# Tag Info

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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 waves. The symmetry means that for every eigenstate there is another with an equal and opposite momentum. So if we populate every momentum eigenstate the net ...

15

If you consider a typical metal the highest energy band (i.e. the conduction band) is partially filled. The conduction band is effectively continuous, so thermal energy can excite electrons within this band leaving holes lower in the band. At absolute zero there is no thermal energy, so electrons fill the band starting from the bottom and there is a sharp ...

12

Any good book in Semiconductor Physics will have a description of the k.p method. Try Fundamentals of Semiconductor Physics by Peter Yu and Manuel Cardona. Another reference for Kane Model and EFA are chapters 2 and 3 of "Wave Mechanics Applied to Semiconductor Heterostructures" by Gerald Bastard. If you want a more mathematically/group theory oriented ...

12

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: No conduction at all. Now, nobody is surprised when you say an empty band can't conduct, but at first it seems surprising that a full band is the same way. ...

9

In calculating the electron dispersion you probably obtained the diagonalized Hamiltonian in the momentum space $$H=\sum_\mathbf{k}\left[c^{\dagger}_{\mathbf{k}A},c^{\dagger}_{\mathbf{k}B}\right]\left[\begin{array}{cc}0 & \Delta(\mathbf{k})\\ \Delta^{\dagger}(\mathbf{k}) &0\end{array}\right]\left[\begin{array}{c}c_{\mathbf{k}A} \\ c_{\mathbf{k}B}\... 8 Yes, your interpretation heuristically makes sense. As you may already know, as a consequence of Heisenberg's uncertainty principle, that an electron has a wave and particle nature. When you think of the wave nature of single particle states you are talking about Bloch states. When you're thinking about the particle nature you are talking about Wannier ... 8 It depends on who you ask. If you ask someone with solid-state physics background, they will probably answer along the lines of Colin McFaul or John Rennie: The fermi level is the same as chemical potential (or maybe one should say "electrochemical potential"), i.e. the energy at which a state has 50% chance of being occupied, while the fermi energy is the ... 7 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 band gap for transparent diamonds is very wide (see this link): Normally, diamond is not a conductor: all the electrons live in the "valence band", and you ... 6 There is no proof of bulk-boundary correspondence for topological phases in general. In fact, topological phases like toric code model does not have gapless excitations on the boundary. For non-interacting fermion systems protected by internal symmetries (as in the "periodic table" classification), bulk-boundary correspondence holds. For non-interacting ... 6 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 Coulomb interaction is typically of the order of the Fermi energy. Nonetheless, thanks to the magic of Fermi liquid theory, this strong interaction somehow only results in ... 6 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. Electrons can move more or less freely through the conduction band and so metals conduct electricity generally well. When a metal is chemically oxidised its outer ... 5 The Fermi energy is as you describe: it is the highest occupied level at absolute zero. The Fermi level is the chemical potential. It is the energy level with 50% chance of being occupied at finite temperature T. The Fermi energy does not depend on temperature; the Fermi level does depend on temperature. 5 Take the solutions of the potential problem of an atom and look at the energy levels. Between the n=1 energy level and the n=2 energy level there is a forbidden gap in energy, i.e. you will not find the electron of the hydrogen atom there. Note the thick line for large n where the energy gaps become so tiny leading to a continuum , i.e. an energy "band" ... 5 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 the field. The electrons get to the junction and find holes to fall into. Now that the electrons are in the P-type material they can find their way to the ... 5 Your second figure is a simplification of the first one, usually in the  \Gamma  point, but it could be any other as well. Regarding your questions: There are multiple lines in valence and conduction band because there are several allowed bands or energy eigen states. Technically there is even an infinite number of allowed bands, but usually you would ... 5 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 absorption of a collection of gas molecules are almost exactly the same as the energy levels that would be observed if you had a single gas molecule in isolation. ... 5 Usually, when talking of the "band structure" of such a system one either refers to the non-interacting band structure (which relates to the free Green functions occuring in many methods to handle the interactions, like perturbation expansions or DMFT), or to the sharp features usually visible in the spectral function (which is more or less experimentally ... 5 Neutron stars are electrically conductive because the neutrons are able to decay into protons and electrons. An equilibrium is setup so that the Fermi energy of the neutrons is equal to the sum of the Fermi energies of the protons and electrons. At typical neutron densities inside a neutron star, the n/p ratio is around 50-100 (the numbers of protons and ... 4 The group velocity v_g of a wave packet (that's the speed of the maximum of the wave packet) is given by v_g=\frac{\partial\omega}{\partial k}. In this case, \frac{\partial\omega}{\partial k}=\frac 1 \hbar\frac{\partial E}{\partial k}, which easily evaluates to v_g=\frac{3ta}{2}=:v_f for k=0. That's actually the definition of v_f: it is the group ... 4 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 few reasons, one of which is that it saves space on the page. If you look at that band gap at \Gamma and follow the lower band down to lower energies, you ... 4 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 (if m^*>0) and hole pockets (if m^*<0). For weakly interacting Fermion systems, according to the Fermi liquid theory, all the low-energy physics ... 4 In quantum mechanics the equation of motion is the SchrÃ¶dinger equation$$ i\hbar\,\frac{\partial}{\partial t}\,|\psi\rangle = H|\psi\rangle  where the (self-adjoint) operator $H$, the Hamiltonian, determines its evolution. The energy levels are, by definition, the eigenvalues of such operator in its domain of definition $\mathcal{D}_H$. Spectral theory ...

4

The Pauli Exclusion Principle means that not every electron can be at the very lowest energy level.

4

When the Fermi level cuts through some bands, only the fraction of the Brillouin zone for which the band is below the Fermi level counts toward occupancy of that spin. Those fractional occupancy values are averages. It's not that an individual electron will flip spins instantly and change bands, but out of many unit cells, that fraction will find that band ...

4

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 "used" in the crystal structure to form bonds to neighbours; none are more "free" than others. source Now dope it with another atom of one higher electron ...

3

which functional gives close value to the experimentally observed band gap of semiconductors Different functionals are accurate under different circumstances, so you can't make a blanket statement that one functional gives accurate band gaps for semiconductors. The only way to know when various functionals are and are not trustworthy is to use them in ...

3

The deep insight of Anderson is that the difference between insulators and conductors is not the energy spectrum. In fact the entire picture we are taught in introductory courses is highly misleading. [Note: Everything I am going to talk about will be about single particle effects, so no interaction.] First lets just remember the introductory picture. We ...

3

Beginner's guide to band structure follows. I've taken considerable liberties with the details to simplify this so don't take it too literally! This is going to seem an odd place to start, but consider filling up the atomic orbitals in an atom with electrons. If you take a noble gas, e.g. Xenon, you'll find each orbital is filled completely with two ...

3

I will ignore the confused statement "the metal Fermi Level is shown as the top of the conduction band, with the entire band filled" and focus on the main part of the question. First, I'll answer within the framework of Schottky-Mott theory, which is where this diagram comes from. In any material, the difference between vacuum level and a particular ...

3

You may think this way: take a perfect infinite crystal where Bloch theorem perfectly work and add potential which makes real crystal finite. Next question you may ask how this potential is "seen" by quasiparticles which have been obtained from infinite crystal consideration. This procedure is perfectly self-consistent and is applicable in all cases. Also, ...

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