28 votes

What is it about the "conduction band" of a material that is distinct from the valence band?

A band is essentially a (near) continuous collection of momentum eigenstates. Within the band the electrons can be treated as free to a reasonable approximation, so their eigenstates are just plane ...
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24 votes
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Why are band maxima / minima often (always?) at high-symmetry points?

$\renewcommand{ket}[1]{|#1\rangle}$ The basic logical connection here is $$\text{symmetry} \rightarrow \text{degeneracy} \rightarrow \text{avoided crossing} \rightarrow \text{band gap} \, .$$ $\...
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22 votes
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Why is diamond transparent while graphite is not?

The answer lies in the band structure of the two materials. The band structure describes how the electrons in a solid are bound, and what other energy states are available to them. Very simply, the ...
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  • 116k
22 votes

Are room temperature superconductors theoretically possible, and through what mechanism?

Room-temperature superconductors are not forbidden by any known theory. However, discovery is difficult, while engineering is possible. One thing about superconductors is that they do not give off any ...
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  • 1,522
16 votes

What is it about the "conduction band" of a material that is distinct from the valence band?

No band is special. A partially full valence band does conduct, just like a partially full conduction band. On the other hand, a perfectly full band conducts just as well as a perfectly empty band: ...
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  • 3,159
16 votes
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Why do group II elements conduct?

Even when an isolated atom has a filled shell, the electron bands in a solid crystal may be partially filled. The reason is that bands that originate from different atomic orbitals may actually ...
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14 votes
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Notations for high symmetry points in the 1st Brillouin zone

For any crystal, the First Brillouin Zone is found using the Wigner-Seitz construction for the reciprocal lattice. The high-symmetry points are labeled by certain letters mainly as a convention--like ...
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12 votes

Are room temperature superconductors theoretically possible, and through what mechanism?

As mentioned here, metallic hydrogen may be a conventional superconductor up to about 290 K. This is then due to the low mass of the metal ions, this leads to a strong coupling of the electrons with ...
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  • 9,640
11 votes

What is an electron/hole pocket and what is the significance?

Fermi pockets (or Fermi surfaces) are contours of Fermi energy in the Brillouin zone. Depending on the effective mass $m^*$ of quasi-particles, the Fermi pockets can be divided into electron pockets (...
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10 votes

Why is there a band structure for strongly correlated systems?

The most truthful answer, to my mind, to this is simply "because it often works in practice." It is not obvious, a priori, that band structure should apply to any realistic solid. The ...
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10 votes
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What is a strongly correlated system (in condensed matter physics)?

(1) Your definition of strongly correlated system is correct "single-particle fails." We can still use ARPES to study strong correlated systems, we just do not see features that would be present in a ...
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10 votes
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Number of bands in 1D tight-binding model

The rule of thumb is that there are a number of bands equal to the "degrees of freedom" of the lattice. You can get additional degrees of freedom from having multiple species of atoms, multiple ...
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9 votes
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Band gaps: are they at the centre or at the edge of the Brillouin zone?

They are shown at the $\Gamma$ point in special diagrams called the reduced zone scheme in which a band will be shown folded back on itself. This way of showing the band structure is convenient for a ...
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What is it about the "conduction band" of a material that is distinct from the valence band?

An example of a doped semiconductor might give an intuitive picture of some aspects of this topic: Consider a material like Germanium. Atoms are structured in a lattice. All valance electrons are "...
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Is conduction band discrete or continuous?

A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in ...
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9 votes
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Can electrons have energies between valence and conduction bands?

This is similar to asking if an electron, in say a hydrogen atom, can occupy an energy level somewhere in between the $n=1$ and $n=2$ levels. In this instance, and in the context of your question, the ...
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  • 24.8k
8 votes

Quantization vs. continuous energy levels

The quantization of energy levels appears both in quantum and classical mechanics, and it is not a consequence of the Schrödinger equation. It is a consequence of confinement. In fact, anytime that a ...
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  • 3,425
8 votes
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Temperature Dependence of Conductivity of a Semiconductor

Kittel (at least my 5th edition) goes through this derivation. Refer to the diagram below and remember that in semiconductor physics the chemical potential $\mu$ is also the Fermi level $E_F$ below. ...
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8 votes

What does it mean if the Fermi level crosses into the valence band? How about into the conduction band?

The terms "conduction band" and "valence band" sort of lose their usefulness if you are not talking about a standard band insulator where you have a filled valence band and the ...
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7 votes
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Why do metals become insulators when oxidized?

Metals are good conductors of electricity because the outer (valence) electrons of the metal atoms are only loosely bound to the nucleus and form molecular orbitals known as the conduction band. ...
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7 votes
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Dispersion relation near a Dirac point

Is there a nice way to look at the dispersion relation near a Dirac point? It turns out there is. Namely, since Dirac points are equivalent to having a linear dispersion relation, $ E(k) \propto k $. ...
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7 votes
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What happens when we add free electrons to an insulator?

Set aside the battery part, and think about what you get when you e.g. inject electrons into a block of insulating plastic. It looks like this: That's a "beam tree", a.k.a. a "Lichtenberg figure". ...
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7 votes
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Proof of necessity of Band Inversion in Topological Insulators

As you specifically mention $\mathbb{Z}_2$ invariants in your comment, I will start my answer with the Fu-Kane $\mathbb{Z}_2$ invariant. In their original paper, they prove that the $\mathbb{Z}_2$ ...
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7 votes

Flat bands and localization in real space

The quoted statement is not precise. A better formulation might be From a band-theory point of view, flat bands lead to dispersionless evolution of wavefunctions. In most cases, they admit localized ...
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7 votes
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Filled Band cannot generate current

$\mathbf{v}_g(\mathbf{k})$ is the velocity of electron in state $\mathbf{k}$. The full current carried by all the electrons is obtained by integrating over all the filled states of the Brillouin zone: ...
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6 votes

Reverse bias P-N junction

Think about why the diode does conduct current when it is forward-biased. In that case, there is an electric field pointing from the P-type end to the N-type end. Negative electrons want to climb up ...
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6 votes

Floquet and Bloch's theorems : connection?

No worries about the order of the differential equation. You can always transform a second or higher order equation to a system of first order differential equations. The Bloch theorem is dealing ...
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6 votes

Quantization vs. continuous energy levels

Technically, both solids and gasses have quantized energy levels. The difference is that molecules of a gas interact with other molecules very weakly, so the energy levels observed in emission or ...
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  • 1,191
6 votes

Why are band maxima / minima often (always?) at high-symmetry points?

If there is only one band maximum in the BZ, this point is one of the high-symmetry points of the BZ. However, there can be cases where there are many points which are a band maximum and they are not ...
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