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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Difficulty on getting vortex solutions from BdG Equation

I am working with BdG Equation in Tight Binding formalism, that is, full microscopic theory of superconductivity. In all references that I read they say that it is possible to generate the Abrikosov ...
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How do (LCD) drawing tablets work?

I recently bought a cheap drawing tablet and the box tells that it work via LCD. So I googled shortly and found this. I only want to confirm that this is correct. Means, are these tablet really ...
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Why is expectation value of velocity of Bloch state not zero?

In condensed matter theory a Bloch state $$\psi_{nk}(x)=u_{nk}(x)e^{ikx}$$ satisfying the eigenvalue equation $$\mathcal{H}\psi_{nk}(x)=E_{nk}\psi_{nk}$$ has the expectation value of velocity given by ...
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Low temperature behavior for ferromagnets: theoretical and experimental discrepancies

This is in reference to page 326, 327 of introduction to solid state physics, 8th edition by Charles Kittel The mean field theory does not give a good description of the variation of $M$ at low ...
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Why hopping term and overlap intergral always real in tight-binding model?

I'm learning tight-binding model of polyacetylene (-CH- chain) and get confused by the off-diagonal matrix elements of Hamiltonian and overlap matrix. For example, in all materials I can find, they ...
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Completeness in Bloch states

We know from the Bloch theorem that, in a periodic potential, the eigen wave functions are $\Phi_{kn}(r) = e^{ikr} u_{kn}(r)$ where n is the band index. So the solution can be expanded by them. ...
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Doubts regarding Ohm's resistance from impurity scattering

It is told that electrons can scatter on impurities in crystals, which leads to resistance and Ohm's law. My problem is that even though the potential is not exactly periodic, the wave packet can move ...
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How can I create 4 atoms basis graphene in Vesta? [closed]

How can I create 4 atoms basis graphene in Vesta? This is the Poscar file for two atoms basis graphene. As an example. Similar to these I got to make a 4 atoms basis graphene primitive cell. graphene ...
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How are electrons filled inside the bands of a semiconductor?

Is it like this: where one energy value which is a single line in the band can be occupied by multiple electrons - and by one energy value I mean that the exact/precise energy of all the electrons in ...
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Position of hole in a semiconductor

If there is a vacancy in the valence band does it imply that the hole is in the conduction band? Since the definition of "hole" is -k, -E. This is the way I interpreted the definition so I ...
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Confusion regarding density of states

Density of states with respect to energy is often defined as the number of states at a particular energy level. But I find this definition ambiguous. Because according to Pauli exclusion principle no ...
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What is Wannier state in solid-state physics? [closed]

I only retrieved information about the Wannier function, but I still don't know exactly what the Wannier state is. I would appreciate it if someone could explain it.
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Is the physics of semiconductors explained by nearly free electron model or is there a better model [duplicate]

I am learning (independently) about semiconductors and the physics behind their properties. Is the current 'accepted' theory for the physics of semiconductors (Electronic band structure) based on the ...
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Transformation matrix for plane directions using Miller indices

Since the change in vector orientations from conventional hexagonal unit cell to an orthorhombic cell of a HCP is not just a simple rotation about the origin, would the transformation matrix of the ...
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How does the highest energy electrons diffuse to the p-side from the CB of n-side shift the entire band structure of n-side down

When an n-type material comes in contact with a p-type material to form pn-junction, electrons with the highest energy in the conduction band will diffuse to the p-side to reach equilibrium so the ...
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Fermi energy is the average energy possessed by electrons participating in conduction in metals at T>0K?

I don't understand why on pg 963 of the following book stating that Fermi energy is the average energy possessed by electrons participating in conduction in metals at T>0K. Should Fermi energy be ...
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Why can't single particle states be taken up by more than one particle in the Fermi Dirac Distribution?

In Ashcroft, a single particle state is specified by k which is the wave vector of a single electron's wave function (without considering spin). Pauli Exclusion Principle says that a single electron ...
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What are the effects of Bravais lattices classification differences in 2D space on the physical properties of the crystals?

There are five possible distinct Bravais lattices in two-dimensional space. For example, if crystal A is Monoclinic (M) and crystal B is Hexagonal (H), how will the difference in their 2D Bravais ...
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Regarding the Maxwell Boltzmann statistics

Maxwell boltzmann distribution is applicable when any number of particles can occupy a single-particle state. But I am confused about what exactly a "state" here refers to. When you think ...
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Relation betwwen the expectation value of the position operator in Bloch state with unitary position operator

Recently, I want to get some knowledge about topological insulators, so I read the A short course on topological insulators. In the chapter 3, the author try to explain why polarization connects with ...
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Why do some minerals prefer diamond structures while others prefer wurtzite structures?

Carbon can exist as both diamond and wurtzite structures (lonsdaleite), but diamonds are much more common than lonsdaleites in nature. Some materials like GaN preferentially form wurtzite structures. ...
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PN junction - Voltage difference in neutral regions

At the very moment when a p material and a n material are put together, the conduction band and valence band of both materials are at approximately the same level. The n side and p side are both ...
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Property of reciprocal lattice

I came across the following property of the reciprocal lattices. Let be $\Lambda$ a Bravais lattice and $\Lambda^*$ its reciprocal lattice; let be $\vec{G} \in \Lambda^*$ and $\vec{G}_0$ the shortest ...
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Width of the Plateauxs in the IQHE

As the title said, Im studying the IQHE and I would like to know if there is some theory or idea to understand the widths of the Plateauxs that can be seen experimentally. As you can see in this ...
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Introduce a model with logarithmic dispersion relation

Having a model Hamiltonian on a lattice, one can compute the band structure of a system by employing the Bloch theorem. Here for simplicity, let's focus on noninteracting models. This procedure for a ...
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Time evolution of operators in linear response theory (Kubo formula)

I am reading the following book Many-body quantum theory in condensed matter physics book by Henrik Bruus and Karsten Flensberg This book mainly focuses on time-independent Hamiltonians only. When ...
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Is it correct to describe the valence electrons in an insulator as being bound to specific atoms?

For some quick background, I work as a high voltage electrician at a major metropolitan utility. In training apprentices, we use books that are often very poor in explaining fundamental electrical ...
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Calculating degeneracy in Landau Gauge with fixed boundary conditions

In another question I asked the differences between aplying periodic boundary conditions and fixed boundary conditions. The answer is that both of them for large enough samples present the same amount ...
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Landau Levels degeneracy in a finite sample

According to different sources: Tong lectures on IQHE (Tong), MIT Open courses (MIT) etc, when calculating the number of states in each Landau Level all of them impose (in the Landau gauge) periodic ...
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Interaction Term in Tomonaga-Luttinger Model

I am studying Tomonaga-Luttinger Model from Altland and Simon's textbook called Condensed Matter Field Theory. From the derivation, I am stuck with showing that the contribution to the interaction ...
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Polarization of conduction and valence bands

As title, this is something that I read in the paper "Quantitative relationship between polarization differences and the zone averaged shift photocurrent" (PRB 96, 075421 (2017)). This paper ...
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How do we measure the crystal momenta and the corresponding energies?

Determination of crystal momentum and the corresponding energy seems to be essential for drawing the band structure. What is the principle that is used to measure the crystal momentum and the ...
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In a doped semiconductor does the Fermi level increase or decrease with increasing/decreasing temperature?

As we all know the Fermi energy level is $E_\mathrm{f}$ and from statistical mechanics we know that the Fermi level for $T>0\;\mathrm{K}$ the level remains almost constant.It changes fro $E_\mathrm{...
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Is the occupation number and density of states equation correct?

The relationship between occupation number (which is the number of particles at a certain energy level) and the density of states is as follows: $$n(E) = D(E)F(E)$$ where $D(E)$ is the DOS and $F(E)$ ...
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How to choose the magnetic unit cell in the square lattice?

We have a square lattice in a homogenous magnetic field $\vec{B}=(0,0,B)$ and we use the magnetic potential $\vec{A}=(0,Bx,0)$. Question. We know that if the flux through each plaquette is $\phi=2\pi \...
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How to understand electron drift velocity?

I know that electron drift velocity can be defined as $I$ = $nAve$, where $I$ is the electric current, $A$ is the cross-sectional area of a conductor, $v$ is the electron drift velocity in question, ...
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Understanding the bandgap in $E-k$ diagram in the nearly free electron model

The nearly free electron model, solved using perturbation theory, reveals that a band gap opens up at each Brillouin zone boundary. Why is a point just below $k=\pi/a$ lowered in energy and a point ...
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Effective mass tensor calculation by fitting band structure along 3 perpendicular direction, correct or not?

The effective mass of charge carriers is defined as $$ \left(\frac{1}{m}\right)_{ij} = \frac{1}{\hbar^2}\frac{\partial^2E }{\partial k_i \partial k_j} $$ Considering that at the CBM we have a parabola....
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Confusion regarding calculation of effective mass tensor

I want to calculate the effective mass tensor as has been done in this paper. The authors go about calculating the effective mass in [100],[010] and [001] for a few different compounds, by curve ...
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Change in electronic dispersion in presence of magnetic moments

What happens to the energy dispersion of electrons in a 1D lattice in presence of localized magnetic moments on the lattice sites? Let's take both of ferromagnetic and antiferromagnetic configurations ...
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Inverse Fourier Transform of $e^{i\mathbf{k}\cdot\mathbf{R}}$ in Brillouin Zone in Proving Orthogonality of Wannier Functions [closed]

The relationship between wannier function and Bloch function like this: $$ |\mathbf{R}_n\rangle = \dfrac{V}{(2\pi)^3} \int_{\mathrm{BZ}} |\psi_{n\mathbf{k}}\rangle e^{-i\mathbf{k}\cdot \mathbf{R}}d\...
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How to distinguish between underdoped and overdoped regime for a high Tc superconductors?

Suppose I have two samples and oxygenate them under the required conditions. Now I find the value of hole concentration using the formula p = 0.16 + 0.11 (1-Tc/Tc,max)^(1/2) or p = 0.16 - 0.11 (1-Tc/...
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What is the meaning of "local" band structure?

In solid state physics, especially when discussing physics of junctions and interfaces, very often diagrams of band edges with respect to position are drawn, such as the following pn junction diagram. ...
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Is this condition $ \Phi=2\pi \frac mn =B \ell^2 $ correct for the magnetic flux per plaquette in 2D square lattice?

We have a 2D square lattice with the lattice constant $\ell$, and put it in a homogeneous magnetic field $B$. We are looking for the magnetic unit cell. As we know we get a periodic unit cell only ...
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Anomalous Hall Conductance by Kubo-Greenwood Formula

The Kubo formula is written below. $$\sigma_{ij}=\frac{e^2}{\hbar}\int_{BZ}\frac{dk_idk_j}{\left(2\pi\right)^2}\frac{1}{e^{\frac{\epsilon_n-\epsilon_{fermi}}{k_BT}}+1}\sum_{n^{'}\neq n}\frac{2Im\...
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Is it possible that a phonon having the same momentum $q$ after an scattering event?

We went through different phonon scattering events in my lecture. We looked at: Surface, surface roughness, impurity and "Umklappen" scattering. All those events changed the wavevector q of ...
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How to calculate the energy of a spring-mass system considering harmonic oscillation of the normal mode? [closed]

For a spring-mass system, we know that the potential and kinetic energy are $$E_p = \frac{1}{2}ku^2 \text{ and } E_k = \frac{1}{2}m\dot{u}^2.$$ where $k$, $m$ and $u$ are the spring constant, mass and ...
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Square lattice in the magnetic field; can someone please explain hopping factor Hofstadter uses?

If we have a square lattice in a homogenous magnetic field $\vec{B}=(0,0,B)$ and we use the Landau gauge for the magnetic potential $\vec{A}=(0,Bx,0)$; then, I have two questions: QUESTION $1$. Is the ...
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Band theory of Photonic crystals

I have a basic question about the band structure of photonic crystals. If I have a periodic potential, then Bloch-theory tells me that the bands yield the energy spectrum of the Hamilonian which is ...
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Why can the charge density be expressed as the Bloch wave integral in the Brillouin zone?

While watching Berry Phase, I saw a formula that says that in an insulating crystal the charge density can be written as: I don't understand the second term, I know the wave function in it is a Bloch ...

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