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11
votes
3answers
132 views

Why is there a band structure for strongly correlated systems?

The existence of band structure of a crystalline solid comes from the Bloch theorem, which relies on the independent-electron approximation. Why do people still talk about the band structure for a ...
10
votes
0answers
1k 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 ...
9
votes
2answers
472 views

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

(inspired by this question.) In every semiconductor that I can think of, the valence band maximum and conduction band minimum are at a high-symmetry point in the Brillouin Zone (BZ). Often the BZ ...
8
votes
5answers
33k 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 ...
8
votes
2answers
785 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
3k 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
1k 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 ...
8
votes
1answer
435 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
432 views

Understanding electronic band structure diagrams

Currently I'm trying to understand electronic band structures such as depicted below: And following questions were arisen. Why are there multiple lines in valence side and conduction side? Where ...
7
votes
2answers
825 views

Floquet and Bloch's theorems : connection?

It is often stated that Bloch's theorem and Floquet's theorem are equivalent, even the Bloch's theorem is often referred as Floquet-Bloch theorem. However, it seems quite confusing to me since the ...
7
votes
3answers
2k 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 $K$ ...
7
votes
1answer
299 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 ...
6
votes
3answers
509 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
2answers
399 views

Why is diamond transparent while graphite is not?

Diamond and graphite are both made of the same atom, carbon. Diamond has a tetrahedron structure while graphite has a flat hexagonal structure. Why is diamond transparent while graphite is not (at ...
5
votes
1answer
4k 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 ...
5
votes
3answers
1k views

How do charge carriers move thermal energy? (Peltier effect)

I am having hard time understanding how the charge carriers (electrons and holes) are able to move thermal energy. I am on a high school physics level, so I will probably have a hard time ...
5
votes
1answer
137 views

What is the physics behind “Bulk-edge correspondence”?

There is a frequently mentioned concept in the field of topological insulator called "bulk-edge correspondence" or "bulk-boundary correspondence", which basically gives the relationship between the ...
5
votes
1answer
681 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
2answers
149 views

For the transition metals, how does counting the number of up-spins and down-spins still give you a non-integer magnetic moment?

The transition metals like Fe, Co and Ni have magnetic moments of 2.2, 1.7 and 0.6 Bohr magnetons, respectively. The band theory says that you get this when you calculate the density-of-states of the ...
4
votes
1answer
4k 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 ...
4
votes
3answers
787 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 ...
4
votes
1answer
1k 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 ...
4
votes
1answer
1k 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
651 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
132 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
1answer
339 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 ...
4
votes
2answers
2k 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 ...
4
votes
2answers
970 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
212 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
503 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
3answers
3k views

Reverse bias P-N junction [duplicate]

I am not able to understand why the PN junction does not conduct when reverse biased. Can't electrons travel from the N side through the power supply to the P side where they can jump from one hole to ...
3
votes
1answer
104 views

Semiconductors and energy bands

The valence and conduction band of a semi-conductor are often drawn as here click. This plot has essentially two features and I would like to understand them. The peak and the valley of the two ...
3
votes
3answers
194 views

Do electrons in the conduction band have a quantum number?

Sorry if this is a silly question, but I haven't seen the concept anywhere and was wondering why. If valence electrons can have a quantum number, why can't conduction electrons? Is there something ...
3
votes
2answers
206 views

Why according to Hund's first rule all electron with same spin should occupy orbitals when partially filling?

I get that because of coulomb repulsion initially all the electrons will not occupy the same site but will single occupy the orbitals.But while doing so how do they know to keep their spins aligned ...
3
votes
3answers
533 views

What does $m^*>m_e$ imply? (the effective mass of electron is larger than its rest mass)

From what I understand, the concept of effective mass is just something people come up with to make electrons and holes obey the equation of motion $$ \vec{F}=m^* \vec{a} $$ without dealing with the ...
3
votes
1answer
106 views

Periodic momentum space in band structure

I often see pictures like this in physics, this one for Silicon band structure. (source, NB: it's the German page for Silicon). There you see the plot of the energy in terms of the momentum $k$. ...
3
votes
2answers
71 views

Nearly Free Electron Model and the Reduced Zone Scheme

When for example studying the vibrational modes of a one dimensional diatomic chain we find that the dispersion relation $\omega(k)$ is periodic in the one dimensional reciprocal lattice vector ...
3
votes
2answers
166 views

Are there measurable quantities which directly depends on the Fermi velocity?

The dispersion relation of electrons in, for example, graphene exhibits Dirac cones. The dispersion relation of a Dirac point at $\mathbf{k}=\mathbf{K}$ is linear in the momentum magnitude: $$E=\pm ...
3
votes
1answer
258 views

Hartree-Fock correction to $e$-$e$ interaction

The corrections to the energy per electron in a jellium model (uniform distribution of positive ion charge approximation to the regulated long range order ionic array) is given by (in units of Ry) ...
3
votes
2answers
1k views

What is the secondary electron cutoff in ultraviolet photoelectron spectroscopy?

While the fasted emitted electrons comes from the fermi level of the material in UPS measurement, where does the slowest, which is called secondary electron cut-off orginate from? I really can't ...
3
votes
1answer
34 views

Momentum operator in effective mass approximation

When we calculate the band structure of some solid then we often find that in the bottom of the conduction band the dispersion looks approximately quadratic with some new effective mass: $$E(k) = ...
3
votes
0answers
20 views

Obtaining a Positive Hall Coefficient for Electrons Near the Top of a Valence Band

Using a Drude model of charge carriers with a charge $q$ and a mass $m$ (which I allow to take either sign at this stage) in a sample with an applied electric field $\mathbf{E}$ and magnetic field ...
3
votes
0answers
76 views

What is the effective electron mass in a plasma?

Is there a way to calculate the effective electron mass in plasmas? Effective electron mass is usually defined as varying from the vacuum electron mass in solid state physics. However, momentum ...
3
votes
1answer
103 views

Can a strained diamond actually become conductive?

According to about.com, "The electrical resistivity of most diamonds is on the order of 1011 to 1018 Ω·m" (source) However, according to the diamond band diagram, it seems that under a certain ...
3
votes
1answer
239 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
237 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
4answers
152 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?
2
votes
1answer
45 views

at $T \approx 0 \, \text{K}$, will all energy levels within the electronic band structure be occupied up to a certain level?

I saw this from the script of my teacher that I don't understand what does it mean If we cool down a crystal to an absolute temperature of T ≈ 0K, all atoms of the crystal will exist at their ...
2
votes
1answer
159 views

Is Chern-number for free fermion system always limited by total band number, i.e. number of orbits with a unit cell?

If so, how to see that? Also I think it has been proven that the total Chern-number for free fermion system is 0? If you know how to prove it, please make some comment or hopefully a sketch of ...
2
votes
1answer
2k 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 ...