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35 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 ...
John Rennie's user avatar
23 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 ...
Dr Xorile's user avatar
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19 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: ...
Nanite's user avatar
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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 ...
Buzz's user avatar
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15 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 ...
compmatsci's user avatar
13 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 ...
Gilbert's user avatar
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12 votes
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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 "...
Steeven's user avatar
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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 ...
Count Iblis's user avatar
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11 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 ...
James Rowland's user avatar
10 votes

Confusion About Energy Bands

No, they don't. The allowed energies for a quantum mechanical system comprise the spectrum $\sigma(H)$ of the system's Hamiltonian operator $H$. This spectrum may consist of discrete points as in ...
J. Murray's user avatar
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10 votes

Why do silicon photodiodes respond to a wavelength range of 190-1100nm?

It's somebody's practical limit. There's usually some sort of thin "dead layer" on the diode surface. It's close to perfectly transparent at long wavelengths, but as you move into the UV, it ...
John Doty's user avatar
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9 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 $. ...
AlQuemist's user avatar
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9 votes

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 ...
anna v's user avatar
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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 ...
joseph h's user avatar
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9 votes
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Why does Hartree-Fock (HF) theory even work?

I think the confusion here is about the number of orbitals vs. the number of electrons in the Slater determinant. In the first equation the indices of $x_i$ enumerate the electrons, but the indices of ...
Roger V.'s user avatar
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8 votes

What do we physically mean by smearing in condensed matter?

The smearing in density functional theory codes means that you occupy the states of the Kohn-Sham system according to a smooth function, e.g., the Fermi distribution. It is introduced to avoid ...
Gregor Michalicek's user avatar
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. ...
CGS's user avatar
  • 2,488
8 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 ...
Nikodem's user avatar
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8 votes
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General Question(s) on Bloch's Theorem

Question 1 The functions $ \newcommand{\bfr}{\mathbf{r}} \newcommand{\bfR}{\mathbf{R}} \newcommand{\bfk}{\mathbf{k}} \newcommand{\bfK}{\mathbf{K}} u_{n,\bfk} $ are solutions to the third equation in ...
Chiral Anomaly's user avatar
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". ...
Bob Jacobsen's user avatar
  • 14.5k
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 $\mathbb{Z}_2$ ...
G.Lang's user avatar
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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: ...
Roger V.'s user avatar
  • 58.9k
7 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 ...
pmal's user avatar
  • 942
7 votes
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One-dimensional tight-binding model with two different hoppings in the limit the hoppings are equal

Here's a way in which we can make sense of the limits in a physical situation in which the limit $t_1\to t_2$ should yield the first Hamiltonian. We could think of the atomic species as being the ...
march's user avatar
  • 7,714
6 votes

What is the physics behind "Bulk-edge correspondence"?

I take your question to mean "topological insulators" in the larger sense of all symmetry classes and all dimensions (which includes the quantum Hall effect case). In this case, referring only to ...
PPR's user avatar
  • 2,004
6 votes

Why is there a band gap in semiconductors but no band gap in conductors?

If you just take the empty bandstructure, you will see that any periodic arrangement of atoms (conductors, semiconductors, insulators) features a set of allowed bands and forbidden regions, so called ...
engineer's user avatar
  • 2,305
6 votes

How does a work function difference cause band bending in equilibrium in Metal-Oxide-Semiconductor (MOS)?

The work function is the energy necessary to move an electron from the Fermi level to the vacuum level. When you bring two materials in contact, here the metal and the semiconductor, thermodynamic ...
freecharly's user avatar
  • 16.1k
6 votes
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Is topological surface state always tangential to bulk bands?

Since the velocity $v_\parallel$ parallel to the surface is given by the derivative $v_\parallel = dE/dp_\parallel$, with $p_\parallel$ the parallel momentum component, the velocity would vary ...
Carlo Beenakker's user avatar
6 votes

Flattened band in band structure

The emergence of a flat band, i.e. a band with low dispersion, can be understood in terms of a tight binding picture. Bringing a set of atoms together, the initially discrete energy levels of the ...
v-joe's user avatar
  • 581

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