Questions tagged [electronic-band-theory]
The electronic-band-theory tag has no usage guidance.
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Why are 2N electrons allowed in an energy band?
In Solid State Physics, there are supposedly 2N electrons allowed in any energy band, with N being the number of atoms in the solid.
Firstly, I understand why there should be N allowed states if ...
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1answer
24 views
What is the binding energy between conduction band and valence band of metals and insulators?
As far as my understanding of solid state physics goes, I can't see a clear connection between binding energy and band gap. But our teacher asked us the question as an assignment but i really can't ...
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1answer
61 views
What does the concept of “free electron” mean in the context of band theory?
Often when conductivity is explained through band theory, the term "free" tends to crop up. As an example, I often come across descriptions of the valence band as a highest filled set of states ...
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1answer
32 views
Energy band gap
I am studying from the Aschroft & Mermim. In the chapter 8 they prove the Bloch theorem and introduce the concept of band.
they say that k is a quantum number that charactrize the eigenfunction ...
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2answers
40 views
Can amorphous solids have energy bands?
One can understand the formation of energy bands from the Kronig-Penny model which assumes a periodic potential. But I heard that even if the potential is aperiodic for example in amorphous substances ...
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1answer
33 views
Is the band theory valid for an electron with energy greater than the potential?
Consider Kroenig Penney model. Here there is a derivation that uses the following potential:
One of the assumption is that the energy of the electron is $E<U_0$. Under this assumption (and others) ...
2
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1answer
35 views
Why does the 2D hexagonal lattice have a different tight binding band structure than Graphene?
Here you can find band structures for various tight binding models. I was wondering, why the 2-D hexagonal lattice has a different band structure than Graphene, even though they have the same lattice.
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11 views
How to calculate conductivity / electron mobility from theory
Is there a way to make quantitative statements about the conductivity of materials with band theory?
If not I should still be able to get information about the conductivity from Green-Kubo relations ...
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1answer
50 views
How can I calculate the chemical potential and the effective masses in an intrinsic semiconductor?
I want to calculate the chemical potential and the effective masses of the germanium charge carriers considering that the relaxation time is the same for the two carriers: electrons and holes. ...
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0answers
22 views
How can I draw the energy bands for the first and second zones of Brillouin? Is it conductor or insulator?
I want to draw the energy ($E$) diagrams for a simple cubic cell of parameter $a$, where each atom provides two electrons for the almost free electron levels for planes [100], [110] and [111].
I ...
2
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2answers
70 views
Orbitals without overlaps in band structures of solids
We know every band in the band structure of solids is the result of overlaps of an orbital type. My question is that when there is not any overlap between a type of orbitals(which may be the lowerest ...
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73 views
Different Creation/Annihilation operators for neighbouring sites in Tight-binding model of Graphene
The treatments that I have seen of Graphene's Band structure assume an overlaying of two inequivalent lattices. However, can the reason for choosing different annihilation and creation operators (such ...
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11 views
Are there any ways to distinguish a certain bonding state in MO spectrum?
Assume we have a relatively small silicon cluster, say Si35H36, saturated with hydrogen atoms. And we can calculate the band structure of it through some ab initio packages like VASP.
Here follow my ...
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1answer
45 views
Is diamond able to conduct electricity given 5.5 eV of energy? How do we then identify insulators and semiconductors?
I have learnt that the band gap for diamond, an insulator, is $5.5\:\rm eV$. Does this mean that diamond is able to conduct electricity if we give it this immense amount of energy (let's assume we do ...
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3answers
98 views
Conduction and Valence band
What is the difference between a conduction and valence band ? How an electron will behave different in conduction and valence bands ? When an electron leaves an atom the atom becomes ion. Does it ...
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1answer
40 views
Can someone give a simple mathematical explanation of the tight binding method?
I'm trying to understand the tight binding method but I'm struggling with a lot of the mathematical formalism. A lot of the mathematical formalism I read jumps into explaining it a few too many steps ...
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0answers
29 views
What is it about metal elements that means their conduction and valence bands overlap, as opposed to non-metal elements where there is no overlap?
I can't see why metals have overlapping bands and a higher Fermi level compared to Non-metals where there is no overlap and the Fermi level is not in the conduction band.
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1answer
39 views
Mental contradiction: Valence electrons do not move at the non-zero wavevector?
I have a mental contradiction. Let's consider the following band structure with the Fermi energy somewhere inside the gap:
where $\Gamma$ point represents the zero value of the wavevector $|\vec{k}|$....
2
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2answers
63 views
What is the significance of the time $\hbar/E_F$ where $E_F$ is the Fermi energy?
For free electrons in a metal, the Fermi energy $E_F$ (defined as the highest filled energy level at $T=0$). It represents a characteristic energy scale of the system as well as the energy of the ...
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0answers
25 views
Rashba effect in 2DEG (how there is non zero electric field)
In the right column of page 20 in this paper, spins in few-electron quantum dots, the paper says "It is at first sight surprising that there
is a net spin-orbit interaction: since the state is bound
...
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0answers
20 views
The Hermicity of k.p Hamiltonian with operator ordering?
I am trying to use the k.p method to study quantum well band structure. One example Hamiltonian look like this [J. Appl. Phys., 116, 033709(2014)]
[]1
where
${{\hat k}_ \pm } = {{\hat k}_x} \pm i{{\...
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2answers
65 views
Is Fermi Level a property of the material?
I have gotten myself confused about the band structure explanation of semi-conductors vs insulators. The Wikipedia picture
and the explanation surrounding it seem to suggest that Fermi Level is a ...
5
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1answer
155 views
Is topological surface state always tangential to bulk bands?
Think of a topologically nontrivial $D$-dimensional system. Its bulk bands form a $D+1$-dimensional manifold ($+1$ from energy). Its surface/edge bands form a $D$-dimensional one. Is the latter always ...
3
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1answer
94 views
What happens when we add free electrons to an insulator?
I'm trying to understand why an insulator doesn't conduct electricity. If I understand correctly, the energies of electrons of an insulator are bound tightly to the nucleus, so there are no free ...
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1answer
36 views
Variational calculus and KKR method for band structure calculation
I’ve been studying the KKR method from the original Kohn and Kostoker’s paper (https://journals.aps.org/pr/abstract/10.1103/PhysRev.94.1111).
On the text, they use variational calculus for dealing ...
3
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0answers
75 views
free electron approximation verses tight binding approximation
What is the relation between electronic band structure that is calculated by using free electron approximation (FEA) and tight binding approximation (TBA)?
My understanding:
In FEA, it seems we ...
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1answer
35 views
Can the graphene's conductivity be explained using only orbitals?
I am trying to find a 'easier' or more 'intuitive' way to calculate the conductivity of graphene. I want do this by using atomic or molecular orbitals. Anyone have a clue about how this can be done? ...
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0answers
65 views
Fermi Dirac probability relative to electrons and holes
I'm having a hard time to understand the following sketch:
especially in case of the second diagramm. What does E against f(E) mean? How do I interpret this? The probability f(E) of an electron is ...
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1answer
38 views
band gap energy (discrete or continous?)
What does the band gap energy mean explicitly? Is it a single, discrete energy or is it a energy region? Sketches always show a "gap" between the conduction and the valence band so I assume there are ...
1
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1answer
67 views
Why is there a difference between Fermi levels in metals and metal-oxide semiconductors (MOS)?
Why are Fermi levels in metals lower than the Fermi level of $\text{p}$-substrates in metal-oxide semiconductors (MOS)? Specifically, why is there a difference of $qV$?
$\hspace{50px}$
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2answers
57 views
Energy of electrons?
Whats meant by energy of electrons in different orbits of atoms. Does this means that the electrons at higher evergy levels have more kinetic energy as compared to the electrons at lower energy level ...
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0answers
23 views
Why do we need to know “two-bands” Hall coefficient and magnetoresistance?
I know only partially filled bands result in current density, and I think there must be not only 2 partially filled bands, but "several" partially filled bands. For each partially filled band, its Ohm'...
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1answer
26 views
Acceptors with very high energy level in semiconductor
I have gallium arsenide (energy gap of 1.4 eV) doped with silicon in concentration of $10^{14} cm^{-3}$ and energy level very close to the conduction band so it's act like a donor. Now we put in also ...
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0answers
21 views
Band theory- Is the conducting band the last orbital with a gap between the two bands?
What I understand is in each atom there are conducting and valence bands
and the valence band, the minimum level for electrons (is the orbital before the last)
Is the conducting band the last ...
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0answers
50 views
Band structure and Density of states (DOS)
Can someone explain how these two plots are related?
How are the peaks in the right are associated with the left figure?
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0answers
29 views
Is band theory applicable only for valence electrons
Is band theory applicable only for the valence energy levels of a metal?
When metal atoms come together the valence electrons occupy a band of energy levels. But does the energy of the inner ...
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2answers
136 views
Fermi-Dirac function electron and hole concentration
I have a question regarding the Fermi-Dirac function. I would like to confirm that my basic understanding is correct.
Is any space under the curve in the CB and VB describe the probability of finding ...
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0answers
18 views
Obtaining low energy effective model of Bernal stacking bilayer graphene
I am now reading some articles about the electronic properties on Bernal stacking bilayer graphene. (https://arxiv.org/abs/1205.6953).
In the section II-C-1, the general procedure of obtaining the ...
0
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1answer
86 views
Pseudopotential in VASP
I am a beginner in learning VASP (Vienna Ab-initio Simulation Package) and quite interested in the PAW (projector augmented wave) method implemented in VASP. As far as I knew, PAW is an all-electron ...
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0answers
50 views
PT-symmetry in Energy Band of Crystals
According to this source, it is proved that, in absence of spin-orbit coupling, spatial inversion symmetry (as a part of point-group symmetry which operates as $\hat{S}\psi(\vec{r})=\psi(-\vec{r})$) ...
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0answers
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What's the transition from “metal” to “electron-degenerate matter” look like?
Question: Say that we had metallic water and compressed it until it qualitatively resembled the state of matter in a white dwarf: what would that transition look like?
Background (revised to be ...
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0answers
60 views
How do you calculate effective mass exactly?
I know about the equation m*/me=hbar^2[(d2E(K)/dK2)]^-1. You need to get the second derivative of the E-K diagram at the point of interest. For electron effective mass, that's the lowest point in the ...
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1answer
47 views
Conventional explanation of basic Semiconductor & Diode behavior unconvincing
I have seen this and this and a few other. Throughout the web and notes I find the explanation of the workings of a simple diode sort of unconvincing and I am depressed by the fact that I am not able ...
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1answer
48 views
The band gap in many-body theory
I would like some help in understanding the definition of the band gap in many-body theory. I have seen several books state that the fundamental band gap is given by
\begin{align*}
E_{\text{gap}} = \...
3
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1answer
414 views
How diffusion and drift current in a PN junction get equal?
Let's consider a PN junction which is at zero biased voltage. Once the junction is formed charges are diffused across the junction and form the depletion region and stops further diffusion. So no ...
3
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0answers
267 views
Reading Band structure plots
I know that there are similar questions already answered here on Physics StackExchange but the following things are still unclear to me:
Is it correct that an electron inside a crystal with a band ...
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0answers
79 views
Relation of carrier density to number of valence electrons in metals
In the classical Drude model, we find that the electrical conductivity of a metal is given by
$$\sigma = \frac{ne^2\tau}{m} $$
where $\tau$ is the relaxation time, $m$ is the electron mass and $n$ is ...
4
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1answer
440 views
Number of bands in 1D tight-binding model
I was reading about the one-dimensional tight-binding Hamiltonian (TBH) with one quantum state per atom $$H=E_0\sum\limits_{n}|n\rangle\langle n|-t\sum\limits_{n}\Big(|n\rangle\langle n+1|+|n+1\rangle\...
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1answer
47 views
How to see s, p, d, and other band in the band diagram? Is it possible?
I am reading this book, to understand magnetism in material.
It is stated there that the d-bands overlap the next higher s-band.
I am aware about Hund's rule.
How to see that in the band diagram? ...
4
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1answer
187 views
Dispersion relation near a Dirac point
I have very simple energy spectrum,
$$E_{\pm}(k_x,k_y)=\sqrt{2+2\cos(k_x)\cos(k_y)}.$$
The band gap closes at (for example) $k_x=0, k_y=\pi$. Both $E_+$ and $E_-$ are zero there. This is seen in the ...
