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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Reproduce band structure Kagome fermi-hubbard - Python

I am trying to reproduce figure 5c) of https://arxiv.org/pdf/2002.03116.pdf in Python. So I would like to plot the band structure of a Fermi-hubbard defined in a Kagome lattice. The eigenvalues are: $\...
relaxon's user avatar
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Density of States, Photoemission and Integrating the Number of States

I'm reading Fowler's theory on photoemission. I'm stuck on a part which Fowler helpfully identifies as "obvious". Fowler sets up the free electron model, suggesting that electrons need a ...
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What causes bands to shift in energy or become narrow?

This is the density of states for pure palladium in bulk : This is the density of states of palladium hydride : clearly the d bands are shifting and becoming narrow. The narrowing of bands is said ...
Ajaykrishnan R's user avatar
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Fermi-Dirac integrals [closed]

I accounted a problem when deriving the Fermi-Dirac integrals shown below Could someone point me out why the lower limit of integtal could subsitutite from $Ec$ to $0$? 20240410 edit I have derived ...
Jack Huang's user avatar
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Einsteins Coefficient of Absorption in solid state

What solid state parameter determines the probability of absorption (Einsteins coefficient B) in a material? Is it material dependent? I think, I cannot say bandgap. Because if I have a source having ...
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Is the Fermi level is same for the all solids?

If the solids at T=0k , the topmost energy level occupied by electrons in valence band is called Fermi level. Is this Fermi level is constant for all the materials? It is shown as same for metal, ...
Rajesh R's user avatar
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Confusion about the LCAO or tight binding model (nearest neighbors)

I'm using the book "Atomic and Electronic Structure of Solids" by Kaxiras. In chapter 4, the author introduces the tight binding or LCAO model for calculating electronic band structures. He ...
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What happens after bulk gold absorbs a photon with its energy at the band gap or higher (wavelength < 500 nm)?

As is explained in the answers of this question: Why are most metals gray/silver? nicely, the responsible transition occurs between the 5d orbital and the 6s orbital, which is relativistically shrunk ...
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Why is the band diagram of metals similar to that of an empty lattice?

The electrons at the bottom of a band diagram correspond to some of the most tightly bound electrons. Why is it the case that the bottom of the band structure of sodium, for instance, can be well ...
Bruno Nowak's user avatar
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How to determine the effective mass for multivariate dispersion relation? [duplicate]

Consider the 1D dispersion obtained by the tight-binding method: $ E(k)=\epsilon_0-t\cos(ka) $ $\epsilon_0$ is the on-site energy and $t$ is the hopping energy. To find the effective mass, you can ...
Anthony K.'s user avatar
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Electron bands in solids and delocalized electrons

Most introductory textbooks introduce electron bands when discussing metal properties which gives the impression that electron bands are strictly affiliated with delocalized electrons. However, bands ...
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Valence band in silicon (semiconductors)

I recently learnt that in a solid lattice there are many energy levels which are so continuous that they look like bands... In silicon' valence band,there are those millions of 3p energy levels with 2 ...
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Can topologically non-trivial edge states exist without an energy gap?

I am relatively new to the field of topological materials, and I came across a paper that claims that they found topologically non-trivial states in a material. Basically, the authors found a type-I ...
Mikhail Petrov's user avatar
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Matrix representation of Slater-Koster parameters

I'm coding a program to calculate electronic bandstructures using the Slater-Koster formalism (I am aware that such programs exist already- this is a pedagogical exercise). I notice that the $p-p$ ...
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For intrinsic semiconductors, is the gap Energy equals $E_c-E_v$ or $E_c+E_v$?

So I have a problem with the intrinsic Fermi Level because by definition it is in the middle of the gap energy, and knowing that Eg=(Ec-Ev), we should have Ei=(Ec-Ev)/2. But when we follow the ...
anass bakour's user avatar
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Can a DC voltage excite a pure semiconductor (or insulator) from the valence band to the conduction band?

I have a question I am sticking around and can't find a satisfying answer. Say I have an intrinsic semidonductor at zero Kelvin (no electrons in conduction band). I apply a DC voltage across it. Can ...
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Determining Fermi Energy for a specific $E(k)$ [closed]

I am currently taking an introductory course on solid state physics. One of the problems I came by while studying asks the following: Suppose we have a 1 dimensional solid of length L, with N ...
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Periodic Zone Scheme - Bloch Theorem in Lattices

I am quite confused about the different representations of the dispersion relation in a lattice. This image makes a lot of sense to me, since it only represents one dispersion curve and transforms it ...
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What do we actually mean by carrier lifetime in perovskite materials and where do charge carrier reside during that time?

During time-resolved photoluminescence studies in perovskite materials, one sometimes says that it has a microsecond carrier lifetime. What do we actually mean by that? Where does the excited electron ...
Balpartap Singh's user avatar
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Bloch functions and covalent bonds in some semiconductors

In a Group IV semiconductor (like Si, Ge), one atom makes 4 covalent bonds with its neighboring atoms. They create in this way the so-called a tetrahedral bond (that of the diamond structure). Each 2 ...
Anky Physics's user avatar
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References on obtaining experimental observables from band structure

I've recently been watching this lecture series in Condensed Matter physics. We have covered second quantization, used it to obtain the tight-binding model and then studied the band structure of ...
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One-dimensional tight-binding model with two different hoppings in the limit the hoppings are equal

I've recently been watching this lecture series on Condensed Matter. The part I'm currently on covers band theory for the tight-binding model in a few different scenarios. We covered two different ...
Níckolas Alves's user avatar
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What is the effect of spin-orbit interaction to the band structure?

I have a question regarding the spin-orbit interaction in zinc blend materials. As far as I understood, the split-off valence band (VB) forms as a result of this interaction, and it is a shift in ...
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How to determine the open circuit voltage of solar cells?

I am reading this paper which is about dye sensitized solar cell, but I do not understand its statement about the open circuit voltage of the cell (page 2242): In page 2242, the paper says that: The ...
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Electron dynamics in a periodic potential: Why wavepackets? Why $\vec{v}=(1/\hbar)\nabla_{\vec{k}}E_n$ is its group velocity?

Electrons in a periodic potential, $V(\vec{ r})$, satisfying $V(\vec{r}+\vec{R}) = V(\vec{ r})$, are described by Bloch states $$\psi_{n,\vec{k}}(\vec{r})=e^{i\vec{k}\cdot\vec{r}}u_{n,\vec{k}}(\vec{r}...
Solidification's user avatar
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If an atom loses electron, it becomes a cation; it does not form a hole. However, when electron is lost from a bond, it forms a hole and not a cation

If an atom loses an electron, it becomes a cation, and when an electron is lost from a bond, it forms a hole. This is what the professor told the class, but I am not able to find the reason for that ...
Logan's user avatar
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Band control metal to insulator transition (BC-MIT)

This is a common diagram seen in describing the metal to insulator transition. I am doing an experiment that involves the Bandwidth control MIT. I think. In other words, I'm changing the temperature ...
Lauren.0's user avatar
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Where can I read about Valleytronics?

Where can I read about Valleytronics? Are there any good books or review papers on this topic? And which are the most influential papers? The question was also posted at the Matter Modeling site.
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Meaning of the momentum vectors $\mathbf{k}$ in electronic band structure

In solid-state physics, I struggle to understand momentum vectors $\mathbf{k}$ in reciprocal space. We usually draw a picture of a Brillouin zone as follows (hexagonal in this case): And we can then ...
Gallifreden's user avatar
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Discretising Hexgonal Brillouin Zone

I am looking at a system at which I have a 2D Hexagonal Brillouin Zone (BZ). The aim is to take the following type of procedure: $$ \frac{A}{(2\pi)^2}\int_{BZ} F(\vec{k}) d\vec{k} \hspace{5pt} \...
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Time reversal operator on conduction band edge function

The bottom of the conduction band of Zinc Blende structure with grand representation $T_{d}$ symmetry group have a 2-dimensional representation at $k=0$ also known as the center of the Brillouin zone ...
EL.K. MORAD's user avatar
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What determines the energy spacing of individual orbitals within an energy band in a material?

Within a material, electrons exist within energy bands, often referred to as the "conduction" band and the "valence" band (and I imagine there can be other named bands as well). I ...
Schoppe's user avatar
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$p$-like or $s$-like bands

What do people mean by $p$-like or $s$-like band structures? I know that d- or f-type electrons are typically more localized, while p and s-type electrons are typically more delocalized, but how would ...
Chan's user avatar
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Polaron vs Electron energy level

i just started my study in organic semiconductor. I realized to increase conductivity, polarons are formed in the polymer backbone. From what i read due to localised energy state level by polaron that ...
taqiuddin yusri's user avatar
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Scaling relation of potential energy per particle of Rashba Spin Orbit Coupled (SOC) 2D electron gas for short and long range interactions

I am trying to prove the scaling relations of potential energy per particle($V(\vec{r}) = \frac{V_0}{|\vec{r}|^\alpha}$) of Rashba Spin Orbit Coupled (SOC) 2D electron gas in uniform liquid phase for ...
aj_01100110's user avatar
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Question about sign convention in electron-hole crystal momentum

I was trying to understand a toy model Raman scattering diagram from a paper on pressure tuned moire phonons, when I realized the standard electron hole pair creation diagram confuses me. By ...
pogmaster's user avatar
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Where is the kinetic energy functional error in the exchange-correlation functional of DFT?

The Kohn-Sham DFT energy functional is: $$E[\rho]=T^S[{\varphi_i}]+J[\rho]+M[\rho]+E^{xc}[\rho]$$ with the kinetic energy functional of non-interacting electrons $T^S$, the Hartree functional $J$, the ...
Guiste's user avatar
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How to conceptually understand bands in a solid?

I am having some trouble making the jump from single electrons to solids. In David Tong's notes, I have worked through the tight binding model section. Here, we solve for the energy levels that result ...
Relativisticcucumber's user avatar
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Given a solid, predict the number of filled electronic bands

Suppose I have ZnS that's described via an fcc lattice with basis [$\frac{1}{4}, \frac{1}{4},\frac{1}{4}$], therefore we have 4 Zn and 4 S per unit cell. Zn has 2 valence electrons and S has 6 valence ...
CoolerThanACooler's user avatar
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Does the total Zak phase always sum to zero?

In 2D, the sum of the Chern numbers over all bands is zero. However, this result relies on the ability to define a Berry curvature, which is only possible in $d \geq 2$ dimensions. In 1D it is ...
TAMOQO's user avatar
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Bloch's wavefuction of solid state phyiscs

The Bloch's wavefunction is written in the form: $$\psi_{\mathbf{k}}(\mathbf{r}) = e^{i\mathbf{k⋅r}}u_{\mathbf{k}}(\mathbf{r})$$ where k is the lattice momentum and $u_\mathbf{k}(\mathbf{r})$ is some ...
Anky Physics's user avatar
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Dispersion Relation for one dimensional monoatomic lattice in Kronig-Penny model and in Tight-Binding Approximation model

In the tight binding approximation model, we have the dispersion relation for a one-dimensional atomic lattice given as: $$E(k) = E_0 - \alpha - 2\beta \cos(ka)$$ Here, $\alpha$ and $\beta$ are ...
Dinesh Katoch's user avatar
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Help understanding the formation of band gap

I need some help understanding how the energy band gap is formed. Here is my understanding so far: Starting on the farthest right (largest interatomic spacing), the Si atoms are separate and thus ...
fordanjen's user avatar
2 votes
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Confusion about linear combination of atomic orbitals (LCAO)

In an YouTube video, that I used some information from it to work out my homework, Link: https://youtu.be/5vOvjeTRcqM?si=NzIcx_9QTNQ9Nhff the linear combination of atomic orbitals (LCAO) was discussed ...
Anky Physics's user avatar
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Orthogonality in the Tight-binding model

In the linear combination of atomic orbitals and the Tight-binding model we write the wave functions for some k as a linear combination of Bloch states like this $$ \Psi_n(\textbf{r}, \textbf{k}) = \...
Anky Physics's user avatar
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Band structure diagrams

In band structure diagrams, usually we show the dispersion relation between energy $E$ and the wave vector $\textbf{k}$. Consider the band structure of $\alpha$-Polonium. Shown in the graph below. ...
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Question about k.p Method

I am reading David Miller's quantum mechanics, and I do not understand the derivation for k.p method: We are particularly interested in the behavior of semiconductors near to maxima and minima. ...
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What happens to the zeroth Landau level of monolayer graphene with broken $A$-$B$ sublattice symmetry?

The (non-interacting) Hamiltonian of an electron in monolayer graphene near the $K$ point in the Brillouin Zone can be approximated as $H = \begin{bmatrix} 0 & v(p_x-i p_y)\\ v(p_x+i p_y) & 0 ...
Archisman Panigrahi's user avatar
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Why do physicists primarily study TMDCs when researching 2D materials, and not focus as much on many other 2D materials? [closed]

Why do physicists primarily study transition metal dichalcogenide (TMDC) monolayers when researching 2D materials, and not focus as much on many other 2D materials? Other 2D materials also have ...
IDs Just's user avatar
2 votes
1 answer
68 views

2-body Umklapp scattering in graphene

It is claimed that the Umklapp scattering is forbidden in two-body collision in graphene due to the crystal symmetry in this paper . I am having a hard time to see why this is the case... why wouldn't ...
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