Questions tagged [electronic-band-theory]

Use this tag to ask about band-structure formation in solids, or about how electrons and holes behave inside them.

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Electron localization in crystal

I tried to use indetermination principle to explain why, electrons that are strongly bounded to the nucleus, are more localized. Unfortunately, the result that I've obtained says the exact opposite. ...
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About the graphene's Dirac points

I am studying Hasan & Kane's colloquim about topological insulators, and a question has emerged when I reahced the 4th page of this thesis. 1 Passages below the equation (3) show that near the ...
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How can the total momentum of a crystal be conserved?

In general, the total momentum of a system is conserved. Nevertheless, the momentum of a single electron or phonon is not conserved in a crystal. In fact, for an electron there are two types of ...
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Momentum conservation in phonon-photon scattering event

I am following a discussion from Kittel´s Introduction to Solid State Physics in the subchapter ‚phonon momentum‘: We have two different conservation laws of momentum in a crystal: Total momentum is ...
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What is the $E$-$k$ relation of electron in valence band?

What is the $E$-$k$ relation of electron in valence band? $E$-$k$ relation for electron in conduction band is known but how to calculate energy of electron in valence band?
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What's actually happening on the level of individual particles when an atom in a solid is vibrating?

For context, I'm trying to understand what happens to the kinetic energy of an electron in semiconductor after it absorbs a photon with more energy than the bandgap. My QM professor said it gets ...
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What happens to the kinetic energy an electron gains from absorbing a photon with more energy than the bandgap?

For context, I'm taking a course on quantum mechanics geared towards electrical engineering majors (so basically the standard curriculum, but with additional focus on EE applications, particularly in ...
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Is effective mass used in calculating kinetic energy of electron in semiconductor?

Is effective mass used in calculating kinetic energy of electron in semiconductor? I recall it was just used to take into account the internal forces so that expression of force fits well. But why $...
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Semiconductor Band Gap

I have a conceptual question. Say at room temperature, electron has thermal energy of the order of 25 milli eV. Consider Germanium having band gap of 0.7 eV, so the corresponding temperature will be ...
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Is Hartree-Fock (HF) a ground state theory?

To calculate the orbitals in Hartree-Fock (HF) theory we imply the variations principle, so we try to find the wavefunction which minimises the energy $\left<\psi|H|\psi\right>$. This ...
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Why does Hartree-Fock (HF) theory even work?

Let’s say we have $N$ electrons and we want to derive the Hartree-Fock (HF) equations. The first step would be to define a Slater determinant of $N$ electrons: $$\psi(x_1,x_2,… x_N) = \frac{1}{\sqrt{...
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Is current density independent of applied fields for Bloch electrons?

Following Ashcroft-Mermin chapter 12 the semiclassical dynamics is governed by $ \dot{\vec{r}} = \vec{v}_n(\vec{k}) = \frac{1}{\hbar}\frac{\partial \epsilon_n(\vec{k})}{\partial \vec{k}} $ and $ \hbar ...
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What is a 'satellite' in solid state physics?

During a course, my professor talked about satellites. He defined them as an excitation which results in an electron-hole pair, in a system of interacting electrons. So that the energy of the ...
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Topological Insulator [closed]

What effect on the Brillouin zone (torus) after applying the magnetic field? As in real space, pressure deforms the torus and up to a certain pressure, this remains invariant topologically. Similar to ...
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Why is the commensurate charge density wave for 1T-$\rm TaSe_2$ based on non-integer dimensions?

I have read several papers that have stated that the commensurate charge density wave (CDW) for 1T-$\rm TaSe_2$ comes from a $ \sqrt{13}a_0$ x $\sqrt{13}a_0$ periodic lattice distortion where $a_0$ ...
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$E$-$k$ diagram under an applied Electric Field

We know from solid-state physics, if an electric field is applied, the band bends in the band diagram. How does this change the $E$-$k$ diagram?
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Understanding effective mass of electron for different $\rm Si$ orientation (001, 111, 110)

I am somewhat familiar with the the constant energy surface of the conduction band picture for $\rm Si$ in the $k$-space (6 ellipsoids). I am also aware that the size of the ellipsoids measured along ...
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2D projection of constant energy contour in momentum space in 2DEG heterostructures or 2D layered materials

When reading about 2D layered materials or 2DEG (two dimensional electron gas) heterostructures , there often is a 2D projection of a constant energy contour onto the plane perpendicular to the ...
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Bending of vacuum level in semiconductor junctions

I am currently learning about semiconductor physics and have some problems understanding the band shifting which occurs at PN-junctions, heterojunctions or even metal-semiconductor junctions. In most ...
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Using Symmetry to Identify When Electron-Phonon Interaction Energy Corrections Are Zero

General question: Under what circumstances are terms involving the expectation value of products of fermionic/bosonic number operators zero? How can one use symmetry to determine when this will be the ...
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Why band inversion leads to non-zero Chern number?

From the formula of Berry curvature $$\Omega_n(k)=\nabla_k\times\langle u_n(k)|i\nabla_k|u_n(k)\rangle$$ and Chern number $$C=\frac{1}{2\pi}\int_{BZ}d^2k \ \Omega_{k_x,k_y}\,,$$ why $C=0$ for normal ...
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How to prove that the lattice potential can be separated into two components in diatomic lattice? [closed]

For a 1-D diatomic lattice with overall period $a$ and atoms $A$, $B$ placed at $\pm \frac{a}{4}(1-\delta)$, I am struggling to prove that $$ U_\frac{2\pi}{a} = \sin(\frac{\pi\delta}{2})(U^A_\frac{2\...
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Why is there no volume term in density of state 3D for harmonic potential like 3D box potential?

I was looking at the derivation for density of states for particle in 3D box potential and 3D harmonic potential. In the case of box potential, there is a volume term where as in the case of harmonic ...
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Why the band gap of >3 $\rm eV$ is considered large for insulators? [duplicate]

I know it sounds stupid but why the band gap of 1.1 $\rm eV$ for silicon is okay and why the band gap of 3 $\rm eV$ for insulators are too high. for silicon diodes and transistors the cut in voltage ...
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Can I use the difference between wave vectors to represent a $k$ path in reciprocal space?

Can I use the difference between wave vectors to represent a $k$ path in reciprocal space? For example, Z (0, 0, 0.5), A (0.5, 0.5, 0.5), M (0.5, 0.5, 0) are three high-symmetry points in the first ...
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Would an ideal, p-n based LED, ever stop producing light if it had a finite amount of doping?

I'm trying to understand how long would an LED last if there were no manufacturing/wear and tear imperfections in the product, just by exhaustion of the material that allows the transduction of ...
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Why do silicon photodiodes respond to a wavelength range of 190-1100nm?

Silicon photodiodes respond to a wavelength range of around 190-1100nm (source: wikipedia). I understand that photodiodes function by having a photon of sufficient energy create an electron-hole pair ...
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What is the single-electron concept?

In the paper I am reading, single electron concept, single-electron gap, single-electron properties, Single-electron tight-binding description kept coming up and I still don't understand what is this ...
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What is the difference between $σ$ and $π$ bond and $σ$ and $π$ bands?

In the paper I am reading, it says: "as in the case of the single layer, the π band is formed in bilayer graphene and the π band is half-filled if the sample is not doped." I know the σ ...
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How is the HOMO-LUMO gap measured?

def: HOMO = Highest Occupied Molecular Orbital LUMO = Lowest Unoccupied Molecular Orbital If the LUMO is unoccupied, how do we measure it? I can imagine that you can excite electrons in the HOMO but ...
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What is meant by "low-lying" electronic states?

In the context of electronic structure and spectroscopy, the term "low-lying electronic states" is quite common but it really isn't defined anywhere. All google search results lead to ...
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Does this video give a useful simplification of semiconductors?

Eugene Khutoryansky has a YouTube channel that is quite popular for its representations of physics concepts. This particular video discusses basic semiconductor theory in an easy to understand way, ...
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Band gap in insulator

I know that insulators have big band gap and electrons normally can't cross the gap unless they are excited by some certain photons. Is it possible to apply an extremely large electric field so that ...
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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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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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What are occupied states in a semiclassical context?

I've been reading this question and the answers it received, and I still have some unresolved questions. It is common to use the semiclassical approximation in describing charge carrier transport in ...
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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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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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How is a material heated by interband transitions?

If we excited the electrons in a material via interband transitions, how do we go from these to the material heating up? Is it due to relaxation of the electronic states back to their ground state? ...
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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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Energy band and applied voltage

What happens to the energy bands when a positive or a negative voltage is applied in a semiconductor ? For example, in a n-type material, a positive voltage makes the fermi level go up(I am not sure ...
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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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Why in creasing the energy on the following Hamiltonian, of an ensemble of Fermions (The Kitaev chain), closes the bulk gap?

On the previous Hamiltonian, it is mentioned that the term μ corresponds to the onsite energy. Which I understood as the energy of one section of the chain. Later is discussed that if μ is increased ...
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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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Tight-binding: aren't the electronic bands just the eigenvalues of the Hamiltonian?

In the tight-binding model we choose a set of atomic orbitals $\{\phi_1(\textbf{r}), ..., \phi_N(\textbf{r})\}$ and estimate a transfer matrix and hopping matrix $$ \begin{cases} S_{ij}(\textbf{k}) = \...
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Hole concentration distribution in MOSCAP

For a given p-type MOSCAP energy band diagram, I was asked to sketch the distribution of holes with respect to position. I understand why the hole concentration at the interface is $10^{10}/cm^3$ and ...
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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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Can the conduction band minimum of a semiconductor fall above the vacuum level?

Is it possible for the conduction band minimum (LUMO) of a semiconductor to be above the vacuum level? If so, what does this physically mean?
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