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To have the right picture in mind, you need to also take into account the Pauli exclusion between the electrons, being fermions, but also more importantly, do not exclude the nucleus from the picture here! Now, Why rule one holds you may ask? Well it clearly cannot be due to dipole dipole interaction between electrons as it's so insanely small (let's say ...

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The maximum you can strain silicon, for example, before crystalline defects are introduced is ~1%, at which point the conductivity would go down. In the diamond case, the diagram indicates that you’d have to strain it by 200% (i.e. the atoms would have to be spaced twice as far apart as their equilibrium distance) to have no bandgap. This would be far too ...

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the Dirac Point on Graphene is protected by hidden symmetry. And it is explained very well in the paper arXiv:1406.3800. It is not that easy to understand the hidden symmetry. Personally speaking, I thought it is combination of inversion, time reversal and reflection symmetry, though the hidden symmetry in that paper has a totally different form with my ...

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If the valence band maximum and the conduction band minimum are on the same position in k-space, this means that you have a direct gap semiconductor (GaAs, InAs, ...). If the CB minimum is at a finite k-value, it would be an indirect gap semiconductor (like Si, Ge, AlAs, ...) The bands appear as parabolas due to the dispersion of a quasi-free electron/hole ...

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Consider two models: A wave packet of a free electron with $m_e$ with negligible mean energy relative to rest state A wave packet with same parameters of an electron in crystal with $m^*$ with negligible mean energy relative to band edge Assuming that wave packet is large enough for the effective mass approximation to hold (i.e. its uncertainty of ...

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Second derivative of kinetic energy with respect to momentum equals inverse mass of a particle. In a metal, you have a band structure defined through the dispersion relation of the form E(k) where k is wave vector of electron. Second derivative of this expression can be also taken to be some sort of inertia of a particle, as you can see by analogy with a ...

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It implies that the band in question would have a narrower bandwidth than would be expected from an electron with free electron mass. In turn, this also means that the electron finds it harder to hop from site to site meaning that the electron is more localized that would be an electron with free electron mass.

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Note that Sommerfeld's model simply generalizes Drude's theory of metals by taking into account the fact that electrons are fermions, so Pauli exclusion becomes a very important factor. In Sommerfeld's model, there's no effective mass to talk about, as one basically ignores the atoms(nuclei) in the system and considers free moving fermions. So there, your ...

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The bigger the crystal is, the closer-together those discrete values of k are. A real crystal might be 1cm long, or 100 million atoms. Then there would be 100 million little dots between the vertical bars on your figure. Those dots would be equally spaced with respect to the horizontal axis. It's too many dots to see, they blend together to look just like a ...

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Even if it's not really appropriate to derivate quantitative results about electrons properties in solids, Jellium model still have some interesting qualitative features. As you correctly pointed, Jellium still a mean-field theory and so fails about dealing with strongly correlated systems. Lets remind a few about jellium model. The starting point is the ...

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This structure consists of a series of potential wells at an atomic level: A quasi-free electron can travel trough this structure, where it is attracted or weakly bound by the individual atoms. In this case, a potential well due to an Al atom (or a virtual AlAs atom) is deeper than for Ga (or a virtual GaAs atom). In a picturesque view, the free electron is ...

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An RTD is a special type of TD, and a double barrier is just one of many possible implementations of resonant tunneling. An RTD is called "resonant" because (under certain conditions) the transmission function is equal to one, i.e. complete transmission. This happens due to wave-like interference between the two barriers. Hence called "resonant": the phase ...

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