Waals force / Casimir Effect

So, I read that in the case of the nonretarded Van der Waals force, two atoms are at a separation distance, so that a virtual photon emitted by one atom cannot reach the other during its lifetime. At ...
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Lattice vibration and sound waves

In general, the acoustic branches of a crystalline solid has a nonlinear dispersion relation. For small values of the wavenumber $k$ or wavelengths large compared to the equilibrium lattice separation,...
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In a common base configuration with a pnp and VBC≈0, why does an output current IC flow when VEB < 0

Suppose a common base configuration of a standard pnp bipolar-transistor with the base grounded. The idea is to use the transistor as an ideal diode (as by the Shockley equation): $$ I_C = I_0 \left(e^...
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Is characteristic temperature $T_0$ of a semiconductor laser geometry independent?

Can I compare $T_0$ of one laser to another one, with different length and width? For example, let's say there are two lasers: Laser A Width: 20 $\mu m$ Length: 500 $\mu m$ $T_0$: X Laser B Width: ...

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