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8
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2answers
725 views

Modern and complete references for the $k\cdot p$ method?

I've recently started studying the $k\cdot p$ method for describing electronic bandstructures near the centre of the Brillouin zone and I've been finding it hard to find any pedagogical references on ...
8
votes
1answer
1k views

Why do electrons in graphene behave as Dirac fermions near the Dirac points?

I've been learning about graphene, and I recently calculated the band structure for it using a nearest-neighbor tight-binding model for the $\pi$ electrons: $$\varepsilon(\vec k)=\pm t\sqrt{3+2 \cos ...
8
votes
1answer
302 views

Intuition on topologically nontrivial 2D-band structures?

I want to get more intuition on topologically nontrivial band structures. There's this popular 2D two-band model for a topological insulator where $H=\sum_{k}h(\boldsymbol{k})$ (see Qi, Hughes, and ...
7
votes
1answer
253 views

What is the simplest possible topological Bloch function?

Kohmoto (1985) pointed out in Topological Invariant and the Quantization of the Hall Conductance how TKNN's calcuation of Hall conducance is related to topology, in which topologically nontriviality ...
7
votes
0answers
605 views

Where does the Berry phase of $\pi$ come from in a topological insulator?

The Berry connection and the Berry phase should be related. Now for a topological insulator (TI) (or to be more precise, for a quantum spin hall state, but I think the Chern parities are calculated in ...
6
votes
5answers
14k views

What's the difference between Fermi Energy and Fermi Level?

I'm a bit confused about the difference between these two concepts. According to Wikipedia the Fermi energy and Fermi level are closely related concepts. From my understanding, the Fermi energy is the ...
6
votes
1answer
499 views

Counterexamples to the bulk-boundary correspondence (topological insulators)

In the literature on topological insulators and superconductors the 'bulk-boundary correspondence' features quite heavily. One version of this conjecture says roughly: "At an interface between two ...
6
votes
2answers
904 views

A question on the existence of Dirac points in graphene?

As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2$\times$2 Hermitian matrix $H(k_x,k_y)$ has two degenerate points $K$ ...
6
votes
3answers
248 views

Are electronic wavefunctions in band gap insulators localized? is a single-particle picture sufficient in this case?

I am having trouble understanding the physics of band gap insulators. Usually in undergrad solid state physics one looks at non-interacting electrons in a periodic potential, with no disorder. Then, ...
5
votes
1answer
214 views

A (smart) way to map out the Brillouin zone of a 2-D material

I am currently writing a tight-binding calculation model for various 2-D cells as part of a homework assignment. Whilst solving the problem set was quite easy I struggle at a smart way to plot the ...
4
votes
1answer
1k views

Transparency of solids using bandgaps and relation to conduction and valence bands

I think I understand how a solid can appear transparent as long as the energy of the photons travelling through it are not absorbed in the material's bandgap. But how does this band gap relate to ...
4
votes
1answer
706 views

Can surface dipoles/charges change the work function of a metal?

As typically drawn in simplified band diagrams (see picture below), the metal Fermi Level is shown as the top of the conduction band, with the entire band filled. In many situations, including ...
4
votes
3answers
55 views

How does temperature affect photovoltaics (PV) efficiency?

I know that photovoltaic panels are more efficient at lower temperatures: As the temperature increases, the output voltage decreases. I am looking for an explanation of the mechanism behind this ...
4
votes
1answer
68 views

Electron degeneracy pressure

Why is it that in stars undergoing gravitational collapse electron degeneracy kicks in? Why couldn't the electrons form energy bands like in semiconductors?
4
votes
2answers
673 views

Need help understanding Semiconductor physics

I am trying to read Kittel for a project, and he mentions the properties on silicon and germanium so briefly, that I don't understand it at all. He talks about p states, and I don't really know what ...
4
votes
1answer
160 views

Is it possible to excite a semiconductor @ k=0?

Let us assume a direct semiconductor with parabolic band structure around the $\Gamma$ point (which is not bad for most semiconductors) in momentum ($k$) space. Now we excite it with light: I ...
4
votes
2answers
222 views

Why are there direct bandgaps?

This Question has been bugging me for sometime. Some semiconductors have direct bandgaps and indirect bandgaps. So what causes a direct bandgap to occur? The physics behind ,why there are direct ...
3
votes
2answers
542 views

How does Bloch's theorem generalize to a finite sized crystal?

I would be fine with a one dimensional lattice for the purpose of answering this question. I am trying to figure out what more general theorem (if any) gives Bloch's theorem as the number of unit ...
3
votes
1answer
201 views

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

What is an electron/hole pocket and what is the significance? I'm trying to get my head around this. I've read what Ashcroft and Mermin have to say on the subject, but it's a little convoluted. They ...
3
votes
1answer
410 views

Dopant concentration and changes in band gap energy

Thanks to this lovely website, I was able to pop out reasonable values for my band gap energies from a translucent material. As expected, I found a decrease in band gap energy due to my treatments. ...
3
votes
1answer
117 views

In a positively biased PN junction, where do the injection carriers come from?

I am not quite understand i-v character of PN-junction diode. Here is the model in textbook. The PN junction diode can be divided into three regions. They are One depletion region near the PN ...
3
votes
1answer
193 views

Confused about charge seperation in solar cells

I'm a bit confused about how solar cells work. My understanding is that there is a p-n junction. A photon is absorbed which creates an electron-hole pair, and the idea is to separate the electron ...
3
votes
2answers
206 views

Bloch oscillations - Scattering to other bands

In the free electron approximation, a Bloch state $|k\rangle$ is the linear superposition of free plane wave states $\sum_G C_G(k) |k+G\rangle$, where $G$ are the conjugate lattice. Since the ...
2
votes
1answer
166 views

Fermi level and conductivity

Can someone in a simple way explain me what the Fermi level is and what does it have to do with conductivity. My teacher said that Cu conducts electric current better than Al because of something in ...
2
votes
1answer
765 views

Valence band and conduction band, trying to get a clear picture!

I am trying to get a clear picture of the valence band, conduction band, and the band gap. Now I've been researching it for a little while now and understand most of what's going on. I'm still a ...
2
votes
1answer
174 views

Connecting Fermi levels and band diagrams to potential diagrams?

I'm trying to make sense of how you can find the potential diagram given the band diagrams of a few adjacent materials. As a simple example, in semiconducting heterostructures, if you have sandwich ...
2
votes
1answer
186 views

Does anyone know the difference and relation between $k\cdot p$ method and tight binding (TB) method?

Among the methods of calculating energy bands for crystals, first-principles method is the most accurate. Besides first principles, two commonly used modeling methods are the $k\cdot p$ method and ...
2
votes
1answer
1k views

What does the Fermi Energy really signify in a Semiconductor?

In understanding the behavior of semiconductors, I'm coming across a description of the Fermi Energy here and at Wikipedia's page (Fermi Energy, Fermi Level). If I understand correctly, the Fermi ...
2
votes
1answer
475 views

Energy band diagram of a system of Silicon Quantum dots

Suppose that we have a system of Silicon nanoparticles embedded in ZnO dielectric matrix. i'm thinking about how to construct the energy band structure of this system , suppose that we already have ...
2
votes
1answer
116 views

Effective mass of a particle

I was reading about concept of effective mass on Wikipedia and came across the line that effective mass of a particle can be negative and even zero. How is this possible?
2
votes
2answers
454 views

How to interpret band structures

I'm currently taking a Solid State Physics class, and is currently reading about the quantum mechanical description of solids. I then came across the following figure: It's supposed to be the band ...
2
votes
0answers
17 views

How to check the ohmic contact to the film?

I have a thin semiconductor film deposited on an isolating substrate. I would like to check different metals to find out do they form the ohmic contact or Schottky barrier. What is the best way to do ...
2
votes
0answers
105 views

Derivation of existence of energy band gap in semiconductor (solid State)

I am looking for both a mathematical and a physical reason for energy band gap in metals. For Physical reason, I was told that at each reciprocal lattice, you could have Bragg scattering, that would ...
2
votes
0answers
187 views

Topological band theory [closed]

Why topological insulators were discovered so late? While the band theory was known long time ago! I mean why the topological properties of electronic bands were not noticed in the past?
2
votes
0answers
108 views

Why does silicon have an indirect gap?

Is there an intuitive explanation as to why silicon has an indirect gap? I have heard that this can explained using pseudopotentials.
1
vote
1answer
223 views

Semiconductors and localization of the electrons

When looking at the band diagram of a semi-conductor, direct conclusion of the invariance under discrete translations, for a filled state with an electron, one does know precisely it's momentum, so my ...
1
vote
4answers
86 views

The conduction electrons in metals is a thermal phenomenon?

When applying an external electric field in a metal at absolute zero, there is electrical current? There must be thermal fluctuations in the electron's band to be occurs current?
1
vote
1answer
179 views

Band gaps: are they at the centre or at the edge of the Brillouin zone?

Reading about electronic band structures, I came across the following: Band gaps open at the edges of the Brillouin zone (BZ), since that is where the Bragg scattering occurs. I am slightly ...
1
vote
1answer
216 views

DFT for bandstructure

Density Functional Theory (DFT) is not appropriate in predicting the band gap of the materials. However, which functional gives close value to the experimentally observed band gap of semiconductors? ...
1
vote
1answer
72 views

Can excitons be understood in terms of classical quantum physics?

From what I understand, an exciton is an electron-hole pair in a semiconductor that exists in a bound state (through the electrostatic potential). I have seen it stated that this pair behaves in a way ...
1
vote
1answer
3k views

Effective Mass and Fermi Velocity of Electrons in Graphene:

In graphene, we have (in the low energy limit) the linear energy-momentum dispersion relation: $E=\hbar v_{\rm{F}}|k|$. This expression arises from a tight-binding model, in fact $E =\frac{3\hbar ...
1
vote
1answer
335 views

Band Structure and Carrier Recombination/Generation

So i've been a bit confused, looking at PN junction, semiconductors and the like (trying to nail down how exactly semiconductors work, transistors and such). I've read the wiki on band structure ...
1
vote
1answer
8 views

Indirect band gap and additional momentum?

For indirect band gaps, an electron needs both energy and momentum in order to be excited from the conduction band. I am not sure I understand the momentum requirement. What does it mean physically? ...
1
vote
1answer
159 views

How bandgap engineering works?

Currently i am reading about bandgap engineering in zinc oxide. I read that using external dopents likes magnesium or cadmium we can increase or decrease bandgap of zinc oxide,thus giving unique ...
1
vote
1answer
2k views

Difference between energy gaps of metal and semiconductor

I have a little question I hope someone could answer. I'm reading some Solid State Physics and I have come across energy bands and energy gaps. As far as I understand the energy band is where the ...
1
vote
1answer
763 views

What is band filling effect?

Could anyone tell me what is band filling effect? I have search Physics.stackexchange and Google, but didn't find any useful information. I'll appreciate it if anyone can tell me the physical image of ...
1
vote
1answer
618 views

What is the reasoning behind hole carriers being able to carry heat?

In the Peltier effect, we consider charge carriers being able to carry heat. As for electrons or ions, this attitude makes sense, since external electric potential drives particles with mass in a ...
1
vote
1answer
32 views

Effective masses for different direction

Assume we have an indirect semiconductor where the effective mass becomes anisotropic in different directions. Usually, one talks about a mass in parallel and perpendicular direction referring to ...
1
vote
0answers
18 views

How can we determine the inbuilt barrierpotential and electric feld for a given band diagram?

Suppose I have got two p type silicon materials of different concentrations (the difference in thier concentrations is small but considerable enough that their fermi levels differ by noticeable ...
1
vote
1answer
64 views

Sold-State Band Structure - connection between Fermi Energy, Fermi Level and Work Fuction

I've been struggling with the concepts of these three terms - Fermi Energy, Fermi Level and work fuction. Now, I was given these definitions (in the context of semi-conductors): Fermi Level is the ...